%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP087^1 : 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 : n027.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 08:55:26 AM UTC 2026
% Result : Theorem 4.05s 2.03s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 162 ( 56 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 278 ( 36 ~; 26 |; 0 &; 207 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 84 usr; 12 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% 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,
correc17873122onKeys: secrecy_specID > $o ).
thf(func_def_35,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_36,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_37,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_38,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_39,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_40,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_41,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_42,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_43,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_44,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_45,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_46,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_47,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_48,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_49,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_50,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_51,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_52,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_53,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_54,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_55,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_56,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(func_def_57,type,
collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
thf(func_def_58,type,
insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_59,type,
insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_60,type,
insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_61,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_62,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_63,type,
is_emp928984296chanID: set_Secrecy_chanID > $o ).
thf(func_def_64,type,
is_emp1849217361specID: set_Secrecy_specID > $o ).
thf(func_def_65,type,
is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
thf(func_def_66,type,
is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
thf(func_def_67,type,
is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
thf(func_def_68,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(func_def_69,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(func_def_70,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_71,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(func_def_72,type,
correctCompositionIn: secrecy_specID > $o ).
thf(func_def_73,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(func_def_74,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(func_def_75,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_76,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_77,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_78,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_79,type,
out: secrecy_specID > set_Secrecy_chanID ).
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,
key: secrecy_Keys ).
thf(func_def_90,type,
m: secrecy_KS ).
thf(func_def_106,type,
sK0: secrecy_Keys > secrecy_specID > secrecy_chanID ).
thf(func_def_107,type,
sK1: secrecy_specID > secrecy_Secrets > secrecy_chanID ).
thf(func_def_108,type,
sK2: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets ).
thf(func_def_109,type,
sK3: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys ).
thf(func_def_110,type,
sK4: secrecy_Keys > secrecy_specID > secrecy_chanID ).
thf(func_def_111,type,
sK5: secrecy_Secrets > secrecy_specID > secrecy_chanID ).
thf(f1072,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1071,f1063]) ).
thf(f1063,plain,
( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ p ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1026,f1049]) ).
thf(f1049,plain,
( m
= ( secrecy_kKS @ key ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,axiom,
( m
= ( secrecy_kKS @ key ) ),
file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_6_a1) ).
thf(f1026,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f961]) ).
thf(f961,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) )
!= $true ),
inference(flattening,[status(thm)],[f912]) ).
thf(f912,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f911]) ).
thf(f911,plain,
~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) ),
file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_2_notKSP) ).
thf(f1071,plain,
( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ p ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f1070,f1056]) ).
thf(f1056,plain,
( ( correctCompositionKS @ pq )
= $true ),
inference(cnf_transformation,[status(thm)],[f480]) ).
thf(f480,plain,
( ( correctCompositionKS @ pq )
= $true ),
inference(fool_elimination,[status(thm)],[f479]) ).
thf(f479,plain,
correctCompositionKS @ pq,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
correctCompositionKS @ pq,
file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_0_cCompKS) ).
thf(f1070,plain,
( ( ( correctCompositionKS @ pq )
!= $true )
| ( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ p ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1069,f1061]) ).
thf(f1061,plain,
( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ q ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1024,f1049]) ).
thf(f1024,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f970]) ).
thf(f970,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) )
!= $true ),
inference(flattening,[status(thm)],[f570]) ).
thf(f570,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f569]) ).
thf(f569,plain,
~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) ),
file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_1_notKSQ) ).
thf(f1069,plain,
( ( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ q ) )
= $true )
| ( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ p ) )
= $true )
| ( ( correctCompositionKS @ pq )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1068]) ).
thf(f1068,plain,
( ( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ q ) )
= $true )
| ( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ p ) )
= $true )
| ( $true != $true )
| ( ( correctCompositionKS @ pq )
!= $true )
| ( ( subcomponents @ pq )
!= ( subcomponents @ pq ) ) ),
inference(superposition,[status(thm)],[f1067,f1064]) ).
thf(f1064,plain,
( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( specKeysSecrets @ pq ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1050,f1049]) ).
thf(f1050,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f959]) ).
thf(f959,plain,
( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) )
= $true ),
inference(flattening,[status(thm)],[f878]) ).
thf(f878,plain,
~ ( ( ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f877]) ).
thf(f877,plain,
~ ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) ),
file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',conj_0) ).
thf(f1067,plain,
! [X0: secrecy_specID,X1: secrecy_KS] :
( ( $true
!= ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X0 ) ) )
| ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ q ) )
= $true )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
= ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ p ) ) )
| ( ( correctCompositionKS @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f1052,f1051]) ).
thf(f1051,plain,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_3_subPQ) ).
thf(f1052,plain,
! [X2: secrecy_specID,X3: secrecy_specID,X0: secrecy_specID,X1: secrecy_KS] :
( ( ( subcomponents @ X2 )
!= ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X0 @ bot_bo1785112429specID ) ) )
| ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X2 ) )
!= $true )
| ( ( correctCompositionKS @ X2 )
!= $true )
| ( $true
= ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X0 ) ) )
| ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X3 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1009]) ).
thf(f1009,plain,
! [X0: secrecy_specID,X1: secrecy_KS,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X3 ) )
= $true )
| ( ( subcomponents @ X2 )
!= ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X0 @ bot_bo1785112429specID ) ) )
| ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X2 ) )
!= $true )
| ( $true
= ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X0 ) ) )
| ( ( correctCompositionKS @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f1008]) ).
thf(f1008,plain,
! [X0: secrecy_specID,X1: secrecy_KS,X2: secrecy_specID,X3: secrecy_specID] :
( ( $true
= ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X0 ) ) )
| ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X3 ) )
= $true )
| ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X2 ) )
!= $true )
| ( ( correctCompositionKS @ X2 )
!= $true )
| ( ( subcomponents @ X2 )
!= ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X0 @ bot_bo1785112429specID ) ) ) ),
inference(ennf_transformation,[status(thm)],[f448]) ).
thf(f448,plain,
! [X0: secrecy_specID,X1: secrecy_KS,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( subcomponents @ X2 )
= ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X0 @ bot_bo1785112429specID ) ) )
=> ( ( ( correctCompositionKS @ X2 )
= $true )
=> ( ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X2 ) )
= $true )
=> ( ( $true
= ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X0 ) ) )
| ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X3 ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f447]) ).
thf(f447,plain,
! [X0: secrecy_specID,X1: secrecy_KS,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( subcomponents @ X2 )
= ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X0 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ X2 )
=> ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X2 ) )
=> ( ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X0 ) )
| ( member_Secrecy_KS @ X1 @ ( specKeysSecrets @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X2: secrecy_specID,X3: secrecy_KS,X0: secrecy_specID,X1: secrecy_specID] :
( ( ( subcomponents @ X0 )
= ( insert1671894227specID @ X1 @ ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ X0 )
=> ( ( member_Secrecy_KS @ X3 @ ( specKeysSecrets @ X0 ) )
=> ( ( member_Secrecy_KS @ X3 @ ( specKeysSecrets @ X2 ) )
| ( member_Secrecy_KS @ X3 @ ( specKeysSecrets @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_7_correctCompositionKS__PQ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP087^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:26:07 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : ITP087^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.45 % Domain : Interactive Theorem Proving
% 0.20/0.45 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_277__3294194_1
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Des21]
% 0.20/0.45 % Names : KnowledgeKeysSecrets/prob_277__3294194_1 [Des21]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.20/0.45 % Syntax : Number of formulae : 447 ( 179 unt; 91 typ; 0 def)
% 0.20/0.45 % Number of atoms : 1264 ( 468 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 13 ( 3 avg)
% 0.20/0.45 % Number of connectives : 3784 ( 277 ~; 51 |; 131 &;2792 @)
% 0.20/0.45 % ( 0 <=>; 533 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 19 ( 7 avg)
% 0.20/0.45 % Number of types : 14 ( 13 usr)
% 0.20/0.45 % Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 79 ( 78 usr; 10 con; 0-3 aty)
% 0.20/0.45 % Number of variables : 989 ( 53 ^; 890 !; 46 ?; 989 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:29.583
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % Could-be-implicit typings (13)
% 0.20/0.45 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.20/0.45 list_S529945141ession: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.20/0.45 set_Secrecy_Secrets: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.20/0.45 set_Secrecy_specID: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.20/0.45 set_Secrecy_chanID: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.20/0.45 set_Secrecy_Keys: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.20/0.45 set_Secrecy_KS: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.20/0.45 secrecy_Expression: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.20/0.45 secrecy_Secrets: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.20/0.45 secrecy_specID: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Secrecy____types__OchanID,type,
% 0.20/0.45 secrecy_chanID: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.20/0.45 secrecy_Keys: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.20/0.45 secrecy_KS: $tType ).
% 0.20/0.45
% 0.20/0.45 thf(ty_n_t__Nat__Onat,type,
% 0.20/0.45 nat: $tType ).
% 0.20/0.45
% 0.20/0.45 % Explicit typings (78)
% 0.20/0.45 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.20/0.45 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.20/0.45 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.20/0.45 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.20/0.45 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.20/0.45 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.20/0.45 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.20/0.45 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.20/0.45 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.20/0.45 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 0.20/0.45 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 0.20/0.45 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 0.20/0.45 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 0.20/0.45 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 0.20/0.45 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.20/0.45 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.20/0.45 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.20/0.45 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.20/0.45 bot_bo443197316chanID: set_Secrecy_chanID ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.20/0.45 bot_bo1785112429specID: set_Secrecy_specID ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.20/0.45 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.20/0.45 correctCompositionKS: secrecy_specID > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Secrecy_OcorrectCompositionKeys,type,
% 0.20/0.45 correc17873122onKeys: secrecy_specID > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Secrecy_Oeout,type,
% 0.20/0.45 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Secrecy_OeoutM,type,
% 0.20/0.45 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Secrecy_OexprChannel,type,
% 0.20/0.45 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Secrecy_Oine,type,
% 0.20/0.45 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.20/0.45
% 0.20/0.45 thf(sy_c_Secrecy_OineM,type,
% 0.20/0.46 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.20/0.46 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.20/0.46 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.20/0.46 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.20/0.46 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.20/0.46 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.20/0.46 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.20/0.46 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.20/0.46 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.20/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.20/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.20/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.20/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.20/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.20/0.46 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.20/0.46 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.20/0.46 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 0.20/0.46 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 0.20/0.46 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 0.20/0.46 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 0.20/0.46 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 0.20/0.46 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 0.20/0.46 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 0.20/0.46 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 0.20/0.46 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 0.20/0.46 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 0.20/0.46 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 0.20/0.46 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 0.20/0.46 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 0.20/0.46 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 0.20/0.46 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 0.20/0.46 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 0.20/0.46 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.20/0.46 correctCompositionIn: secrecy_specID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.20/0.46 correc965049635ionLoc: secrecy_specID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.20/0.46 correc990227761ionOut: secrecy_specID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_OinStream,type,
% 0.20/0.46 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_Oins,type,
% 0.20/0.46 ins: secrecy_specID > set_Secrecy_chanID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_Oloc,type,
% 0.20/0.46 loc: secrecy_specID > set_Secrecy_chanID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_OlocStream,type,
% 0.20/0.46 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_Oout,type,
% 0.20/0.46 out: secrecy_specID > set_Secrecy_chanID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_inout_Osubcomponents,type,
% 0.20/0.46 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.20/0.46 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.20/0.46 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.20/0.46 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 0.20/0.46 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 0.20/0.46 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_P,type,
% 0.20/0.46 p: secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_PQ,type,
% 0.20/0.46 pq: secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_Q,type,
% 0.20/0.46 q: secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_key____,type,
% 0.20/0.46 key: secrecy_Keys ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_m,type,
% 0.20/0.46 m: secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 % Relevant facts (355)
% 0.20/0.46 thf(fact_0_cCompKS,axiom,
% 0.20/0.46 correctCompositionKS @ pq ).
% 0.20/0.46
% 0.20/0.46 % cCompKS
% 0.20/0.46 thf(fact_1_notKSQ,axiom,
% 0.20/0.46 ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) ) ).
% 0.20/0.46
% 0.20/0.46 % notKSQ
% 0.20/0.46 thf(fact_2_notKSP,axiom,
% 0.20/0.46 ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) ) ).
% 0.20/0.46
% 0.20/0.46 % notKSP
% 0.20/0.46 thf(fact_3_subPQ,axiom,
% 0.20/0.46 ( ( subcomponents @ pq )
% 0.20/0.46 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subPQ
% 0.20/0.46 thf(fact_4_cCompI,axiom,
% 0.20/0.46 correctCompositionIn @ pq ).
% 0.20/0.46
% 0.20/0.46 % cCompI
% 0.20/0.46 thf(fact_5_assms_I3_J,axiom,
% 0.20/0.46 knowle945212990e_know @ p @ m ).
% 0.20/0.46
% 0.20/0.46 % assms(3)
% 0.20/0.46 thf(fact_6_a1,axiom,
% 0.20/0.46 ( m
% 0.20/0.46 = ( secrecy_kKS @ key ) ) ).
% 0.20/0.46
% 0.20/0.46 % a1
% 0.20/0.46 thf(fact_7_correctCompositionKS__PQ,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.20/0.46 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_PQ
% 0.20/0.46 thf(fact_8_correctCompositionKS__neg1,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_neg1
% 0.20/0.46 thf(fact_9_correctCompositionKS__negP,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_negP
% 0.20/0.46 thf(fact_10_correctCompositionKS__negQ,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_negQ
% 0.20/0.46 thf(fact_11_singletonI,axiom,
% 0.20/0.46 ! [A: secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonI
% 0.20/0.46 thf(fact_12_singletonI,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets] : ( member2138796287ecrets @ A @ ( insert565337510ecrets @ A @ bot_bo1124690338ecrets ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonI
% 0.20/0.46 thf(fact_13_singletonI,axiom,
% 0.20/0.46 ! [A: secrecy_Keys] : ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonI
% 0.20/0.46 thf(fact_14_singletonI,axiom,
% 0.20/0.46 ! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonI
% 0.20/0.46 thf(fact_15_singletonI,axiom,
% 0.20/0.46 ! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonI
% 0.20/0.46 thf(fact_16_KS_Oinject_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.20/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.20/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.20/0.46 = ( X1 = Y1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.inject(1)
% 0.20/0.46 thf(fact_17_insertCI,axiom,
% 0.20/0.46 ! [A: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.20/0.46 ( ( ~ ( member_Secrecy_KS @ A @ B )
% 0.20/0.46 => ( A = B2 ) )
% 0.20/0.46 => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertCI
% 0.20/0.46 thf(fact_18_insertCI,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.20/0.46 ( ( ~ ( member1967978193chanID @ A @ B )
% 0.20/0.46 => ( A = B2 ) )
% 0.20/0.46 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertCI
% 0.20/0.46 thf(fact_19_insertCI,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.20/0.46 ( ( ~ ( member740727610specID @ A @ B )
% 0.20/0.46 => ( A = B2 ) )
% 0.20/0.46 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertCI
% 0.20/0.46 thf(fact_20_insertCI,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.20/0.46 ( ( ~ ( member2138796287ecrets @ A @ B )
% 0.20/0.46 => ( A = B2 ) )
% 0.20/0.46 => ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertCI
% 0.20/0.46 thf(fact_21_insertCI,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.20/0.46 ( ( ~ ( member_Secrecy_Keys @ A @ B )
% 0.20/0.46 => ( A = B2 ) )
% 0.20/0.46 => ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertCI
% 0.20/0.46 thf(fact_22_insert__iff,axiom,
% 0.20/0.46 ! [A: secrecy_KS,B2: secrecy_KS,A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ A2 ) )
% 0.20/0.46 = ( ( A = B2 )
% 0.20/0.46 | ( member_Secrecy_KS @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_iff
% 0.20/0.46 thf(fact_23_insert__iff,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 0.20/0.46 = ( ( A = B2 )
% 0.20/0.46 | ( member1967978193chanID @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_iff
% 0.20/0.46 thf(fact_24_insert__iff,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 0.20/0.46 = ( ( A = B2 )
% 0.20/0.46 | ( member740727610specID @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_iff
% 0.20/0.46 thf(fact_25_insert__iff,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,B2: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ A2 ) )
% 0.20/0.46 = ( ( A = B2 )
% 0.20/0.46 | ( member2138796287ecrets @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_iff
% 0.20/0.46 thf(fact_26_insert__iff,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,B2: secrecy_Keys,A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ A2 ) )
% 0.20/0.46 = ( ( A = B2 )
% 0.20/0.46 | ( member_Secrecy_Keys @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_iff
% 0.20/0.46 thf(fact_27_insert__absorb2,axiom,
% 0.20/0.46 ! [X: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A2 ) )
% 0.20/0.46 = ( insert1671894227specID @ X @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb2
% 0.20/0.46 thf(fact_28_insert__absorb2,axiom,
% 0.20/0.46 ! [X: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A2 ) )
% 0.20/0.46 = ( insert751661162chanID @ X @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb2
% 0.20/0.46 thf(fact_29_empty__iff,axiom,
% 0.20/0.46 ! [C: secrecy_KS] :
% 0.20/0.46 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 0.20/0.46
% 0.20/0.46 % empty_iff
% 0.20/0.46 thf(fact_30_empty__iff,axiom,
% 0.20/0.46 ! [C: secrecy_Secrets] :
% 0.20/0.46 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 0.20/0.46
% 0.20/0.46 % empty_iff
% 0.20/0.46 thf(fact_31_empty__iff,axiom,
% 0.20/0.46 ! [C: secrecy_Keys] :
% 0.20/0.46 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 0.20/0.46
% 0.20/0.46 % empty_iff
% 0.20/0.46 thf(fact_32_empty__iff,axiom,
% 0.20/0.46 ! [C: secrecy_specID] :
% 0.20/0.46 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 0.20/0.46
% 0.20/0.46 % empty_iff
% 0.20/0.46 thf(fact_33_empty__iff,axiom,
% 0.20/0.46 ! [C: secrecy_chanID] :
% 0.20/0.46 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 0.20/0.46
% 0.20/0.46 % empty_iff
% 0.20/0.46 thf(fact_34_all__not__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( ! [X2: secrecy_KS] :
% 0.20/0.46 ~ ( member_Secrecy_KS @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 = bot_bo1943466239ecy_KS ) ) ).
% 0.20/0.46
% 0.20/0.46 % all_not_in_conv
% 0.20/0.46 thf(fact_35_all__not__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( ! [X2: secrecy_Secrets] :
% 0.20/0.46 ~ ( member2138796287ecrets @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 = bot_bo1124690338ecrets ) ) ).
% 0.20/0.46
% 0.20/0.46 % all_not_in_conv
% 0.20/0.46 thf(fact_36_all__not__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( ! [X2: secrecy_Keys] :
% 0.20/0.46 ~ ( member_Secrecy_Keys @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 = bot_bo701486667y_Keys ) ) ).
% 0.20/0.46
% 0.20/0.46 % all_not_in_conv
% 0.20/0.46 thf(fact_37_all__not__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( ! [X2: secrecy_specID] :
% 0.20/0.46 ~ ( member740727610specID @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 = bot_bo1785112429specID ) ) ).
% 0.20/0.46
% 0.20/0.46 % all_not_in_conv
% 0.20/0.46 thf(fact_38_all__not__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ! [X2: secrecy_chanID] :
% 0.20/0.46 ~ ( member1967978193chanID @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 = bot_bo443197316chanID ) ) ).
% 0.20/0.46
% 0.20/0.46 % all_not_in_conv
% 0.20/0.46 thf(fact_39_Collect__empty__eq,axiom,
% 0.20/0.46 ! [P: secrecy_specID > $o] :
% 0.20/0.46 ( ( ( collec1545797240specID @ P )
% 0.20/0.46 = bot_bo1785112429specID )
% 0.20/0.46 = ( ! [X2: secrecy_specID] :
% 0.20/0.46 ~ ( P @ X2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_empty_eq
% 0.20/0.46 thf(fact_40_Collect__empty__eq,axiom,
% 0.20/0.46 ! [P: secrecy_chanID > $o] :
% 0.20/0.46 ( ( ( collec625564175chanID @ P )
% 0.20/0.46 = bot_bo443197316chanID )
% 0.20/0.46 = ( ! [X2: secrecy_chanID] :
% 0.20/0.46 ~ ( P @ X2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_empty_eq
% 0.20/0.46 thf(fact_41_empty__Collect__eq,axiom,
% 0.20/0.46 ! [P: secrecy_specID > $o] :
% 0.20/0.46 ( ( bot_bo1785112429specID
% 0.20/0.46 = ( collec1545797240specID @ P ) )
% 0.20/0.46 = ( ! [X2: secrecy_specID] :
% 0.20/0.46 ~ ( P @ X2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % empty_Collect_eq
% 0.20/0.46 thf(fact_42_empty__Collect__eq,axiom,
% 0.20/0.46 ! [P: secrecy_chanID > $o] :
% 0.20/0.46 ( ( bot_bo443197316chanID
% 0.20/0.46 = ( collec625564175chanID @ P ) )
% 0.20/0.46 = ( ! [X2: secrecy_chanID] :
% 0.20/0.46 ~ ( P @ X2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % empty_Collect_eq
% 0.20/0.46 thf(fact_43_singletonD,axiom,
% 0.20/0.46 ! [B2: secrecy_KS,A: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
% 0.20/0.46 => ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonD
% 0.20/0.46 thf(fact_44_singletonD,axiom,
% 0.20/0.46 ! [B2: secrecy_Secrets,A: secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A @ bot_bo1124690338ecrets ) )
% 0.20/0.46 => ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonD
% 0.20/0.46 thf(fact_45_singletonD,axiom,
% 0.20/0.46 ! [B2: secrecy_Keys,A: secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) )
% 0.20/0.46 => ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonD
% 0.20/0.46 thf(fact_46_singletonD,axiom,
% 0.20/0.46 ! [B2: secrecy_specID,A: secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 0.20/0.46 => ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonD
% 0.20/0.46 thf(fact_47_singletonD,axiom,
% 0.20/0.46 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 0.20/0.46 => ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singletonD
% 0.20/0.46 thf(fact_48_bot__set__def,axiom,
% 0.20/0.46 ( bot_bo1785112429specID
% 0.20/0.46 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_set_def
% 0.20/0.46 thf(fact_49_bot__set__def,axiom,
% 0.20/0.46 ( bot_bo443197316chanID
% 0.20/0.46 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_set_def
% 0.20/0.46 thf(fact_50_ex__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( ? [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 != bot_bo1943466239ecy_KS ) ) ).
% 0.20/0.46
% 0.20/0.46 % ex_in_conv
% 0.20/0.46 thf(fact_51_ex__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( ? [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 != bot_bo1124690338ecrets ) ) ).
% 0.20/0.46
% 0.20/0.46 % ex_in_conv
% 0.20/0.46 thf(fact_52_ex__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( ? [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 != bot_bo701486667y_Keys ) ) ).
% 0.20/0.46
% 0.20/0.46 % ex_in_conv
% 0.20/0.46 thf(fact_53_ex__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( ? [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 != bot_bo1785112429specID ) ) ).
% 0.20/0.46
% 0.20/0.46 % ex_in_conv
% 0.20/0.46 thf(fact_54_ex__in__conv,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ? [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 0.20/0.46 = ( A2 != bot_bo443197316chanID ) ) ).
% 0.20/0.46
% 0.20/0.46 % ex_in_conv
% 0.20/0.46 thf(fact_55_equals0I,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS] :
% 0.20/0.46 ( ! [Y: secrecy_KS] :
% 0.20/0.46 ~ ( member_Secrecy_KS @ Y @ A2 )
% 0.20/0.46 => ( A2 = bot_bo1943466239ecy_KS ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0I
% 0.20/0.46 thf(fact_56_equals0I,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ! [Y: secrecy_Secrets] :
% 0.20/0.46 ~ ( member2138796287ecrets @ Y @ A2 )
% 0.20/0.46 => ( A2 = bot_bo1124690338ecrets ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0I
% 0.20/0.46 thf(fact_57_equals0I,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ! [Y: secrecy_Keys] :
% 0.20/0.46 ~ ( member_Secrecy_Keys @ Y @ A2 )
% 0.20/0.46 => ( A2 = bot_bo701486667y_Keys ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0I
% 0.20/0.46 thf(fact_58_equals0I,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID] :
% 0.20/0.46 ( ! [Y: secrecy_specID] :
% 0.20/0.46 ~ ( member740727610specID @ Y @ A2 )
% 0.20/0.46 => ( A2 = bot_bo1785112429specID ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0I
% 0.20/0.46 thf(fact_59_equals0I,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ! [Y: secrecy_chanID] :
% 0.20/0.46 ~ ( member1967978193chanID @ Y @ A2 )
% 0.20/0.46 => ( A2 = bot_bo443197316chanID ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0I
% 0.20/0.46 thf(fact_60_equals0D,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,A: secrecy_KS] :
% 0.20/0.46 ( ( A2 = bot_bo1943466239ecy_KS )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ A @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0D
% 0.20/0.46 thf(fact_61_equals0D,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Secrets,A: secrecy_Secrets] :
% 0.20/0.46 ( ( A2 = bot_bo1124690338ecrets )
% 0.20/0.46 => ~ ( member2138796287ecrets @ A @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0D
% 0.20/0.46 thf(fact_62_equals0D,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Keys,A: secrecy_Keys] :
% 0.20/0.46 ( ( A2 = bot_bo701486667y_Keys )
% 0.20/0.46 => ~ ( member_Secrecy_Keys @ A @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0D
% 0.20/0.46 thf(fact_63_equals0D,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID,A: secrecy_specID] :
% 0.20/0.46 ( ( A2 = bot_bo1785112429specID )
% 0.20/0.46 => ~ ( member740727610specID @ A @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0D
% 0.20/0.46 thf(fact_64_equals0D,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,A: secrecy_chanID] :
% 0.20/0.46 ( ( A2 = bot_bo443197316chanID )
% 0.20/0.46 => ~ ( member1967978193chanID @ A @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % equals0D
% 0.20/0.46 thf(fact_65_emptyE,axiom,
% 0.20/0.46 ! [A: secrecy_KS] :
% 0.20/0.46 ~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ).
% 0.20/0.46
% 0.20/0.46 % emptyE
% 0.20/0.46 thf(fact_66_emptyE,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets] :
% 0.20/0.46 ~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ) ).
% 0.20/0.46
% 0.20/0.46 % emptyE
% 0.20/0.46 thf(fact_67_emptyE,axiom,
% 0.20/0.46 ! [A: secrecy_Keys] :
% 0.20/0.46 ~ ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) ).
% 0.20/0.46
% 0.20/0.46 % emptyE
% 0.20/0.46 thf(fact_68_emptyE,axiom,
% 0.20/0.46 ! [A: secrecy_specID] :
% 0.20/0.46 ~ ( member740727610specID @ A @ bot_bo1785112429specID ) ).
% 0.20/0.46
% 0.20/0.46 % emptyE
% 0.20/0.46 thf(fact_69_emptyE,axiom,
% 0.20/0.46 ! [A: secrecy_chanID] :
% 0.20/0.46 ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ) ).
% 0.20/0.46
% 0.20/0.46 % emptyE
% 0.20/0.46 thf(fact_70_mk__disjoint__insert,axiom,
% 0.20/0.46 ! [A: secrecy_KS,A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ A @ A2 )
% 0.20/0.46 => ? [B3: set_Secrecy_KS] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_Secrecy_KS @ A @ B3 ) )
% 0.20/0.46 & ~ ( member_Secrecy_KS @ A @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mk_disjoint_insert
% 0.20/0.46 thf(fact_71_mk__disjoint__insert,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ A @ A2 )
% 0.20/0.46 => ? [B3: set_Secrecy_chanID] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert751661162chanID @ A @ B3 ) )
% 0.20/0.46 & ~ ( member1967978193chanID @ A @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mk_disjoint_insert
% 0.20/0.46 thf(fact_72_mk__disjoint__insert,axiom,
% 0.20/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ A @ A2 )
% 0.20/0.46 => ? [B3: set_Secrecy_specID] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert1671894227specID @ A @ B3 ) )
% 0.20/0.46 & ~ ( member740727610specID @ A @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mk_disjoint_insert
% 0.20/0.46 thf(fact_73_mk__disjoint__insert,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ A @ A2 )
% 0.20/0.46 => ? [B3: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert565337510ecrets @ A @ B3 ) )
% 0.20/0.46 & ~ ( member2138796287ecrets @ A @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mk_disjoint_insert
% 0.20/0.46 thf(fact_74_mk__disjoint__insert,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ A @ A2 )
% 0.20/0.46 => ? [B3: set_Secrecy_Keys] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_Secrecy_Keys @ A @ B3 ) )
% 0.20/0.46 & ~ ( member_Secrecy_Keys @ A @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % mk_disjoint_insert
% 0.20/0.46 thf(fact_75_insert__commute,axiom,
% 0.20/0.46 ! [X: secrecy_specID,Y2: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y2 @ A2 ) )
% 0.20/0.46 = ( insert1671894227specID @ Y2 @ ( insert1671894227specID @ X @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_commute
% 0.20/0.46 thf(fact_76_insert__commute,axiom,
% 0.20/0.46 ! [X: secrecy_chanID,Y2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y2 @ A2 ) )
% 0.20/0.46 = ( insert751661162chanID @ Y2 @ ( insert751661162chanID @ X @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_commute
% 0.20/0.46 thf(fact_77_insert__eq__iff,axiom,
% 0.20/0.46 ! [A: secrecy_KS,A2: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ~ ( member_Secrecy_KS @ A @ A2 )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 0.20/0.46 => ( ( ( insert_Secrecy_KS @ A @ A2 )
% 0.20/0.46 = ( insert_Secrecy_KS @ B2 @ B ) )
% 0.20/0.46 = ( ( ( A = B2 )
% 0.20/0.46 => ( A2 = B ) )
% 0.20/0.46 & ( ( A != B2 )
% 0.20/0.46 => ? [C2: set_Secrecy_KS] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 0.20/0.46 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert_Secrecy_KS @ A @ C2 ) )
% 0.20/0.46 & ~ ( member_Secrecy_KS @ A @ C2 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_eq_iff
% 0.20/0.46 thf(fact_78_insert__eq__iff,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( member1967978193chanID @ A @ A2 )
% 0.20/0.46 => ( ~ ( member1967978193chanID @ B2 @ B )
% 0.20/0.46 => ( ( ( insert751661162chanID @ A @ A2 )
% 0.20/0.46 = ( insert751661162chanID @ B2 @ B ) )
% 0.20/0.46 = ( ( ( A = B2 )
% 0.20/0.46 => ( A2 = B ) )
% 0.20/0.46 & ( ( A != B2 )
% 0.20/0.46 => ? [C2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert751661162chanID @ B2 @ C2 ) )
% 0.20/0.46 & ~ ( member1967978193chanID @ B2 @ C2 )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert751661162chanID @ A @ C2 ) )
% 0.20/0.46 & ~ ( member1967978193chanID @ A @ C2 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_eq_iff
% 0.20/0.46 thf(fact_79_insert__eq__iff,axiom,
% 0.20/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ~ ( member740727610specID @ A @ A2 )
% 0.20/0.46 => ( ~ ( member740727610specID @ B2 @ B )
% 0.20/0.46 => ( ( ( insert1671894227specID @ A @ A2 )
% 0.20/0.46 = ( insert1671894227specID @ B2 @ B ) )
% 0.20/0.46 = ( ( ( A = B2 )
% 0.20/0.46 => ( A2 = B ) )
% 0.20/0.46 & ( ( A != B2 )
% 0.20/0.46 => ? [C2: set_Secrecy_specID] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert1671894227specID @ B2 @ C2 ) )
% 0.20/0.46 & ~ ( member740727610specID @ B2 @ C2 )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert1671894227specID @ A @ C2 ) )
% 0.20/0.46 & ~ ( member740727610specID @ A @ C2 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_eq_iff
% 0.20/0.46 thf(fact_80_insert__eq__iff,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,A2: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.20/0.46 ( ~ ( member2138796287ecrets @ A @ A2 )
% 0.20/0.46 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 0.20/0.46 => ( ( ( insert565337510ecrets @ A @ A2 )
% 0.20/0.46 = ( insert565337510ecrets @ B2 @ B ) )
% 0.20/0.46 = ( ( ( A = B2 )
% 0.20/0.46 => ( A2 = B ) )
% 0.20/0.46 & ( ( A != B2 )
% 0.20/0.46 => ? [C2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert565337510ecrets @ B2 @ C2 ) )
% 0.20/0.46 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert565337510ecrets @ A @ C2 ) )
% 0.20/0.46 & ~ ( member2138796287ecrets @ A @ C2 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_eq_iff
% 0.20/0.46 thf(fact_81_insert__eq__iff,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,A2: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 0.20/0.46 ( ~ ( member_Secrecy_Keys @ A @ A2 )
% 0.20/0.46 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 0.20/0.46 => ( ( ( insert_Secrecy_Keys @ A @ A2 )
% 0.20/0.46 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 0.20/0.46 = ( ( ( A = B2 )
% 0.20/0.46 => ( A2 = B ) )
% 0.20/0.46 & ( ( A != B2 )
% 0.20/0.46 => ? [C2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 0.20/0.46 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert_Secrecy_Keys @ A @ C2 ) )
% 0.20/0.46 & ~ ( member_Secrecy_Keys @ A @ C2 ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_eq_iff
% 0.20/0.46 thf(fact_82_insert__absorb,axiom,
% 0.20/0.46 ! [A: secrecy_KS,A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ A @ A2 )
% 0.20/0.46 => ( ( insert_Secrecy_KS @ A @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb
% 0.20/0.46 thf(fact_83_insert__absorb,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ A @ A2 )
% 0.20/0.46 => ( ( insert751661162chanID @ A @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb
% 0.20/0.46 thf(fact_84_insert__absorb,axiom,
% 0.20/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ A @ A2 )
% 0.20/0.46 => ( ( insert1671894227specID @ A @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb
% 0.20/0.46 thf(fact_85_insert__absorb,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ A @ A2 )
% 0.20/0.46 => ( ( insert565337510ecrets @ A @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb
% 0.20/0.46 thf(fact_86_insert__absorb,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ A @ A2 )
% 0.20/0.46 => ( ( insert_Secrecy_Keys @ A @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_absorb
% 0.20/0.46 thf(fact_87_insert__ident,axiom,
% 0.20/0.46 ! [X: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ~ ( member_Secrecy_KS @ X @ A2 )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ X @ B )
% 0.20/0.46 => ( ( ( insert_Secrecy_KS @ X @ A2 )
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ B ) )
% 0.20/0.46 = ( A2 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_ident
% 0.20/0.46 thf(fact_88_insert__ident,axiom,
% 0.20/0.46 ! [X: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( member1967978193chanID @ X @ A2 )
% 0.20/0.46 => ( ~ ( member1967978193chanID @ X @ B )
% 0.20/0.46 => ( ( ( insert751661162chanID @ X @ A2 )
% 0.20/0.46 = ( insert751661162chanID @ X @ B ) )
% 0.20/0.46 = ( A2 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_ident
% 0.20/0.46 thf(fact_89_insert__ident,axiom,
% 0.20/0.46 ! [X: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ~ ( member740727610specID @ X @ A2 )
% 0.20/0.46 => ( ~ ( member740727610specID @ X @ B )
% 0.20/0.46 => ( ( ( insert1671894227specID @ X @ A2 )
% 0.20/0.46 = ( insert1671894227specID @ X @ B ) )
% 0.20/0.46 = ( A2 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_ident
% 0.20/0.46 thf(fact_90_insert__ident,axiom,
% 0.20/0.46 ! [X: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.20/0.46 ( ~ ( member2138796287ecrets @ X @ A2 )
% 0.20/0.46 => ( ~ ( member2138796287ecrets @ X @ B )
% 0.20/0.46 => ( ( ( insert565337510ecrets @ X @ A2 )
% 0.20/0.46 = ( insert565337510ecrets @ X @ B ) )
% 0.20/0.46 = ( A2 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_ident
% 0.20/0.46 thf(fact_91_insert__ident,axiom,
% 0.20/0.46 ! [X: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.20/0.46 ( ~ ( member_Secrecy_Keys @ X @ A2 )
% 0.20/0.46 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 0.20/0.46 => ( ( ( insert_Secrecy_Keys @ X @ A2 )
% 0.20/0.46 = ( insert_Secrecy_Keys @ X @ B ) )
% 0.20/0.46 = ( A2 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_ident
% 0.20/0.46 thf(fact_92_Set_Oset__insert,axiom,
% 0.20/0.46 ! [X: secrecy_KS,A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X @ A2 )
% 0.20/0.46 => ~ ! [B3: set_Secrecy_KS] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ B3 ) )
% 0.20/0.46 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.set_insert
% 0.20/0.46 thf(fact_93_Set_Oset__insert,axiom,
% 0.20/0.46 ! [X: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X @ A2 )
% 0.20/0.46 => ~ ! [B3: set_Secrecy_chanID] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert751661162chanID @ X @ B3 ) )
% 0.20/0.46 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.set_insert
% 0.20/0.46 thf(fact_94_Set_Oset__insert,axiom,
% 0.20/0.46 ! [X: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ X @ A2 )
% 0.20/0.46 => ~ ! [B3: set_Secrecy_specID] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert1671894227specID @ X @ B3 ) )
% 0.20/0.46 => ( member740727610specID @ X @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.set_insert
% 0.20/0.46 thf(fact_95_Set_Oset__insert,axiom,
% 0.20/0.46 ! [X: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ X @ A2 )
% 0.20/0.46 => ~ ! [B3: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert565337510ecrets @ X @ B3 ) )
% 0.20/0.46 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.set_insert
% 0.20/0.46 thf(fact_96_Set_Oset__insert,axiom,
% 0.20/0.46 ! [X: secrecy_Keys,A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ X @ A2 )
% 0.20/0.46 => ~ ! [B3: set_Secrecy_Keys] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 0.20/0.46 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.set_insert
% 0.20/0.46 thf(fact_97_insertI2,axiom,
% 0.20/0.46 ! [A: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ A @ B )
% 0.20/0.46 => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI2
% 0.20/0.46 thf(fact_98_insertI2,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ A @ B )
% 0.20/0.46 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI2
% 0.20/0.46 thf(fact_99_insertI2,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ A @ B )
% 0.20/0.46 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI2
% 0.20/0.46 thf(fact_100_insertI2,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ A @ B )
% 0.20/0.46 => ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI2
% 0.20/0.46 thf(fact_101_insertI2,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ A @ B )
% 0.20/0.46 => ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI2
% 0.20/0.46 thf(fact_102_insertI1,axiom,
% 0.20/0.46 ! [A: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI1
% 0.20/0.46 thf(fact_103_insertI1,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI1
% 0.20/0.46 thf(fact_104_insertI1,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI1
% 0.20/0.46 thf(fact_105_insertI1,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A @ ( insert565337510ecrets @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI1
% 0.20/0.46 thf(fact_106_insertI1,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ A @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertI1
% 0.20/0.46 thf(fact_107_insertE,axiom,
% 0.20/0.46 ! [A: secrecy_KS,B2: secrecy_KS,A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ A2 ) )
% 0.20/0.46 => ( ( A != B2 )
% 0.20/0.46 => ( member_Secrecy_KS @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertE
% 0.20/0.46 thf(fact_108_insertE,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 0.20/0.46 => ( ( A != B2 )
% 0.20/0.46 => ( member1967978193chanID @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertE
% 0.20/0.46 thf(fact_109_insertE,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 0.20/0.46 => ( ( A != B2 )
% 0.20/0.46 => ( member740727610specID @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertE
% 0.20/0.46 thf(fact_110_insertE,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,B2: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ A2 ) )
% 0.20/0.46 => ( ( A != B2 )
% 0.20/0.46 => ( member2138796287ecrets @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertE
% 0.20/0.46 thf(fact_111_insertE,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,B2: secrecy_Keys,A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ A2 ) )
% 0.20/0.46 => ( ( A != B2 )
% 0.20/0.46 => ( member_Secrecy_Keys @ A @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insertE
% 0.20/0.46 thf(fact_112_singleton__inject,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B2: secrecy_specID] :
% 0.20/0.46 ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
% 0.20/0.46 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.20/0.46 => ( A = B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_inject
% 0.20/0.46 thf(fact_113_singleton__inject,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B2: secrecy_chanID] :
% 0.20/0.46 ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
% 0.20/0.46 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.20/0.46 => ( A = B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_inject
% 0.20/0.46 thf(fact_114_insert__not__empty,axiom,
% 0.20/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( insert1671894227specID @ A @ A2 )
% 0.20/0.46 != bot_bo1785112429specID ) ).
% 0.20/0.46
% 0.20/0.46 % insert_not_empty
% 0.20/0.46 thf(fact_115_insert__not__empty,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( insert751661162chanID @ A @ A2 )
% 0.20/0.46 != bot_bo443197316chanID ) ).
% 0.20/0.46
% 0.20/0.46 % insert_not_empty
% 0.20/0.46 thf(fact_116_doubleton__eq__iff,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 0.20/0.46 ( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.20/0.46 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 0.20/0.46 = ( ( ( A = C )
% 0.20/0.46 & ( B2 = D ) )
% 0.20/0.46 | ( ( A = D )
% 0.20/0.46 & ( B2 = C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % doubleton_eq_iff
% 0.20/0.46 thf(fact_117_doubleton__eq__iff,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 0.20/0.46 ( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.20/0.46 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 0.20/0.46 = ( ( ( A = C )
% 0.20/0.46 & ( B2 = D ) )
% 0.20/0.46 | ( ( A = D )
% 0.20/0.46 & ( B2 = C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % doubleton_eq_iff
% 0.20/0.46 thf(fact_118_singleton__iff,axiom,
% 0.20/0.46 ! [B2: secrecy_KS,A: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
% 0.20/0.46 = ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_iff
% 0.20/0.46 thf(fact_119_singleton__iff,axiom,
% 0.20/0.46 ! [B2: secrecy_Secrets,A: secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A @ bot_bo1124690338ecrets ) )
% 0.20/0.46 = ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_iff
% 0.20/0.46 thf(fact_120_singleton__iff,axiom,
% 0.20/0.46 ! [B2: secrecy_Keys,A: secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) )
% 0.20/0.46 = ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_iff
% 0.20/0.46 thf(fact_121_singleton__iff,axiom,
% 0.20/0.46 ! [B2: secrecy_specID,A: secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 0.20/0.46 = ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_iff
% 0.20/0.46 thf(fact_122_singleton__iff,axiom,
% 0.20/0.46 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 0.20/0.46 = ( B2 = A ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_iff
% 0.20/0.46 thf(fact_123_the__elem__eq,axiom,
% 0.20/0.46 ! [X: secrecy_specID] :
% 0.20/0.46 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % the_elem_eq
% 0.20/0.46 thf(fact_124_the__elem__eq,axiom,
% 0.20/0.46 ! [X: secrecy_chanID] :
% 0.20/0.46 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % the_elem_eq
% 0.20/0.46 thf(fact_125_is__singletonI,axiom,
% 0.20/0.46 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI
% 0.20/0.46 thf(fact_126_is__singletonI,axiom,
% 0.20/0.46 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI
% 0.20/0.46 thf(fact_127_a11,axiom,
% 0.20/0.46 ine @ p @ ( secrecy_kE @ key ) ).
% 0.20/0.46
% 0.20/0.46 % a11
% 0.20/0.46 thf(fact_128_TBtheorem3b,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ~ ( ineM @ P @ M @ E )
% 0.20/0.46 => ( ~ ( ineM @ Q @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem3b
% 0.20/0.46 thf(fact_129_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: secrecy_KS,P: secrecy_KS > $o] :
% 0.20/0.46 ( ( member_Secrecy_KS @ A @ ( collect_Secrecy_KS @ P ) )
% 0.20/0.46 = ( P @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_130_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,P: secrecy_chanID > $o] :
% 0.20/0.46 ( ( member1967978193chanID @ A @ ( collec625564175chanID @ P ) )
% 0.20/0.46 = ( P @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_131_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: secrecy_specID,P: secrecy_specID > $o] :
% 0.20/0.46 ( ( member740727610specID @ A @ ( collec1545797240specID @ P ) )
% 0.20/0.46 = ( P @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_132_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.20/0.46 ( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ P ) )
% 0.20/0.46 = ( P @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_133_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ A @ ( collect_Secrecy_Keys @ P ) )
% 0.20/0.46 = ( P @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_134_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( collect_Secrecy_KS
% 0.20/0.46 @ ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_135_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( collec625564175chanID
% 0.20/0.46 @ ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_136_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( collec1545797240specID
% 0.20/0.46 @ ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_137_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( collec836099393ecrets
% 0.20/0.46 @ ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_138_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( collect_Secrecy_Keys
% 0.20/0.46 @ ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_139_TBtheorem1b,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( ineM @ PQ @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( ineM @ P @ M @ E )
% 0.20/0.46 | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem1b
% 0.20/0.46 thf(fact_140_a11ext,axiom,
% 0.20/0.46 ( ( ine @ p @ ( secrecy_kE @ key ) )
% 0.20/0.46 | ( ine @ q @ ( secrecy_kE @ key ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % a11ext
% 0.20/0.46 thf(fact_141_Set_Ois__empty__def,axiom,
% 0.20/0.46 ( is_emp1849217361specID
% 0.20/0.46 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.is_empty_def
% 0.20/0.46 thf(fact_142_Set_Ois__empty__def,axiom,
% 0.20/0.46 ( is_emp928984296chanID
% 0.20/0.46 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Set.is_empty_def
% 0.20/0.46 thf(fact_143_correctCompositionIn__prop1,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.20/0.46 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionIn_prop1
% 0.20/0.46 thf(fact_144_correctCompositionIn__L2,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionIn_L2
% 0.20/0.46 thf(fact_145_is__singleton__def,axiom,
% 0.20/0.46 ( is_sin1501507247specID
% 0.20/0.46 = ( ^ [A3: set_Secrecy_specID] :
% 0.20/0.46 ? [X2: secrecy_specID] :
% 0.20/0.46 ( A3
% 0.20/0.46 = ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singleton_def
% 0.20/0.46 thf(fact_146_is__singleton__def,axiom,
% 0.20/0.46 ( is_sin581274182chanID
% 0.20/0.46 = ( ^ [A3: set_Secrecy_chanID] :
% 0.20/0.46 ? [X2: secrecy_chanID] :
% 0.20/0.46 ( A3
% 0.20/0.46 = ( insert751661162chanID @ X2 @ bot_bo443197316chanID ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singleton_def
% 0.20/0.46 thf(fact_147_Expression_Oinject_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.20/0.46 ( ( ( secrecy_kE @ X1 )
% 0.20/0.46 = ( secrecy_kE @ Y1 ) )
% 0.20/0.46 = ( X1 = Y1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Expression.inject(1)
% 0.20/0.46 thf(fact_148_not__ine__ineM,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( ine @ P @ E )
% 0.20/0.46 => ~ ( ineM @ P @ M @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_ine_ineM
% 0.20/0.46 thf(fact_149_ineM__ine,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( ineM @ P @ M @ E )
% 0.20/0.46 => ( ine @ P @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % ineM_ine
% 0.20/0.46 thf(fact_150_not__know__k__not__ine,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M2: secrecy_Keys] :
% 0.20/0.46 ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 => ~ ( ine @ A2 @ ( secrecy_kE @ M2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_know_k_not_ine
% 0.20/0.46 thf(fact_151_is__singleton__the__elem,axiom,
% 0.20/0.46 ( is_sin1501507247specID
% 0.20/0.46 = ( ^ [A3: set_Secrecy_specID] :
% 0.20/0.46 ( A3
% 0.20/0.46 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singleton_the_elem
% 0.20/0.46 thf(fact_152_is__singleton__the__elem,axiom,
% 0.20/0.46 ( is_sin581274182chanID
% 0.20/0.46 = ( ^ [A3: set_Secrecy_chanID] :
% 0.20/0.46 ( A3
% 0.20/0.46 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singleton_the_elem
% 0.20/0.46 thf(fact_153_is__singletonI_H,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( A2 != bot_bo1943466239ecy_KS )
% 0.20/0.46 => ( ! [X3: secrecy_KS,Y: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X3 @ A2 )
% 0.20/0.46 => ( ( member_Secrecy_KS @ Y @ A2 )
% 0.20/0.46 => ( X3 = Y ) ) )
% 0.20/0.46 => ( is_sin1442426433ecy_KS @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI'
% 0.20/0.46 thf(fact_154_is__singletonI_H,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( A2 != bot_bo1124690338ecrets )
% 0.20/0.46 => ( ! [X3: secrecy_Secrets,Y: secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ X3 @ A2 )
% 0.20/0.46 => ( ( member2138796287ecrets @ Y @ A2 )
% 0.20/0.46 => ( X3 = Y ) ) )
% 0.20/0.46 => ( is_sin1002224330ecrets @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI'
% 0.20/0.46 thf(fact_155_is__singletonI_H,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( A2 != bot_bo701486667y_Keys )
% 0.20/0.46 => ( ! [X3: secrecy_Keys,Y: secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ X3 @ A2 )
% 0.20/0.46 => ( ( member_Secrecy_Keys @ Y @ A2 )
% 0.20/0.46 => ( X3 = Y ) ) )
% 0.20/0.46 => ( is_sin1096471309y_Keys @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI'
% 0.20/0.46 thf(fact_156_is__singletonI_H,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( A2 != bot_bo1785112429specID )
% 0.20/0.46 => ( ! [X3: secrecy_specID,Y: secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ X3 @ A2 )
% 0.20/0.46 => ( ( member740727610specID @ Y @ A2 )
% 0.20/0.46 => ( X3 = Y ) ) )
% 0.20/0.46 => ( is_sin1501507247specID @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI'
% 0.20/0.46 thf(fact_157_is__singletonI_H,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( A2 != bot_bo443197316chanID )
% 0.20/0.46 => ( ! [X3: secrecy_chanID,Y: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ A2 )
% 0.20/0.46 => ( ( member1967978193chanID @ Y @ A2 )
% 0.20/0.46 => ( X3 = Y ) ) )
% 0.20/0.46 => ( is_sin581274182chanID @ A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonI'
% 0.20/0.46 thf(fact_158_TBtheorem1a,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( ine @ PQ @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( ine @ P @ E )
% 0.20/0.46 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem1a
% 0.20/0.46 thf(fact_159_TBtheorem3a,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ~ ( ine @ P @ E )
% 0.20/0.46 => ( ~ ( ine @ Q @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem3a
% 0.20/0.46 thf(fact_160_is__singletonE,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( is_sin1501507247specID @ A2 )
% 0.20/0.46 => ~ ! [X3: secrecy_specID] :
% 0.20/0.46 ( A2
% 0.20/0.46 != ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonE
% 0.20/0.46 thf(fact_161_is__singletonE,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( is_sin581274182chanID @ A2 )
% 0.20/0.46 => ~ ! [X3: secrecy_chanID] :
% 0.20/0.46 ( A2
% 0.20/0.46 != ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % is_singletonE
% 0.20/0.46 thf(fact_162_bot__empty__eq,axiom,
% 0.20/0.46 ( bot_bot_Secrecy_KS_o
% 0.20/0.46 = ( ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ bot_bo1943466239ecy_KS ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_empty_eq
% 0.20/0.46 thf(fact_163_bot__empty__eq,axiom,
% 0.20/0.46 ( bot_bo1909946299rets_o
% 0.20/0.46 = ( ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ bot_bo1124690338ecrets ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_empty_eq
% 0.20/0.46 thf(fact_164_bot__empty__eq,axiom,
% 0.20/0.46 ( bot_bo2072920570Keys_o
% 0.20/0.46 = ( ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ bot_bo701486667y_Keys ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_empty_eq
% 0.20/0.46 thf(fact_165_bot__empty__eq,axiom,
% 0.20/0.46 ( bot_bo1767780696ecID_o
% 0.20/0.46 = ( ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_empty_eq
% 0.20/0.46 thf(fact_166_bot__empty__eq,axiom,
% 0.20/0.46 ( bot_bo1012329985anID_o
% 0.20/0.46 = ( ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_empty_eq
% 0.20/0.46 thf(fact_167_Collect__empty__eq__bot,axiom,
% 0.20/0.46 ! [P: secrecy_specID > $o] :
% 0.20/0.46 ( ( ( collec1545797240specID @ P )
% 0.20/0.46 = bot_bo1785112429specID )
% 0.20/0.46 = ( P = bot_bo1767780696ecID_o ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_empty_eq_bot
% 0.20/0.46 thf(fact_168_Collect__empty__eq__bot,axiom,
% 0.20/0.46 ! [P: secrecy_chanID > $o] :
% 0.20/0.46 ( ( ( collec625564175chanID @ P )
% 0.20/0.46 = bot_bo443197316chanID )
% 0.20/0.46 = ( P = bot_bo1012329985anID_o ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_empty_eq_bot
% 0.20/0.46 thf(fact_169_TBlemma3b,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.20/0.46 ( ~ ( ineM @ P @ M @ E )
% 0.20/0.46 => ( ~ ( ineM @ Q @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ M )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.20/0.46 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBlemma3b
% 0.20/0.46 thf(fact_170_correctCompositionIn__L1,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionIn_L1
% 0.20/0.46 thf(fact_171_KS2Expression_Osimps_I1_J,axiom,
% 0.20/0.46 ! [M2: secrecy_Keys] :
% 0.20/0.46 ( ( secrec1016742679ession @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 = ( secrecy_kE @ M2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS2Expression.simps(1)
% 0.20/0.46 thf(fact_172_TBtheorem4a__empty,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ( ine @ P @ E )
% 0.20/0.46 | ( ine @ Q @ E ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( ( loc @ PQ )
% 0.20/0.46 = bot_bo443197316chanID )
% 0.20/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4a_empty
% 0.20/0.46 thf(fact_173_know_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M2: secrecy_Keys] :
% 0.20/0.46 ( ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 = ( ( ine @ A2 @ ( secrecy_kE @ M2 ) )
% 0.20/0.46 | ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know.simps(1)
% 0.20/0.46 thf(fact_174_correctCompositionKS__exprChannel__k__P,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_k_P
% 0.20/0.46 thf(fact_175_LocalSecretsComposition__neg__loc__k,axiom,
% 0.20/0.46 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.20/0.46 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.20/0.46 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg_loc_k
% 0.20/0.46 thf(fact_176_LocalSecretsComposition1,axiom,
% 0.20/0.46 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition1
% 0.20/0.46 thf(fact_177_LocalSecretsComposition__exprChannel__k,axiom,
% 0.20/0.46 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.20/0.46 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.20/0.46 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_exprChannel_k
% 0.20/0.46 thf(fact_178_ine__def,axiom,
% 0.20/0.46 ( ine
% 0.20/0.46 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.20/0.46 ? [Ch2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 0.20/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_def
% 0.20/0.46 thf(fact_179_ine__ins__neg1,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M2: secrecy_Expression,X: secrecy_chanID] :
% 0.20/0.46 ( ~ ( ine @ P @ M2 )
% 0.20/0.46 => ( ( exprChannel @ X @ M2 )
% 0.20/0.46 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_ins_neg1
% 0.20/0.46 thf(fact_180_ineM__L1,axiom,
% 0.20/0.46 ! [Ch: secrecy_chanID,M: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch @ M )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ E )
% 0.20/0.46 => ( ineM @ P @ M @ E ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ineM_L1
% 0.20/0.46 thf(fact_181_ineM__def,axiom,
% 0.20/0.46 ( ineM
% 0.20/0.46 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.20/0.46 ? [Ch2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 0.20/0.46 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.20/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ineM_def
% 0.20/0.46 thf(fact_182_correctCompositionInLoc__exprChannel,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M2: secrecy_Expression] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ M2 )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 0.20/0.46 => ~ ( exprChannel @ X3 @ M2 ) )
% 0.20/0.46 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionInLoc_exprChannel
% 0.20/0.46 thf(fact_183_TBtheorem4a__PQ,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ( ine @ P @ E )
% 0.20/0.46 | ( ine @ Q @ E ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 0.20/0.46 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.20/0.46 & ( exprChannel @ Ch3 @ E )
% 0.20/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4a_PQ
% 0.20/0.46 thf(fact_184_TBtheorem4a__P,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( ine @ P @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 0.20/0.46 & ( exprChannel @ Ch3 @ E )
% 0.20/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4a_P
% 0.20/0.46 thf(fact_185_TBtheorem4b__PQ,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ( ineM @ P @ M @ E )
% 0.20/0.46 | ( ineM @ Q @ M @ E ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 0.20/0.46 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ M )
% 0.20/0.46 & ( exprChannel @ Ch3 @ E )
% 0.20/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4b_PQ
% 0.20/0.46 thf(fact_186_TBtheorem4b__P,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( ineM @ P @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch3 @ ( ins @ Q ) )
% 0.20/0.46 & ( exprChannel @ Ch3 @ E )
% 0.20/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ M ) )
% 0.20/0.46 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4b_P
% 0.20/0.46 thf(fact_187_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ? [Ch4: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_k_Qex
% 0.20/0.46 thf(fact_188_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ? [Ch4: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_k_Pex
% 0.20/0.46 thf(fact_189_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_k_Q
% 0.20/0.46 thf(fact_190_TBtheorem4b__notP1,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ineM @ P @ M @ E )
% 0.20/0.46 => ( ~ ( ineM @ Q @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ M )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4b_notP1
% 0.20/0.46 thf(fact_191_TBtheorem4a__notP1,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ine @ P @ E )
% 0.20/0.46 => ( ~ ( ine @ Q @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4a_notP1
% 0.20/0.46 thf(fact_192_LocalSecretsComposition__neg1__k,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg1_k
% 0.20/0.46 thf(fact_193_LocalSecretsComposition__ine2__k,axiom,
% 0.20/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.20/0.46 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_ine2_k
% 0.20/0.46 thf(fact_194_LocalSecretsComposition__ine1__k,axiom,
% 0.20/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.20/0.46 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_ine1_k
% 0.20/0.46 thf(fact_195_TBtheorem4b__notPQ,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.20/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4b_notPQ
% 0.20/0.46 thf(fact_196_TBtheorem4b__notP2,axiom,
% 0.20/0.46 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( ineM @ Q @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4b_notP2
% 0.20/0.46 thf(fact_197_ine__exprChannelSingle__Set,axiom,
% 0.20/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.20/0.46 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_exprChannelSingle_Set
% 0.20/0.46 thf(fact_198_ine__exprChannelSet__Single,axiom,
% 0.20/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.20/0.46 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_exprChannelSet_Single
% 0.20/0.46 thf(fact_199_ine__exprChannelSet__def,axiom,
% 0.20/0.46 ( ine_exprChannelSet
% 0.20/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.20/0.46 ( ! [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 0.20/0.46 => ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 0.20/0.46 & ( exprChannel @ X2 @ E2 ) ) )
% 0.20/0.46 & ! [X2: secrecy_chanID] :
% 0.20/0.46 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 0.20/0.46 & ( member1967978193chanID @ X2 @ ( ins @ SP ) ) )
% 0.20/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_exprChannelSet_def
% 0.20/0.46 thf(fact_200_ine__empty__exprChannelSet,axiom,
% 0.20/0.46 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.20/0.46 => ( ( ChSet = bot_bo443197316chanID )
% 0.20/0.46 => ~ ( ine @ P @ E ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_empty_exprChannelSet
% 0.20/0.46 thf(fact_201_ine__nonempty__exprChannelSet,axiom,
% 0.20/0.46 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.20/0.46 => ( ( ChSet != bot_bo443197316chanID )
% 0.20/0.46 => ( ine @ P @ E ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_nonempty_exprChannelSet
% 0.20/0.46 thf(fact_202_ine__exprChannelSingle__def,axiom,
% 0.20/0.46 ( ine_ex1303305700Single
% 0.20/0.46 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 0.20/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.20/0.46 & ! [X2: secrecy_chanID,T: nat] :
% 0.20/0.46 ( ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 0.20/0.46 & ( X2 != Ch2 ) )
% 0.20/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ine_exprChannelSingle_def
% 0.20/0.46 thf(fact_203_TBtheorem4a__notP2,axiom,
% 0.20/0.46 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( ine @ Q @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4a_notP2
% 0.20/0.46 thf(fact_204_TBtheorem4a__notPQ,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.20/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem4a_notPQ
% 0.20/0.46 thf(fact_205_subcomponents__loc,axiom,
% 0.20/0.46 ! [X: secrecy_specID] :
% 0.20/0.46 ( ( correc965049635ionLoc @ X )
% 0.20/0.46 => ( ( ( subcomponents @ X )
% 0.20/0.46 = bot_bo1785112429specID )
% 0.20/0.46 => ( ( loc @ X )
% 0.20/0.46 = bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subcomponents_loc
% 0.20/0.46 thf(fact_206_LocalSecretsComposition__neg__k,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Keys] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ M2 ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg_k
% 0.20/0.46 thf(fact_207_correctCompositionKS__exprChannel__s__P,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_s_P
% 0.20/0.46 thf(fact_208_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_s_Q
% 0.20/0.46 thf(fact_209_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ? [Ch4: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_s_Pex
% 0.20/0.46 thf(fact_210_UnCI,axiom,
% 0.20/0.46 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( ~ ( member740727610specID @ C @ B )
% 0.20/0.46 => ( member740727610specID @ C @ A2 ) )
% 0.20/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_211_UnCI,axiom,
% 0.20/0.46 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( ~ ( member2138796287ecrets @ C @ B )
% 0.20/0.46 => ( member2138796287ecrets @ C @ A2 ) )
% 0.20/0.46 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_212_UnCI,axiom,
% 0.20/0.46 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 0.20/0.46 => ( member_Secrecy_Keys @ C @ A2 ) )
% 0.20/0.46 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_213_UnCI,axiom,
% 0.20/0.46 ! [C: secrecy_KS,B: set_Secrecy_KS,A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 0.20/0.46 => ( member_Secrecy_KS @ C @ A2 ) )
% 0.20/0.46 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_214_UnCI,axiom,
% 0.20/0.46 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ~ ( member1967978193chanID @ C @ B )
% 0.20/0.46 => ( member1967978193chanID @ C @ A2 ) )
% 0.20/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnCI
% 0.20/0.46 thf(fact_215_Un__iff,axiom,
% 0.20/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 0.20/0.46 = ( ( member740727610specID @ C @ A2 )
% 0.20/0.46 | ( member740727610specID @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_216_Un__iff,axiom,
% 0.20/0.46 ! [C: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) )
% 0.20/0.46 = ( ( member2138796287ecrets @ C @ A2 )
% 0.20/0.46 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_217_Un__iff,axiom,
% 0.20/0.46 ! [C: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) )
% 0.20/0.46 = ( ( member_Secrecy_Keys @ C @ A2 )
% 0.20/0.46 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_218_Un__iff,axiom,
% 0.20/0.46 ! [C: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 0.20/0.46 = ( ( member_Secrecy_KS @ C @ A2 )
% 0.20/0.46 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_219_Un__iff,axiom,
% 0.20/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.20/0.46 = ( ( member1967978193chanID @ C @ A2 )
% 0.20/0.46 | ( member1967978193chanID @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_iff
% 0.20/0.46 thf(fact_220_KS_Oinject_I2_J,axiom,
% 0.20/0.46 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.20/0.46 ( ( ( secrecy_sKS @ X22 )
% 0.20/0.46 = ( secrecy_sKS @ Y22 ) )
% 0.20/0.46 = ( X22 = Y22 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.inject(2)
% 0.20/0.46 thf(fact_221_Expression_Oinject_I2_J,axiom,
% 0.20/0.46 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.20/0.46 ( ( ( secrecy_sE @ X22 )
% 0.20/0.46 = ( secrecy_sE @ Y22 ) )
% 0.20/0.46 = ( X22 = Y22 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Expression.inject(2)
% 0.20/0.46 thf(fact_222_Un__empty,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ( ( sup_su1301156759ecy_KS @ A2 @ B )
% 0.20/0.46 = bot_bo1943466239ecy_KS )
% 0.20/0.46 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.20/0.46 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty
% 0.20/0.46 thf(fact_223_Un__empty,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ( ( sup_su1712599557specID @ A2 @ B )
% 0.20/0.46 = bot_bo1785112429specID )
% 0.20/0.46 = ( ( A2 = bot_bo1785112429specID )
% 0.20/0.46 & ( B = bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty
% 0.20/0.46 thf(fact_224_Un__empty,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( sup_su370684444chanID @ A2 @ B )
% 0.20/0.46 = bot_bo443197316chanID )
% 0.20/0.46 = ( ( A2 = bot_bo443197316chanID )
% 0.20/0.46 & ( B = bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty
% 0.20/0.46 thf(fact_225_Un__insert__right,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID,A: secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 0.20/0.46 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_insert_right
% 0.20/0.46 thf(fact_226_Un__insert__right,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,A: secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ A2 @ ( insert_Secrecy_KS @ A @ B ) )
% 0.20/0.46 = ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_insert_right
% 0.20/0.46 thf(fact_227_Un__insert__right,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,A: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 0.20/0.46 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_insert_right
% 0.20/0.46 thf(fact_228_Un__insert__left,axiom,
% 0.20/0.46 ! [A: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 0.20/0.46 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_insert_left
% 0.20/0.46 thf(fact_229_Un__insert__left,axiom,
% 0.20/0.46 ! [A: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ B ) @ C3 )
% 0.20/0.46 = ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_insert_left
% 0.20/0.46 thf(fact_230_Un__insert__left,axiom,
% 0.20/0.46 ! [A: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 0.20/0.46 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_insert_left
% 0.20/0.46 thf(fact_231_UnE,axiom,
% 0.20/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 0.20/0.46 => ( ~ ( member740727610specID @ C @ A2 )
% 0.20/0.46 => ( member740727610specID @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnE
% 0.20/0.46 thf(fact_232_UnE,axiom,
% 0.20/0.46 ! [C: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) )
% 0.20/0.46 => ( ~ ( member2138796287ecrets @ C @ A2 )
% 0.20/0.46 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnE
% 0.20/0.46 thf(fact_233_UnE,axiom,
% 0.20/0.46 ! [C: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_Keys @ C @ A2 )
% 0.20/0.46 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnE
% 0.20/0.46 thf(fact_234_UnE,axiom,
% 0.20/0.46 ! [C: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ C @ A2 )
% 0.20/0.46 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnE
% 0.20/0.46 thf(fact_235_UnE,axiom,
% 0.20/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.20/0.46 => ( ~ ( member1967978193chanID @ C @ A2 )
% 0.20/0.46 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnE
% 0.20/0.46 thf(fact_236_UnI1,axiom,
% 0.20/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ C @ A2 )
% 0.20/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI1
% 0.20/0.46 thf(fact_237_UnI1,axiom,
% 0.20/0.46 ! [C: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ C @ A2 )
% 0.20/0.46 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI1
% 0.20/0.46 thf(fact_238_UnI1,axiom,
% 0.20/0.46 ! [C: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ C @ A2 )
% 0.20/0.46 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI1
% 0.20/0.46 thf(fact_239_UnI1,axiom,
% 0.20/0.46 ! [C: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ C @ A2 )
% 0.20/0.46 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI1
% 0.20/0.46 thf(fact_240_UnI1,axiom,
% 0.20/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ C @ A2 )
% 0.20/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI1
% 0.20/0.46 thf(fact_241_UnI2,axiom,
% 0.20/0.46 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ C @ B )
% 0.20/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI2
% 0.20/0.46 thf(fact_242_UnI2,axiom,
% 0.20/0.46 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 0.20/0.46 ( ( member2138796287ecrets @ C @ B )
% 0.20/0.46 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI2
% 0.20/0.46 thf(fact_243_UnI2,axiom,
% 0.20/0.46 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A2: set_Secrecy_Keys] :
% 0.20/0.46 ( ( member_Secrecy_Keys @ C @ B )
% 0.20/0.46 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI2
% 0.20/0.46 thf(fact_244_UnI2,axiom,
% 0.20/0.46 ! [C: secrecy_KS,B: set_Secrecy_KS,A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ C @ B )
% 0.20/0.46 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI2
% 0.20/0.46 thf(fact_245_UnI2,axiom,
% 0.20/0.46 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ C @ B )
% 0.20/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % UnI2
% 0.20/0.46 thf(fact_246_bex__Un,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.20/0.46 ( ( ? [X2: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 0.20/0.46 & ( P @ X2 ) ) )
% 0.20/0.46 = ( ? [X2: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X2 @ A2 )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 | ? [X2: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X2 @ B )
% 0.20/0.46 & ( P @ X2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bex_Un
% 0.20/0.46 thf(fact_247_bex__Un,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.20/0.46 ( ( ? [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.20/0.46 & ( P @ X2 ) ) )
% 0.20/0.46 = ( ? [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ A2 )
% 0.20/0.46 & ( P @ X2 ) )
% 0.20/0.46 | ? [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ B )
% 0.20/0.46 & ( P @ X2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bex_Un
% 0.20/0.46 thf(fact_248_ball__Un,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.20/0.46 ( ( ! [X2: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 0.20/0.46 => ( P @ X2 ) ) )
% 0.20/0.46 = ( ! [X2: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X2 @ A2 )
% 0.20/0.46 => ( P @ X2 ) )
% 0.20/0.46 & ! [X2: secrecy_KS] :
% 0.20/0.46 ( ( member_Secrecy_KS @ X2 @ B )
% 0.20/0.46 => ( P @ X2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ball_Un
% 0.20/0.46 thf(fact_249_ball__Un,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.20/0.46 ( ( ! [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.20/0.46 => ( P @ X2 ) ) )
% 0.20/0.46 = ( ! [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ A2 )
% 0.20/0.46 => ( P @ X2 ) )
% 0.20/0.46 & ! [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ B )
% 0.20/0.46 => ( P @ X2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ball_Un
% 0.20/0.46 thf(fact_250_Un__assoc,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A2 @ B ) @ C3 )
% 0.20/0.46 = ( sup_su1301156759ecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_assoc
% 0.20/0.46 thf(fact_251_Un__assoc,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 )
% 0.20/0.46 = ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_assoc
% 0.20/0.46 thf(fact_252_Un__absorb,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ A2 @ A2 )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Un_absorb
% 0.20/0.46 thf(fact_253_Un__absorb,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ A2 @ A2 )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Un_absorb
% 0.20/0.46 thf(fact_254_Un__commute,axiom,
% 0.20/0.46 ( sup_su1301156759ecy_KS
% 0.20/0.46 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_commute
% 0.20/0.46 thf(fact_255_Un__commute,axiom,
% 0.20/0.46 ( sup_su370684444chanID
% 0.20/0.46 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_commute
% 0.20/0.46 thf(fact_256_Un__left__absorb,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 0.20/0.46 = ( sup_su1301156759ecy_KS @ A2 @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_left_absorb
% 0.20/0.46 thf(fact_257_Un__left__absorb,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.20/0.46 = ( sup_su370684444chanID @ A2 @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_left_absorb
% 0.20/0.46 thf(fact_258_Un__left__commute,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 0.20/0.46 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A2 @ C3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_left_commute
% 0.20/0.46 thf(fact_259_Un__left__commute,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) )
% 0.20/0.46 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A2 @ C3 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_left_commute
% 0.20/0.46 thf(fact_260_KS2Expression_Osimps_I2_J,axiom,
% 0.20/0.46 ! [M2: secrecy_Secrets] :
% 0.20/0.46 ( ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 = ( secrecy_sE @ M2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS2Expression.simps(2)
% 0.20/0.46 thf(fact_261_Un__empty__right,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty_right
% 0.20/0.46 thf(fact_262_Un__empty__right,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty_right
% 0.20/0.46 thf(fact_263_Un__empty__right,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty_right
% 0.20/0.46 thf(fact_264_Un__empty__left,axiom,
% 0.20/0.46 ! [B: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 0.20/0.46 = B ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty_left
% 0.20/0.46 thf(fact_265_Un__empty__left,axiom,
% 0.20/0.46 ! [B: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 0.20/0.46 = B ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty_left
% 0.20/0.46 thf(fact_266_Un__empty__left,axiom,
% 0.20/0.46 ! [B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 0.20/0.46 = B ) ).
% 0.20/0.46
% 0.20/0.46 % Un_empty_left
% 0.20/0.46 thf(fact_267_not__know__s__not__ine,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M2: secrecy_Secrets] :
% 0.20/0.46 ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 => ~ ( ine @ A2 @ ( secrecy_sE @ M2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_know_s_not_ine
% 0.20/0.46 thf(fact_268_KS_Oexhaust,axiom,
% 0.20/0.46 ! [Y2: secrecy_KS] :
% 0.20/0.46 ( ! [X12: secrecy_Keys] :
% 0.20/0.46 ( Y2
% 0.20/0.46 != ( secrecy_kKS @ X12 ) )
% 0.20/0.46 => ~ ! [X23: secrecy_Secrets] :
% 0.20/0.46 ( Y2
% 0.20/0.46 != ( secrecy_sKS @ X23 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.exhaust
% 0.20/0.46 thf(fact_269_KS_Oinduct,axiom,
% 0.20/0.46 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.20/0.46 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 0.20/0.46 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 0.20/0.46 => ( P @ KS ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.induct
% 0.20/0.46 thf(fact_270_KS_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.20/0.46 ( ( secrecy_kKS @ X1 )
% 0.20/0.46 != ( secrecy_sKS @ X22 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.distinct(1)
% 0.20/0.46 thf(fact_271_Expression_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.20/0.46 ( ( secrecy_kE @ X1 )
% 0.20/0.46 != ( secrecy_sE @ X22 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Expression.distinct(1)
% 0.20/0.46 thf(fact_272_know_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M2: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 = ( ( ine @ A2 @ ( secrecy_sE @ M2 ) )
% 0.20/0.46 | ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know.simps(2)
% 0.20/0.46 thf(fact_273_singleton__Un__iff,axiom,
% 0.20/0.46 ! [X: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.20/0.46 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 0.20/0.46 = ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 0.20/0.46 = ( ( ( A2 = bot_bo1943466239ecy_KS )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.20/0.46 & ( B = bot_bo1943466239ecy_KS ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_Un_iff
% 0.20/0.46 thf(fact_274_singleton__Un__iff,axiom,
% 0.20/0.46 ! [X: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.20/0.46 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 0.20/0.46 = ( sup_su1712599557specID @ A2 @ B ) )
% 0.20/0.46 = ( ( ( A2 = bot_bo1785112429specID )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.20/0.46 & ( B = bot_bo1785112429specID ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_Un_iff
% 0.20/0.46 thf(fact_275_singleton__Un__iff,axiom,
% 0.20/0.46 ! [X: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 0.20/0.46 = ( sup_su370684444chanID @ A2 @ B ) )
% 0.20/0.46 = ( ( ( A2 = bot_bo443197316chanID )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.20/0.46 & ( B = bot_bo443197316chanID ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % singleton_Un_iff
% 0.20/0.46 thf(fact_276_Un__singleton__iff,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 0.20/0.46 ( ( ( sup_su1301156759ecy_KS @ A2 @ B )
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.20/0.46 = ( ( ( A2 = bot_bo1943466239ecy_KS )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.20/0.46 & ( B = bot_bo1943466239ecy_KS ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_singleton_iff
% 0.20/0.46 thf(fact_277_Un__singleton__iff,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 0.20/0.46 ( ( ( sup_su1712599557specID @ A2 @ B )
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.20/0.46 = ( ( ( A2 = bot_bo1785112429specID )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.20/0.46 & ( B = bot_bo1785112429specID ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_singleton_iff
% 0.20/0.46 thf(fact_278_Un__singleton__iff,axiom,
% 0.20/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 0.20/0.46 ( ( ( sup_su370684444chanID @ A2 @ B )
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.20/0.46 = ( ( ( A2 = bot_bo443197316chanID )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.20/0.46 & ( B = bot_bo443197316chanID ) )
% 0.20/0.46 | ( ( A2
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.20/0.46 & ( B
% 0.20/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Un_singleton_iff
% 0.20/0.46 thf(fact_279_insert__is__Un,axiom,
% 0.20/0.46 ( insert_Secrecy_KS
% 0.20/0.46 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_is_Un
% 0.20/0.46 thf(fact_280_insert__is__Un,axiom,
% 0.20/0.46 ( insert1671894227specID
% 0.20/0.46 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_is_Un
% 0.20/0.46 thf(fact_281_insert__is__Un,axiom,
% 0.20/0.46 ( insert751661162chanID
% 0.20/0.46 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_is_Un
% 0.20/0.46 thf(fact_282_LocalSecretsComposition__neg__loc__s,axiom,
% 0.20/0.46 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.20/0.46 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.20/0.46 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg_loc_s
% 0.20/0.46 thf(fact_283_LocalSecretsComposition__neg__s,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Secrets] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ M2 ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg_s
% 0.20/0.46 thf(fact_284_LocalSecretsComposition__ine1__s,axiom,
% 0.20/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.20/0.46 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_ine1_s
% 0.20/0.46 thf(fact_285_LocalSecretsComposition__ine2__s,axiom,
% 0.20/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.20/0.46 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_ine2_s
% 0.20/0.46 thf(fact_286_LocalSecretsComposition__neg1__s,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg1_s
% 0.20/0.46 thf(fact_287_LocalSecretsComposition__exprChannel__s,axiom,
% 0.20/0.46 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.20/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.20/0.46 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.20/0.46 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_exprChannel_s
% 0.20/0.46 thf(fact_288_LocalSecretsComposition__neg,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.20/0.46 => ( ! [M4: secrecy_Keys] :
% 0.20/0.46 ( ( Ks
% 0.20/0.46 = ( secrecy_kKS @ M4 ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.20/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.20/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.20/0.46 ( ( Ks
% 0.20/0.46 = ( secrecy_sKS @ M4 ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.20/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg
% 0.20/0.46 thf(fact_289_LocalSecretsComposition__neg1,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.20/0.46 => ( ! [M4: secrecy_Keys] :
% 0.20/0.46 ( ( Ks
% 0.20/0.46 = ( secrecy_kKS @ M4 ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.20/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.20/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.20/0.46 ( ( Ks
% 0.20/0.46 = ( secrecy_sKS @ M4 ) )
% 0.20/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.20/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % LocalSecretsComposition_neg1
% 0.20/0.46 thf(fact_290_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correctCompositionKS @ PQ )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.20/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.20/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.20/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.20/0.46 => ( ( correctCompositionIn @ PQ )
% 0.20/0.46 => ? [Ch4: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.20/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_exprChannel_s_Qex
% 0.20/0.46 thf(fact_291_sup__bot_Oright__neutral,axiom,
% 0.20/0.46 ! [A: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.right_neutral
% 0.20/0.46 thf(fact_292_sup__bot_Oright__neutral,axiom,
% 0.20/0.46 ! [A: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.right_neutral
% 0.20/0.46 thf(fact_293_sup__bot_Oright__neutral,axiom,
% 0.20/0.46 ! [A: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.right_neutral
% 0.20/0.46 thf(fact_294_sup__bot_Oneutr__eq__iff,axiom,
% 0.20/0.46 ! [A: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.20/0.46 ( ( bot_bo1943466239ecy_KS
% 0.20/0.46 = ( sup_su1301156759ecy_KS @ A @ B2 ) )
% 0.20/0.46 = ( ( A = bot_bo1943466239ecy_KS )
% 0.20/0.46 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.neutr_eq_iff
% 0.20/0.46 thf(fact_295_sup__bot_Oneutr__eq__iff,axiom,
% 0.20/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.20/0.46 ( ( bot_bo1785112429specID
% 0.20/0.46 = ( sup_su1712599557specID @ A @ B2 ) )
% 0.20/0.46 = ( ( A = bot_bo1785112429specID )
% 0.20/0.46 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.neutr_eq_iff
% 0.20/0.46 thf(fact_296_sup__bot_Oneutr__eq__iff,axiom,
% 0.20/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( bot_bo443197316chanID
% 0.20/0.46 = ( sup_su370684444chanID @ A @ B2 ) )
% 0.20/0.46 = ( ( A = bot_bo443197316chanID )
% 0.20/0.46 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.neutr_eq_iff
% 0.20/0.46 thf(fact_297_sup__bot_Oleft__neutral,axiom,
% 0.20/0.46 ! [A: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.left_neutral
% 0.20/0.46 thf(fact_298_sup__bot_Oleft__neutral,axiom,
% 0.20/0.46 ! [A: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.left_neutral
% 0.20/0.46 thf(fact_299_sup__bot_Oleft__neutral,axiom,
% 0.20/0.46 ! [A: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
% 0.20/0.46 = A ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.left_neutral
% 0.20/0.46 thf(fact_300_sup__bot_Oeq__neutr__iff,axiom,
% 0.20/0.46 ! [A: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.20/0.46 ( ( ( sup_su1301156759ecy_KS @ A @ B2 )
% 0.20/0.46 = bot_bo1943466239ecy_KS )
% 0.20/0.46 = ( ( A = bot_bo1943466239ecy_KS )
% 0.20/0.46 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.eq_neutr_iff
% 0.20/0.46 thf(fact_301_sup__bot_Oeq__neutr__iff,axiom,
% 0.20/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.20/0.46 ( ( ( sup_su1712599557specID @ A @ B2 )
% 0.20/0.46 = bot_bo1785112429specID )
% 0.20/0.46 = ( ( A = bot_bo1785112429specID )
% 0.20/0.46 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.eq_neutr_iff
% 0.20/0.46 thf(fact_302_sup__bot_Oeq__neutr__iff,axiom,
% 0.20/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( sup_su370684444chanID @ A @ B2 )
% 0.20/0.46 = bot_bo443197316chanID )
% 0.20/0.46 = ( ( A = bot_bo443197316chanID )
% 0.20/0.46 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot.eq_neutr_iff
% 0.20/0.46 thf(fact_303_sup__eq__bot__iff,axiom,
% 0.20/0.46 ! [X: set_Secrecy_KS,Y2: set_Secrecy_KS] :
% 0.20/0.46 ( ( ( sup_su1301156759ecy_KS @ X @ Y2 )
% 0.20/0.46 = bot_bo1943466239ecy_KS )
% 0.20/0.46 = ( ( X = bot_bo1943466239ecy_KS )
% 0.20/0.46 & ( Y2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_eq_bot_iff
% 0.20/0.46 thf(fact_304_sup__eq__bot__iff,axiom,
% 0.20/0.46 ! [X: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.20/0.46 ( ( ( sup_su1712599557specID @ X @ Y2 )
% 0.20/0.46 = bot_bo1785112429specID )
% 0.20/0.46 = ( ( X = bot_bo1785112429specID )
% 0.20/0.46 & ( Y2 = bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_eq_bot_iff
% 0.20/0.46 thf(fact_305_sup__eq__bot__iff,axiom,
% 0.20/0.46 ! [X: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( sup_su370684444chanID @ X @ Y2 )
% 0.20/0.46 = bot_bo443197316chanID )
% 0.20/0.46 = ( ( X = bot_bo443197316chanID )
% 0.20/0.46 & ( Y2 = bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sup_eq_bot_iff
% 0.20/0.46 thf(fact_306_sup__bot__left,axiom,
% 0.20/0.46 ! [X: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot_left
% 0.20/0.46 thf(fact_307_sup__bot__left,axiom,
% 0.20/0.46 ! [X: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot_left
% 0.20/0.46 thf(fact_308_sup__bot__left,axiom,
% 0.20/0.46 ! [X: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot_left
% 0.20/0.46 thf(fact_309_sup__bot__right,axiom,
% 0.20/0.46 ! [X: set_Secrecy_KS] :
% 0.20/0.46 ( ( sup_su1301156759ecy_KS @ X @ bot_bo1943466239ecy_KS )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot_right
% 0.20/0.46 thf(fact_310_sup__bot__right,axiom,
% 0.20/0.46 ! [X: set_Secrecy_specID] :
% 0.20/0.46 ( ( sup_su1712599557specID @ X @ bot_bo1785112429specID )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot_right
% 0.20/0.46 thf(fact_311_sup__bot__right,axiom,
% 0.20/0.46 ! [X: set_Secrecy_chanID] :
% 0.20/0.46 ( ( sup_su370684444chanID @ X @ bot_bo443197316chanID )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 % sup_bot_right
% 0.20/0.46 thf(fact_312_bot__eq__sup__iff,axiom,
% 0.20/0.46 ! [X: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.20/0.46 ( ( bot_bo1785112429specID
% 0.20/0.46 = ( sup_su1712599557specID @ X @ Y2 ) )
% 0.20/0.46 = ( ( X = bot_bo1785112429specID )
% 0.20/0.46 & ( Y2 = bot_bo1785112429specID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_eq_sup_iff
% 0.20/0.46 thf(fact_313_bot__eq__sup__iff,axiom,
% 0.20/0.46 ! [X: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.20/0.46 ( ( bot_bo443197316chanID
% 0.20/0.46 = ( sup_su370684444chanID @ X @ Y2 ) )
% 0.20/0.46 = ( ( X = bot_bo443197316chanID )
% 0.20/0.46 & ( Y2 = bot_bo443197316chanID ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % bot_eq_sup_iff
% 0.20/0.46 thf(fact_314_ineM__Un1,axiom,
% 0.20/0.46 ! [P: secrecy_specID,A2: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ineM @ P @ A2 @ E )
% 0.20/0.46 => ( ineM @ P @ ( sup_su370684444chanID @ A2 @ B ) @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % ineM_Un1
% 0.20/0.46 thf(fact_315_locStream__def,axiom,
% 0.20/0.46 ( locStream
% 0.20/0.46 = ( ^ [X2: secrecy_specID] :
% 0.20/0.46 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 0.20/0.46 @ ( loc @ X2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % locStream_def
% 0.20/0.46 thf(fact_316_inStream__def,axiom,
% 0.20/0.46 ( inStream
% 0.20/0.46 = ( ^ [X2: secrecy_specID] :
% 0.20/0.46 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 0.20/0.46 @ ( ins @ X2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inStream_def
% 0.20/0.46 thf(fact_317_notSpecKeysSecretsExpr__def,axiom,
% 0.20/0.46 ( notSpe1586871396tsExpr
% 0.20/0.46 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 0.20/0.46 ( ! [X2: secrecy_Keys] :
% 0.20/0.46 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X2 ) @ E3 )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.20/0.46 & ! [Y4: secrecy_Secrets] :
% 0.20/0.46 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y4 ) @ E3 )
% 0.20/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % notSpecKeysSecretsExpr_def
% 0.20/0.46 thf(fact_318_TBtheorem5a__empty,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ( eout @ P @ E )
% 0.20/0.46 | ( eout @ Q @ E ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ( ( loc @ PQ )
% 0.20/0.46 = bot_bo443197316chanID )
% 0.20/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5a_empty
% 0.20/0.46 thf(fact_319_correctCompositionKS__subcomp4,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.20/0.46 ( ( correctCompositionKS @ C3 )
% 0.20/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.20/0.46 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 0.20/0.46 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_subcomp4
% 0.20/0.46 thf(fact_320_correctCompositionKS__subcomp3,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.20/0.46 ( ( correctCompositionKS @ C3 )
% 0.20/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.20/0.46 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.20/0.46 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_subcomp3
% 0.20/0.46 thf(fact_321_TBtheorem2a,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( eout @ PQ @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ( eout @ P @ E )
% 0.20/0.46 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem2a
% 0.20/0.46 thf(fact_322_correctCompositionKS__subcomp1,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.20/0.46 ( ( correctCompositionKS @ C3 )
% 0.20/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.20/0.46 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 0.20/0.46 => ? [X3: secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.20/0.46 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_subcomp1
% 0.20/0.46 thf(fact_323_correctCompositionKS__subcomp2,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.20/0.46 ( ( correctCompositionKS @ C3 )
% 0.20/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.20/0.46 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 0.20/0.46 => ? [X3: secrecy_specID] :
% 0.20/0.46 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.20/0.46 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % correctCompositionKS_subcomp2
% 0.20/0.46 thf(fact_324_TBtheorem5a__notP1,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( eout @ P @ E )
% 0.20/0.46 => ( ~ ( eout @ Q @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5a_notP1
% 0.20/0.46 thf(fact_325_TBtheorem5a__notP2,axiom,
% 0.20/0.46 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( eout @ Q @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5a_notP2
% 0.20/0.46 thf(fact_326_TBtheorem5a__notPQ,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.20/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5a_notPQ
% 0.20/0.46 thf(fact_327_out__exprChannelSet__Single,axiom,
% 0.20/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.20/0.46 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % out_exprChannelSet_Single
% 0.20/0.46 thf(fact_328_out__exprChannelSingle__Set,axiom,
% 0.20/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.20/0.46 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % out_exprChannelSingle_Set
% 0.20/0.46 thf(fact_329_TBtheorem5b__notPQ,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 0.20/0.46 ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.20/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.20/0.46 => ( ( M
% 0.20/0.46 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5b_notPQ
% 0.20/0.46 thf(fact_330_eout__know__s,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,M2: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 = ( ( eout @ C3 @ ( secrecy_sE @ M2 ) )
% 0.20/0.46 = ( ( member2138796287ecrets @ M2 @ ( specSecrets @ C3 ) )
% 0.20/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eout_know_s
% 0.20/0.46 thf(fact_331_not__know__s__not__eout,axiom,
% 0.20/0.46 ! [M2: secrecy_Secrets,A2: secrecy_specID] :
% 0.20/0.46 ( ~ ( member2138796287ecrets @ M2 @ ( specSecrets @ A2 ) )
% 0.20/0.46 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 => ( ( knowle233900195orrect @ A2 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 => ~ ( eout @ A2 @ ( secrecy_sE @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_know_s_not_eout
% 0.20/0.46 thf(fact_332_not__eout__eoutM,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( eout @ P @ E )
% 0.20/0.46 => ~ ( eoutM @ P @ M @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_eout_eoutM
% 0.20/0.46 thf(fact_333_eoutM__eout,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.20/0.46 ( ( eoutM @ P @ M @ E )
% 0.20/0.46 => ( eout @ P @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutM_eout
% 0.20/0.46 thf(fact_334_TBtheorem2b,axiom,
% 0.20/0.46 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( eoutM @ PQ @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ( eoutM @ P @ M @ E )
% 0.20/0.46 | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem2b
% 0.20/0.46 thf(fact_335_TBtheorem5b__notP2,axiom,
% 0.20/0.46 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.20/0.46 ( ~ ( eoutM @ Q @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.20/0.46 => ( ! [X3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.20/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5b_notP2
% 0.20/0.46 thf(fact_336_TBtheorem5b__notP1,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( eoutM @ P @ M @ E )
% 0.20/0.46 => ( ~ ( eoutM @ Q @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ M )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5b_notP1
% 0.20/0.46 thf(fact_337_eout__know__k,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,M2: secrecy_Keys] :
% 0.20/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 = ( ( eout @ C3 @ ( secrecy_kE @ M2 ) )
% 0.20/0.46 = ( ( member_Secrecy_Keys @ M2 @ ( specKeys @ C3 ) )
% 0.20/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eout_know_k
% 0.20/0.46 thf(fact_338_not__know__k__not__eout,axiom,
% 0.20/0.46 ! [M2: secrecy_Keys,A2: secrecy_specID] :
% 0.20/0.46 ( ~ ( member_Secrecy_Keys @ M2 @ ( specKeys @ A2 ) )
% 0.20/0.46 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 => ( ( knowle233900195orrect @ A2 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 => ~ ( eout @ A2 @ ( secrecy_kE @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % not_know_k_not_eout
% 0.20/0.46 thf(fact_339_eoutKnowCorrect__L1k,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,M2: secrecy_Keys] :
% 0.20/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 => ( ( eout @ C3 @ ( secrecy_kE @ M2 ) )
% 0.20/0.46 => ( ( member_Secrecy_Keys @ M2 @ ( specKeys @ C3 ) )
% 0.20/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutKnowCorrect_L1k
% 0.20/0.46 thf(fact_340_eout__know__nonKS__k,axiom,
% 0.20/0.46 ! [M2: secrecy_Keys,A2: secrecy_specID] :
% 0.20/0.46 ( ~ ( member_Secrecy_Keys @ M2 @ ( specKeys @ A2 ) )
% 0.20/0.46 => ( ( eout @ A2 @ ( secrecy_kE @ M2 ) )
% 0.20/0.46 => ( ( knowle233900195orrect @ A2 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.46 => ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eout_know_nonKS_k
% 0.20/0.46 thf(fact_341_eout__know__nonKS__s,axiom,
% 0.20/0.46 ! [M2: secrecy_Secrets,A2: secrecy_specID] :
% 0.20/0.46 ( ~ ( member2138796287ecrets @ M2 @ ( specSecrets @ A2 ) )
% 0.20/0.46 => ( ( eout @ A2 @ ( secrecy_sE @ M2 ) )
% 0.20/0.46 => ( ( knowle233900195orrect @ A2 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 => ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eout_know_nonKS_s
% 0.20/0.46 thf(fact_342_eoutKnowCorrect__L1s,axiom,
% 0.20/0.46 ! [C3: secrecy_specID,M2: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.46 => ( ( eout @ C3 @ ( secrecy_sE @ M2 ) )
% 0.20/0.46 => ( ( member2138796287ecrets @ M2 @ ( specSecrets @ C3 ) )
% 0.20/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutKnowCorrect_L1s
% 0.20/0.46 thf(fact_343_TBtheorem5b__PQ,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ( eoutM @ P @ M @ E )
% 0.20/0.46 | ( eoutM @ Q @ M @ E ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 0.20/0.46 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ M )
% 0.20/0.46 & ( exprChannel @ Ch3 @ E )
% 0.20/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5b_PQ
% 0.20/0.46 thf(fact_344_TBtheore54b__P,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.46 ( ( eoutM @ P @ M @ E )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch3 @ ( out @ Q ) )
% 0.20/0.46 & ( exprChannel @ Ch3 @ E )
% 0.20/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 0.20/0.46 & ( member1967978193chanID @ Ch3 @ M ) )
% 0.20/0.46 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheore54b_P
% 0.20/0.46 thf(fact_345_TBtheorem5a__PQ,axiom,
% 0.20/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.20/0.46 ( ( ( eout @ P @ E )
% 0.20/0.46 | ( eout @ Q @ E ) )
% 0.20/0.46 => ( ( ( subcomponents @ PQ )
% 0.20/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.46 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 0.20/0.46 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 0.20/0.46 & ( exprChannel @ Ch3 @ E )
% 0.20/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % TBtheorem5a_PQ
% 0.20/0.46 thf(fact_346_eout__def,axiom,
% 0.20/0.46 ( eout
% 0.20/0.46 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.20/0.46 ? [Ch2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 0.20/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eout_def
% 0.20/0.46 thf(fact_347_eoutM__def,axiom,
% 0.20/0.46 ( eoutM
% 0.20/0.46 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.20/0.46 ? [Ch2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 0.20/0.46 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.20/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutM_def
% 0.20/0.46 thf(fact_348_out__exprChannelSet__def,axiom,
% 0.20/0.46 ( out_exprChannelSet
% 0.20/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.20/0.46 ( ! [X2: secrecy_chanID] :
% 0.20/0.46 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 0.20/0.46 => ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 0.20/0.46 & ( exprChannel @ X2 @ E2 ) ) )
% 0.20/0.46 & ! [X2: secrecy_chanID] :
% 0.20/0.46 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 0.20/0.46 & ( member1967978193chanID @ X2 @ ( out @ SP ) ) )
% 0.20/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % out_exprChannelSet_def
% 0.20/0.47 thf(fact_349_out__exprChannelSingle__def,axiom,
% 0.20/0.47 ( out_ex985543062Single
% 0.20/0.47 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.20/0.47 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 0.20/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.20/0.47 & ! [X2: secrecy_chanID,T: nat] :
% 0.20/0.47 ( ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 0.20/0.47 & ( X2 != Ch2 ) )
% 0.20/0.47 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % out_exprChannelSingle_def
% 0.20/0.47 thf(fact_350_correctCompositionOut__prop1,axiom,
% 0.20/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.20/0.47 ( ( ( subcomponents @ PQ )
% 0.20/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.47 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 0.20/0.47 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 0.20/0.47 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % correctCompositionOut_prop1
% 0.20/0.47 thf(fact_351_TBtheorem45a__P,axiom,
% 0.20/0.47 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.20/0.47 ( ( eout @ P @ E )
% 0.20/0.47 => ( ( ( subcomponents @ PQ )
% 0.20/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.20/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.20/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.20/0.47 ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 0.20/0.47 & ( exprChannel @ Ch3 @ E )
% 0.20/0.47 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.20/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % TBtheorem45a_P
% 0.20/0.47 thf(fact_352_adv__not__know2,axiom,
% 0.20/0.47 ! [P: secrecy_specID,A2: secrecy_specID,M2: secrecy_Secrets] :
% 0.20/0.47 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A2 ) )
% 0.20/0.47 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 0.20/0.47 => ~ ( eout @ P @ ( secrecy_sE @ M2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % adv_not_know2
% 0.20/0.47 thf(fact_353_adv__not__know1,axiom,
% 0.20/0.47 ! [P: secrecy_specID,A2: secrecy_specID,M2: secrecy_Keys] :
% 0.20/0.47 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A2 ) )
% 0.20/0.47 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 0.20/0.47 => ~ ( eout @ P @ ( secrecy_kE @ M2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % adv_not_know1
% 0.20/0.47 thf(fact_354_correctCompositionKeys__subcomp1,axiom,
% 0.20/0.47 ! [C3: secrecy_specID,X: secrecy_specID,Xb: secrecy_Keys] :
% 0.20/0.47 ( ( correc17873122onKeys @ C3 )
% 0.20/0.47 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.20/0.47 => ( ( member_Secrecy_Keys @ Xb @ ( specKeys @ C3 ) )
% 0.20/0.47 => ? [X3: secrecy_specID] :
% 0.20/0.47 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.20/0.47 & ( member_Secrecy_Keys @ Xb @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % correctCompositionKeys_subcomp1
% 0.20/0.47
% 0.20/0.47 % Conjectures (1)
% 0.20/0.47 thf(conj_0,conjecture,
% 0.20/0.47 ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 3.15/1.86 ---- Embedded in THF ---
% 3.15/1.86 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.15/1.86 %%% Generated on Tue Feb 24 08:26:08 EST 2026
% 3.15/1.86 %%% using '$$dhol' embedding, version 1.3.0.
% 3.15/1.86 %%% Logic specification used:
% 3.15/1.86 %%% thf(spec, logic, $$dhol).
% 3.15/1.86
% 3.15/1.86 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2DTF18108.p
% See solution above
% 3.15/1.86 ------------------------
% 3.15/1.89 ---- Cleaned THF ---
% 3.15/1.89 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 3.15/1.89 list_S529945141ession: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 3.15/1.89 set_Secrecy_Secrets: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 3.15/1.89 set_Secrecy_specID: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.15/1.89 set_Secrecy_chanID: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 3.15/1.89 set_Secrecy_Keys: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 3.15/1.89 set_Secrecy_KS: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Secrecy____types__OExpression,type,
% 3.15/1.89 secrecy_Expression: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 3.15/1.89 secrecy_Secrets: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Secrecy____types__OspecID,type,
% 3.15/1.89 secrecy_specID: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Secrecy____types__OchanID,type,
% 3.15/1.89 secrecy_chanID: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Secrecy____types__OKeys,type,
% 3.15/1.89 secrecy_Keys: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Secrecy____types__OKS,type,
% 3.15/1.89 secrecy_KS: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(ty_n_t__Nat__Onat,type,
% 3.15/1.89 nat: $tType ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 3.15/1.89 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 3.15/1.89 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 3.15/1.89 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 3.15/1.89 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 3.15/1.89 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 3.15/1.89 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.15/1.89 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 3.15/1.89 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 3.15/1.89 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 3.15/1.89 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 3.15/1.89 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 3.15/1.89 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 3.15/1.89 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 3.15/1.89 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 3.15/1.89 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 3.15/1.89 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 3.15/1.89 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.15/1.89 bot_bo443197316chanID: set_Secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 3.15/1.89 bot_bo1785112429specID: set_Secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.15/1.89 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 3.15/1.89 correctCompositionKS: secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OcorrectCompositionKeys,type,
% 3.15/1.89 correc17873122onKeys: secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_Oeout,type,
% 3.15/1.89 eout: secrecy_specID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OeoutM,type,
% 3.15/1.89 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OexprChannel,type,
% 3.15/1.89 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_Oine,type,
% 3.15/1.89 ine: secrecy_specID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OineM,type,
% 3.15/1.89 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 3.15/1.89 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 3.15/1.89 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 3.15/1.89 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 3.15/1.89 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 3.15/1.89 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OspecKeys,type,
% 3.15/1.89 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 3.15/1.89 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy_OspecSecrets,type,
% 3.15/1.89 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 3.15/1.89 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 3.15/1.89 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 3.15/1.89 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 3.15/1.89 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 3.15/1.89 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 3.15/1.89 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 3.15/1.89 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 3.15/1.89 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 3.15/1.89 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 3.15/1.89 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 3.15/1.89 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 3.15/1.89 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 3.15/1.89 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 3.15/1.89 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 3.15/1.89 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 3.15/1.89 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 3.15/1.89 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 3.15/1.89 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 3.15/1.89 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 3.15/1.89 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 3.15/1.89 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 3.15/1.89 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 3.15/1.89 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 3.15/1.89 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_OcorrectCompositionIn,type,
% 3.15/1.89 correctCompositionIn: secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 3.15/1.89 correc965049635ionLoc: secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_OcorrectCompositionOut,type,
% 3.15/1.89 correc990227761ionOut: secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_OinStream,type,
% 3.15/1.89 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_Oins,type,
% 3.15/1.89 ins: secrecy_specID > set_Secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_Oloc,type,
% 3.15/1.89 loc: secrecy_specID > set_Secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_OlocStream,type,
% 3.15/1.89 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_Oout,type,
% 3.15/1.89 out: secrecy_specID > set_Secrecy_chanID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_inout_Osubcomponents,type,
% 3.15/1.89 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 3.15/1.89 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 3.15/1.89 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 3.15/1.89 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 3.15/1.89 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 3.15/1.89 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 3.15/1.89
% 3.15/1.89 thf(sy_v_P,type,
% 3.15/1.89 p: secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_v_PQ,type,
% 3.15/1.89 pq: secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_v_Q,type,
% 3.15/1.89 q: secrecy_specID ).
% 3.15/1.89
% 3.15/1.89 thf(sy_v_key____,type,
% 3.15/1.89 key: secrecy_Keys ).
% 3.15/1.89
% 3.15/1.89 thf(sy_v_m,type,
% 3.15/1.89 m: secrecy_KS ).
% 3.15/1.89
% 3.15/1.89 thf(fact_0_cCompKS,axiom,
% 3.15/1.89 correctCompositionKS @ pq ).
% 3.15/1.89
% 3.15/1.89 thf(fact_1_notKSQ,axiom,
% 3.15/1.89 ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ q ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_2_notKSP,axiom,
% 3.15/1.89 ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ p ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_3_subPQ,axiom,
% 3.15/1.89 ( ( subcomponents @ pq )
% 3.15/1.89 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_4_cCompI,axiom,
% 3.15/1.89 correctCompositionIn @ pq ).
% 3.15/1.89
% 3.15/1.89 thf(fact_5_assms_I3_J,axiom,
% 3.15/1.89 knowle945212990e_know @ p @ m ).
% 3.15/1.89
% 3.15/1.89 thf(fact_6_a1,axiom,
% 3.15/1.89 ( m
% 3.15/1.89 = ( secrecy_kKS @ key ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_7_correctCompositionKS__PQ,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.15/1.89 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_8_correctCompositionKS__neg1,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_9_correctCompositionKS__negP,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_10_correctCompositionKS__negQ,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_11_singletonI,axiom,
% 3.15/1.89 ! [A: secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_12_singletonI,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets] : ( member2138796287ecrets @ A @ ( insert565337510ecrets @ A @ bot_bo1124690338ecrets ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_13_singletonI,axiom,
% 3.15/1.89 ! [A: secrecy_Keys] : ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_14_singletonI,axiom,
% 3.15/1.89 ! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_15_singletonI,axiom,
% 3.15/1.89 ! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_16_KS_Oinject_I1_J,axiom,
% 3.15/1.89 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.15/1.89 ( ( ( secrecy_kKS @ X1 )
% 3.15/1.89 = ( secrecy_kKS @ Y1 ) )
% 3.15/1.89 = ( X1 = Y1 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_17_insertCI,axiom,
% 3.15/1.89 ! [A: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 3.15/1.89 ( ( ~ ( member_Secrecy_KS @ A @ B )
% 3.15/1.89 => ( A = B2 ) )
% 3.15/1.89 => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_18_insertCI,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 3.15/1.89 ( ( ~ ( member1967978193chanID @ A @ B )
% 3.15/1.89 => ( A = B2 ) )
% 3.15/1.89 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_19_insertCI,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 3.15/1.89 ( ( ~ ( member740727610specID @ A @ B )
% 3.15/1.89 => ( A = B2 ) )
% 3.15/1.89 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_20_insertCI,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 3.15/1.89 ( ( ~ ( member2138796287ecrets @ A @ B )
% 3.15/1.89 => ( A = B2 ) )
% 3.15/1.89 => ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_21_insertCI,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 3.15/1.89 ( ( ~ ( member_Secrecy_Keys @ A @ B )
% 3.15/1.89 => ( A = B2 ) )
% 3.15/1.89 => ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_22_insert__iff,axiom,
% 3.15/1.89 ! [A: secrecy_KS,B2: secrecy_KS,A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ A2 ) )
% 3.15/1.89 = ( ( A = B2 )
% 3.15/1.89 | ( member_Secrecy_KS @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_23_insert__iff,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 3.15/1.89 = ( ( A = B2 )
% 3.15/1.89 | ( member1967978193chanID @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_24_insert__iff,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 3.15/1.89 = ( ( A = B2 )
% 3.15/1.89 | ( member740727610specID @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_25_insert__iff,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,B2: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ A2 ) )
% 3.15/1.89 = ( ( A = B2 )
% 3.15/1.89 | ( member2138796287ecrets @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_26_insert__iff,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,B2: secrecy_Keys,A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ A2 ) )
% 3.15/1.89 = ( ( A = B2 )
% 3.15/1.89 | ( member_Secrecy_Keys @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_27_insert__absorb2,axiom,
% 3.15/1.89 ! [X: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A2 ) )
% 3.15/1.89 = ( insert1671894227specID @ X @ A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_28_insert__absorb2,axiom,
% 3.15/1.89 ! [X: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A2 ) )
% 3.15/1.89 = ( insert751661162chanID @ X @ A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_29_empty__iff,axiom,
% 3.15/1.89 ! [C: secrecy_KS] :
% 3.15/1.89 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_30_empty__iff,axiom,
% 3.15/1.89 ! [C: secrecy_Secrets] :
% 3.15/1.89 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_31_empty__iff,axiom,
% 3.15/1.89 ! [C: secrecy_Keys] :
% 3.15/1.89 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_32_empty__iff,axiom,
% 3.15/1.89 ! [C: secrecy_specID] :
% 3.15/1.89 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_33_empty__iff,axiom,
% 3.15/1.89 ! [C: secrecy_chanID] :
% 3.15/1.89 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_34_all__not__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( ! [X2: secrecy_KS] :
% 3.15/1.89 ~ ( member_Secrecy_KS @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 = bot_bo1943466239ecy_KS ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_35_all__not__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( ! [X2: secrecy_Secrets] :
% 3.15/1.89 ~ ( member2138796287ecrets @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 = bot_bo1124690338ecrets ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_36_all__not__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( ! [X2: secrecy_Keys] :
% 3.15/1.89 ~ ( member_Secrecy_Keys @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 = bot_bo701486667y_Keys ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_37_all__not__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( ! [X2: secrecy_specID] :
% 3.15/1.89 ~ ( member740727610specID @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 = bot_bo1785112429specID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_38_all__not__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ! [X2: secrecy_chanID] :
% 3.15/1.89 ~ ( member1967978193chanID @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 = bot_bo443197316chanID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_39_Collect__empty__eq,axiom,
% 3.15/1.89 ! [P: secrecy_specID > $o] :
% 3.15/1.89 ( ( ( collec1545797240specID @ P )
% 3.15/1.89 = bot_bo1785112429specID )
% 3.15/1.89 = ( ! [X2: secrecy_specID] :
% 3.15/1.89 ~ ( P @ X2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_40_Collect__empty__eq,axiom,
% 3.15/1.89 ! [P: secrecy_chanID > $o] :
% 3.15/1.89 ( ( ( collec625564175chanID @ P )
% 3.15/1.89 = bot_bo443197316chanID )
% 3.15/1.89 = ( ! [X2: secrecy_chanID] :
% 3.15/1.89 ~ ( P @ X2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_41_empty__Collect__eq,axiom,
% 3.15/1.89 ! [P: secrecy_specID > $o] :
% 3.15/1.89 ( ( bot_bo1785112429specID
% 3.15/1.89 = ( collec1545797240specID @ P ) )
% 3.15/1.89 = ( ! [X2: secrecy_specID] :
% 3.15/1.89 ~ ( P @ X2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_42_empty__Collect__eq,axiom,
% 3.15/1.89 ! [P: secrecy_chanID > $o] :
% 3.15/1.89 ( ( bot_bo443197316chanID
% 3.15/1.89 = ( collec625564175chanID @ P ) )
% 3.15/1.89 = ( ! [X2: secrecy_chanID] :
% 3.15/1.89 ~ ( P @ X2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_43_singletonD,axiom,
% 3.15/1.89 ! [B2: secrecy_KS,A: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
% 3.15/1.89 => ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_44_singletonD,axiom,
% 3.15/1.89 ! [B2: secrecy_Secrets,A: secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A @ bot_bo1124690338ecrets ) )
% 3.15/1.89 => ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_45_singletonD,axiom,
% 3.15/1.89 ! [B2: secrecy_Keys,A: secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) )
% 3.15/1.89 => ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_46_singletonD,axiom,
% 3.15/1.89 ! [B2: secrecy_specID,A: secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 3.15/1.89 => ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_47_singletonD,axiom,
% 3.15/1.89 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 3.15/1.89 => ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_48_bot__set__def,axiom,
% 3.15/1.89 ( bot_bo1785112429specID
% 3.15/1.89 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_49_bot__set__def,axiom,
% 3.15/1.89 ( bot_bo443197316chanID
% 3.15/1.89 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_50_ex__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( ? [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 != bot_bo1943466239ecy_KS ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_51_ex__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( ? [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 != bot_bo1124690338ecrets ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_52_ex__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( ? [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 != bot_bo701486667y_Keys ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_53_ex__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( ? [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 != bot_bo1785112429specID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_54_ex__in__conv,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ? [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 3.15/1.89 = ( A2 != bot_bo443197316chanID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_55_equals0I,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS] :
% 3.15/1.89 ( ! [Y: secrecy_KS] :
% 3.15/1.89 ~ ( member_Secrecy_KS @ Y @ A2 )
% 3.15/1.89 => ( A2 = bot_bo1943466239ecy_KS ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_56_equals0I,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ! [Y: secrecy_Secrets] :
% 3.15/1.89 ~ ( member2138796287ecrets @ Y @ A2 )
% 3.15/1.89 => ( A2 = bot_bo1124690338ecrets ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_57_equals0I,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ! [Y: secrecy_Keys] :
% 3.15/1.89 ~ ( member_Secrecy_Keys @ Y @ A2 )
% 3.15/1.89 => ( A2 = bot_bo701486667y_Keys ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_58_equals0I,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID] :
% 3.15/1.89 ( ! [Y: secrecy_specID] :
% 3.15/1.89 ~ ( member740727610specID @ Y @ A2 )
% 3.15/1.89 => ( A2 = bot_bo1785112429specID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_59_equals0I,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ! [Y: secrecy_chanID] :
% 3.15/1.89 ~ ( member1967978193chanID @ Y @ A2 )
% 3.15/1.89 => ( A2 = bot_bo443197316chanID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_60_equals0D,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,A: secrecy_KS] :
% 3.15/1.89 ( ( A2 = bot_bo1943466239ecy_KS )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ A @ A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_61_equals0D,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Secrets,A: secrecy_Secrets] :
% 3.15/1.89 ( ( A2 = bot_bo1124690338ecrets )
% 3.15/1.89 => ~ ( member2138796287ecrets @ A @ A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_62_equals0D,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Keys,A: secrecy_Keys] :
% 3.15/1.89 ( ( A2 = bot_bo701486667y_Keys )
% 3.15/1.89 => ~ ( member_Secrecy_Keys @ A @ A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_63_equals0D,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID,A: secrecy_specID] :
% 3.15/1.89 ( ( A2 = bot_bo1785112429specID )
% 3.15/1.89 => ~ ( member740727610specID @ A @ A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_64_equals0D,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,A: secrecy_chanID] :
% 3.15/1.89 ( ( A2 = bot_bo443197316chanID )
% 3.15/1.89 => ~ ( member1967978193chanID @ A @ A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_65_emptyE,axiom,
% 3.15/1.89 ! [A: secrecy_KS] :
% 3.15/1.89 ~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_66_emptyE,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets] :
% 3.15/1.89 ~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_67_emptyE,axiom,
% 3.15/1.89 ! [A: secrecy_Keys] :
% 3.15/1.89 ~ ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_68_emptyE,axiom,
% 3.15/1.89 ! [A: secrecy_specID] :
% 3.15/1.89 ~ ( member740727610specID @ A @ bot_bo1785112429specID ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_69_emptyE,axiom,
% 3.15/1.89 ! [A: secrecy_chanID] :
% 3.15/1.89 ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_70_mk__disjoint__insert,axiom,
% 3.15/1.89 ! [A: secrecy_KS,A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ A @ A2 )
% 3.15/1.89 => ? [B3: set_Secrecy_KS] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert_Secrecy_KS @ A @ B3 ) )
% 3.15/1.89 & ~ ( member_Secrecy_KS @ A @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_71_mk__disjoint__insert,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ A @ A2 )
% 3.15/1.89 => ? [B3: set_Secrecy_chanID] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert751661162chanID @ A @ B3 ) )
% 3.15/1.89 & ~ ( member1967978193chanID @ A @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_72_mk__disjoint__insert,axiom,
% 3.15/1.89 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ A @ A2 )
% 3.15/1.89 => ? [B3: set_Secrecy_specID] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert1671894227specID @ A @ B3 ) )
% 3.15/1.89 & ~ ( member740727610specID @ A @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_73_mk__disjoint__insert,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ A @ A2 )
% 3.15/1.89 => ? [B3: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert565337510ecrets @ A @ B3 ) )
% 3.15/1.89 & ~ ( member2138796287ecrets @ A @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_74_mk__disjoint__insert,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ A @ A2 )
% 3.15/1.89 => ? [B3: set_Secrecy_Keys] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert_Secrecy_Keys @ A @ B3 ) )
% 3.15/1.89 & ~ ( member_Secrecy_Keys @ A @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_75_insert__commute,axiom,
% 3.15/1.89 ! [X: secrecy_specID,Y2: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y2 @ A2 ) )
% 3.15/1.89 = ( insert1671894227specID @ Y2 @ ( insert1671894227specID @ X @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_76_insert__commute,axiom,
% 3.15/1.89 ! [X: secrecy_chanID,Y2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y2 @ A2 ) )
% 3.15/1.89 = ( insert751661162chanID @ Y2 @ ( insert751661162chanID @ X @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_77_insert__eq__iff,axiom,
% 3.15/1.89 ! [A: secrecy_KS,A2: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ~ ( member_Secrecy_KS @ A @ A2 )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 3.15/1.89 => ( ( ( insert_Secrecy_KS @ A @ A2 )
% 3.15/1.89 = ( insert_Secrecy_KS @ B2 @ B ) )
% 3.15/1.89 = ( ( ( A = B2 )
% 3.15/1.89 => ( A2 = B ) )
% 3.15/1.89 & ( ( A != B2 )
% 3.15/1.89 => ? [C2: set_Secrecy_KS] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 3.15/1.89 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert_Secrecy_KS @ A @ C2 ) )
% 3.15/1.89 & ~ ( member_Secrecy_KS @ A @ C2 ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_78_insert__eq__iff,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( member1967978193chanID @ A @ A2 )
% 3.15/1.89 => ( ~ ( member1967978193chanID @ B2 @ B )
% 3.15/1.89 => ( ( ( insert751661162chanID @ A @ A2 )
% 3.15/1.89 = ( insert751661162chanID @ B2 @ B ) )
% 3.15/1.89 = ( ( ( A = B2 )
% 3.15/1.89 => ( A2 = B ) )
% 3.15/1.89 & ( ( A != B2 )
% 3.15/1.89 => ? [C2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert751661162chanID @ B2 @ C2 ) )
% 3.15/1.89 & ~ ( member1967978193chanID @ B2 @ C2 )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert751661162chanID @ A @ C2 ) )
% 3.15/1.89 & ~ ( member1967978193chanID @ A @ C2 ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_79_insert__eq__iff,axiom,
% 3.15/1.89 ! [A: secrecy_specID,A2: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ~ ( member740727610specID @ A @ A2 )
% 3.15/1.89 => ( ~ ( member740727610specID @ B2 @ B )
% 3.15/1.89 => ( ( ( insert1671894227specID @ A @ A2 )
% 3.15/1.89 = ( insert1671894227specID @ B2 @ B ) )
% 3.15/1.89 = ( ( ( A = B2 )
% 3.15/1.89 => ( A2 = B ) )
% 3.15/1.89 & ( ( A != B2 )
% 3.15/1.89 => ? [C2: set_Secrecy_specID] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert1671894227specID @ B2 @ C2 ) )
% 3.15/1.89 & ~ ( member740727610specID @ B2 @ C2 )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert1671894227specID @ A @ C2 ) )
% 3.15/1.89 & ~ ( member740727610specID @ A @ C2 ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_80_insert__eq__iff,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,A2: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.15/1.89 ( ~ ( member2138796287ecrets @ A @ A2 )
% 3.15/1.89 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 3.15/1.89 => ( ( ( insert565337510ecrets @ A @ A2 )
% 3.15/1.89 = ( insert565337510ecrets @ B2 @ B ) )
% 3.15/1.89 = ( ( ( A = B2 )
% 3.15/1.89 => ( A2 = B ) )
% 3.15/1.89 & ( ( A != B2 )
% 3.15/1.89 => ? [C2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert565337510ecrets @ B2 @ C2 ) )
% 3.15/1.89 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert565337510ecrets @ A @ C2 ) )
% 3.15/1.89 & ~ ( member2138796287ecrets @ A @ C2 ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_81_insert__eq__iff,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,A2: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 3.15/1.89 ( ~ ( member_Secrecy_Keys @ A @ A2 )
% 3.15/1.89 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 3.15/1.89 => ( ( ( insert_Secrecy_Keys @ A @ A2 )
% 3.15/1.89 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 3.15/1.89 = ( ( ( A = B2 )
% 3.15/1.89 => ( A2 = B ) )
% 3.15/1.89 & ( ( A != B2 )
% 3.15/1.89 => ? [C2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 3.15/1.89 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert_Secrecy_Keys @ A @ C2 ) )
% 3.15/1.89 & ~ ( member_Secrecy_Keys @ A @ C2 ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_82_insert__absorb,axiom,
% 3.15/1.89 ! [A: secrecy_KS,A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ A @ A2 )
% 3.15/1.89 => ( ( insert_Secrecy_KS @ A @ A2 )
% 3.15/1.89 = A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_83_insert__absorb,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ A @ A2 )
% 3.15/1.89 => ( ( insert751661162chanID @ A @ A2 )
% 3.15/1.89 = A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_84_insert__absorb,axiom,
% 3.15/1.89 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ A @ A2 )
% 3.15/1.89 => ( ( insert1671894227specID @ A @ A2 )
% 3.15/1.89 = A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_85_insert__absorb,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ A @ A2 )
% 3.15/1.89 => ( ( insert565337510ecrets @ A @ A2 )
% 3.15/1.89 = A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_86_insert__absorb,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ A @ A2 )
% 3.15/1.89 => ( ( insert_Secrecy_Keys @ A @ A2 )
% 3.15/1.89 = A2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_87_insert__ident,axiom,
% 3.15/1.89 ! [X: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ~ ( member_Secrecy_KS @ X @ A2 )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ X @ B )
% 3.15/1.89 => ( ( ( insert_Secrecy_KS @ X @ A2 )
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ B ) )
% 3.15/1.89 = ( A2 = B ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_88_insert__ident,axiom,
% 3.15/1.89 ! [X: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( member1967978193chanID @ X @ A2 )
% 3.15/1.89 => ( ~ ( member1967978193chanID @ X @ B )
% 3.15/1.89 => ( ( ( insert751661162chanID @ X @ A2 )
% 3.15/1.89 = ( insert751661162chanID @ X @ B ) )
% 3.15/1.89 = ( A2 = B ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_89_insert__ident,axiom,
% 3.15/1.89 ! [X: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ~ ( member740727610specID @ X @ A2 )
% 3.15/1.89 => ( ~ ( member740727610specID @ X @ B )
% 3.15/1.89 => ( ( ( insert1671894227specID @ X @ A2 )
% 3.15/1.89 = ( insert1671894227specID @ X @ B ) )
% 3.15/1.89 = ( A2 = B ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_90_insert__ident,axiom,
% 3.15/1.89 ! [X: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.15/1.89 ( ~ ( member2138796287ecrets @ X @ A2 )
% 3.15/1.89 => ( ~ ( member2138796287ecrets @ X @ B )
% 3.15/1.89 => ( ( ( insert565337510ecrets @ X @ A2 )
% 3.15/1.89 = ( insert565337510ecrets @ X @ B ) )
% 3.15/1.89 = ( A2 = B ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_91_insert__ident,axiom,
% 3.15/1.89 ! [X: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.15/1.89 ( ~ ( member_Secrecy_Keys @ X @ A2 )
% 3.15/1.89 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 3.15/1.89 => ( ( ( insert_Secrecy_Keys @ X @ A2 )
% 3.15/1.89 = ( insert_Secrecy_Keys @ X @ B ) )
% 3.15/1.89 = ( A2 = B ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_92_Set_Oset__insert,axiom,
% 3.15/1.89 ! [X: secrecy_KS,A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X @ A2 )
% 3.15/1.89 => ~ ! [B3: set_Secrecy_KS] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ B3 ) )
% 3.15/1.89 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_93_Set_Oset__insert,axiom,
% 3.15/1.89 ! [X: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X @ A2 )
% 3.15/1.89 => ~ ! [B3: set_Secrecy_chanID] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert751661162chanID @ X @ B3 ) )
% 3.15/1.89 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_94_Set_Oset__insert,axiom,
% 3.15/1.89 ! [X: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ X @ A2 )
% 3.15/1.89 => ~ ! [B3: set_Secrecy_specID] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert1671894227specID @ X @ B3 ) )
% 3.15/1.89 => ( member740727610specID @ X @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_95_Set_Oset__insert,axiom,
% 3.15/1.89 ! [X: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ X @ A2 )
% 3.15/1.89 => ~ ! [B3: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert565337510ecrets @ X @ B3 ) )
% 3.15/1.89 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_96_Set_Oset__insert,axiom,
% 3.15/1.89 ! [X: secrecy_Keys,A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ X @ A2 )
% 3.15/1.89 => ~ ! [B3: set_Secrecy_Keys] :
% 3.15/1.89 ( ( A2
% 3.15/1.89 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 3.15/1.89 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_97_insertI2,axiom,
% 3.15/1.89 ! [A: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ A @ B )
% 3.15/1.89 => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_98_insertI2,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ A @ B )
% 3.15/1.89 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_99_insertI2,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ A @ B )
% 3.15/1.89 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_100_insertI2,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ A @ B )
% 3.15/1.89 => ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_101_insertI2,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ A @ B )
% 3.15/1.89 => ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_102_insertI1,axiom,
% 3.15/1.89 ! [A: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ B ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_103_insertI1,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_104_insertI1,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_105_insertI1,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A @ ( insert565337510ecrets @ A @ B ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_106_insertI1,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ A @ B ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_107_insertE,axiom,
% 3.15/1.89 ! [A: secrecy_KS,B2: secrecy_KS,A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B2 @ A2 ) )
% 3.15/1.89 => ( ( A != B2 )
% 3.15/1.89 => ( member_Secrecy_KS @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_108_insertE,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 3.15/1.89 => ( ( A != B2 )
% 3.15/1.89 => ( member1967978193chanID @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_109_insertE,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 3.15/1.89 => ( ( A != B2 )
% 3.15/1.89 => ( member740727610specID @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_110_insertE,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,B2: secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ A @ ( insert565337510ecrets @ B2 @ A2 ) )
% 3.15/1.89 => ( ( A != B2 )
% 3.15/1.89 => ( member2138796287ecrets @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_111_insertE,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,B2: secrecy_Keys,A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ A @ ( insert_Secrecy_Keys @ B2 @ A2 ) )
% 3.15/1.89 => ( ( A != B2 )
% 3.15/1.89 => ( member_Secrecy_Keys @ A @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_112_singleton__inject,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B2: secrecy_specID] :
% 3.15/1.89 ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
% 3.15/1.89 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 3.15/1.89 => ( A = B2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_113_singleton__inject,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B2: secrecy_chanID] :
% 3.15/1.89 ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
% 3.15/1.89 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 3.15/1.89 => ( A = B2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_114_insert__not__empty,axiom,
% 3.15/1.89 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( insert1671894227specID @ A @ A2 )
% 3.15/1.89 != bot_bo1785112429specID ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_115_insert__not__empty,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( insert751661162chanID @ A @ A2 )
% 3.15/1.89 != bot_bo443197316chanID ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_116_doubleton__eq__iff,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 3.15/1.89 ( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 3.15/1.89 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 3.15/1.89 = ( ( ( A = C )
% 3.15/1.89 & ( B2 = D ) )
% 3.15/1.89 | ( ( A = D )
% 3.15/1.89 & ( B2 = C ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_117_doubleton__eq__iff,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 3.15/1.89 ( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 3.15/1.89 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 3.15/1.89 = ( ( ( A = C )
% 3.15/1.89 & ( B2 = D ) )
% 3.15/1.89 | ( ( A = D )
% 3.15/1.89 & ( B2 = C ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_118_singleton__iff,axiom,
% 3.15/1.89 ! [B2: secrecy_KS,A: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
% 3.15/1.89 = ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_119_singleton__iff,axiom,
% 3.15/1.89 ! [B2: secrecy_Secrets,A: secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A @ bot_bo1124690338ecrets ) )
% 3.15/1.89 = ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_120_singleton__iff,axiom,
% 3.15/1.89 ! [B2: secrecy_Keys,A: secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) )
% 3.15/1.89 = ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_121_singleton__iff,axiom,
% 3.15/1.89 ! [B2: secrecy_specID,A: secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 3.15/1.89 = ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_122_singleton__iff,axiom,
% 3.15/1.89 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 3.15/1.89 = ( B2 = A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_123_the__elem__eq,axiom,
% 3.15/1.89 ! [X: secrecy_specID] :
% 3.15/1.89 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_124_the__elem__eq,axiom,
% 3.15/1.89 ! [X: secrecy_chanID] :
% 3.15/1.89 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_125_is__singletonI,axiom,
% 3.15/1.89 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_126_is__singletonI,axiom,
% 3.15/1.89 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_127_a11,axiom,
% 3.15/1.89 ine @ p @ ( secrecy_kE @ key ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_128_TBtheorem3b,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ~ ( ineM @ P @ M @ E )
% 3.15/1.89 => ( ~ ( ineM @ Q @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_129_mem__Collect__eq,axiom,
% 3.15/1.89 ! [A: secrecy_KS,P: secrecy_KS > $o] :
% 3.15/1.89 ( ( member_Secrecy_KS @ A @ ( collect_Secrecy_KS @ P ) )
% 3.15/1.89 = ( P @ A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_130_mem__Collect__eq,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,P: secrecy_chanID > $o] :
% 3.15/1.89 ( ( member1967978193chanID @ A @ ( collec625564175chanID @ P ) )
% 3.15/1.89 = ( P @ A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_131_mem__Collect__eq,axiom,
% 3.15/1.89 ! [A: secrecy_specID,P: secrecy_specID > $o] :
% 3.15/1.89 ( ( member740727610specID @ A @ ( collec1545797240specID @ P ) )
% 3.15/1.89 = ( P @ A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_132_mem__Collect__eq,axiom,
% 3.15/1.89 ! [A: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 3.15/1.89 ( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ P ) )
% 3.15/1.89 = ( P @ A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_133_mem__Collect__eq,axiom,
% 3.15/1.89 ! [A: secrecy_Keys,P: secrecy_Keys > $o] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ A @ ( collect_Secrecy_Keys @ P ) )
% 3.15/1.89 = ( P @ A ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_134_Collect__mem__eq,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( collect_Secrecy_KS
% 3.15/1.89 @ ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A2 ) )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_135_Collect__mem__eq,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( collec625564175chanID
% 3.15/1.89 @ ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_136_Collect__mem__eq,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( collec1545797240specID
% 3.15/1.89 @ ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_137_Collect__mem__eq,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( collec836099393ecrets
% 3.15/1.89 @ ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A2 ) )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_138_Collect__mem__eq,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( collect_Secrecy_Keys
% 3.15/1.89 @ ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A2 ) )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_139_TBtheorem1b,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( ineM @ PQ @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( ineM @ P @ M @ E )
% 3.15/1.89 | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_140_a11ext,axiom,
% 3.15/1.89 ( ( ine @ p @ ( secrecy_kE @ key ) )
% 3.15/1.89 | ( ine @ q @ ( secrecy_kE @ key ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_141_Set_Ois__empty__def,axiom,
% 3.15/1.89 ( is_emp1849217361specID
% 3.15/1.89 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_142_Set_Ois__empty__def,axiom,
% 3.15/1.89 ( is_emp928984296chanID
% 3.15/1.89 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_143_correctCompositionIn__prop1,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 3.15/1.89 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_144_correctCompositionIn__L2,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_145_is__singleton__def,axiom,
% 3.15/1.89 ( is_sin1501507247specID
% 3.15/1.89 = ( ^ [A3: set_Secrecy_specID] :
% 3.15/1.89 ? [X2: secrecy_specID] :
% 3.15/1.89 ( A3
% 3.15/1.89 = ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_146_is__singleton__def,axiom,
% 3.15/1.89 ( is_sin581274182chanID
% 3.15/1.89 = ( ^ [A3: set_Secrecy_chanID] :
% 3.15/1.89 ? [X2: secrecy_chanID] :
% 3.15/1.89 ( A3
% 3.15/1.89 = ( insert751661162chanID @ X2 @ bot_bo443197316chanID ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_147_Expression_Oinject_I1_J,axiom,
% 3.15/1.89 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.15/1.89 ( ( ( secrecy_kE @ X1 )
% 3.15/1.89 = ( secrecy_kE @ Y1 ) )
% 3.15/1.89 = ( X1 = Y1 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_148_not__ine__ineM,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( ine @ P @ E )
% 3.15/1.89 => ~ ( ineM @ P @ M @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_149_ineM__ine,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( ineM @ P @ M @ E )
% 3.15/1.89 => ( ine @ P @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_150_not__know__k__not__ine,axiom,
% 3.15/1.89 ! [A2: secrecy_specID,M2: secrecy_Keys] :
% 3.15/1.89 ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 => ~ ( ine @ A2 @ ( secrecy_kE @ M2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_151_is__singleton__the__elem,axiom,
% 3.15/1.89 ( is_sin1501507247specID
% 3.15/1.89 = ( ^ [A3: set_Secrecy_specID] :
% 3.15/1.89 ( A3
% 3.15/1.89 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_152_is__singleton__the__elem,axiom,
% 3.15/1.89 ( is_sin581274182chanID
% 3.15/1.89 = ( ^ [A3: set_Secrecy_chanID] :
% 3.15/1.89 ( A3
% 3.15/1.89 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_153_is__singletonI_H,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( A2 != bot_bo1943466239ecy_KS )
% 3.15/1.89 => ( ! [X3: secrecy_KS,Y: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X3 @ A2 )
% 3.15/1.89 => ( ( member_Secrecy_KS @ Y @ A2 )
% 3.15/1.89 => ( X3 = Y ) ) )
% 3.15/1.89 => ( is_sin1442426433ecy_KS @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_154_is__singletonI_H,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( A2 != bot_bo1124690338ecrets )
% 3.15/1.89 => ( ! [X3: secrecy_Secrets,Y: secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ X3 @ A2 )
% 3.15/1.89 => ( ( member2138796287ecrets @ Y @ A2 )
% 3.15/1.89 => ( X3 = Y ) ) )
% 3.15/1.89 => ( is_sin1002224330ecrets @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_155_is__singletonI_H,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( A2 != bot_bo701486667y_Keys )
% 3.15/1.89 => ( ! [X3: secrecy_Keys,Y: secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ X3 @ A2 )
% 3.15/1.89 => ( ( member_Secrecy_Keys @ Y @ A2 )
% 3.15/1.89 => ( X3 = Y ) ) )
% 3.15/1.89 => ( is_sin1096471309y_Keys @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_156_is__singletonI_H,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( A2 != bot_bo1785112429specID )
% 3.15/1.89 => ( ! [X3: secrecy_specID,Y: secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ X3 @ A2 )
% 3.15/1.89 => ( ( member740727610specID @ Y @ A2 )
% 3.15/1.89 => ( X3 = Y ) ) )
% 3.15/1.89 => ( is_sin1501507247specID @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_157_is__singletonI_H,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( A2 != bot_bo443197316chanID )
% 3.15/1.89 => ( ! [X3: secrecy_chanID,Y: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ A2 )
% 3.15/1.89 => ( ( member1967978193chanID @ Y @ A2 )
% 3.15/1.89 => ( X3 = Y ) ) )
% 3.15/1.89 => ( is_sin581274182chanID @ A2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_158_TBtheorem1a,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( ine @ PQ @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( ine @ P @ E )
% 3.15/1.89 | ( ine @ Q @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_159_TBtheorem3a,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ~ ( ine @ P @ E )
% 3.15/1.89 => ( ~ ( ine @ Q @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_160_is__singletonE,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( is_sin1501507247specID @ A2 )
% 3.15/1.89 => ~ ! [X3: secrecy_specID] :
% 3.15/1.89 ( A2
% 3.15/1.89 != ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_161_is__singletonE,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( is_sin581274182chanID @ A2 )
% 3.15/1.89 => ~ ! [X3: secrecy_chanID] :
% 3.15/1.89 ( A2
% 3.15/1.89 != ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_162_bot__empty__eq,axiom,
% 3.15/1.89 ( bot_bot_Secrecy_KS_o
% 3.15/1.89 = ( ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ bot_bo1943466239ecy_KS ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_163_bot__empty__eq,axiom,
% 3.15/1.89 ( bot_bo1909946299rets_o
% 3.15/1.89 = ( ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ bot_bo1124690338ecrets ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_164_bot__empty__eq,axiom,
% 3.15/1.89 ( bot_bo2072920570Keys_o
% 3.15/1.89 = ( ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ bot_bo701486667y_Keys ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_165_bot__empty__eq,axiom,
% 3.15/1.89 ( bot_bo1767780696ecID_o
% 3.15/1.89 = ( ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_166_bot__empty__eq,axiom,
% 3.15/1.89 ( bot_bo1012329985anID_o
% 3.15/1.89 = ( ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_167_Collect__empty__eq__bot,axiom,
% 3.15/1.89 ! [P: secrecy_specID > $o] :
% 3.15/1.89 ( ( ( collec1545797240specID @ P )
% 3.15/1.89 = bot_bo1785112429specID )
% 3.15/1.89 = ( P = bot_bo1767780696ecID_o ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_168_Collect__empty__eq__bot,axiom,
% 3.15/1.89 ! [P: secrecy_chanID > $o] :
% 3.15/1.89 ( ( ( collec625564175chanID @ P )
% 3.15/1.89 = bot_bo443197316chanID )
% 3.15/1.89 = ( P = bot_bo1012329985anID_o ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_169_TBlemma3b,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 3.15/1.89 ( ~ ( ineM @ P @ M @ E )
% 3.15/1.89 => ( ~ ( ineM @ Q @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ M )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.15/1.89 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_170_correctCompositionIn__L1,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_171_KS2Expression_Osimps_I1_J,axiom,
% 3.15/1.89 ! [M2: secrecy_Keys] :
% 3.15/1.89 ( ( secrec1016742679ession @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 = ( secrecy_kE @ M2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_172_TBtheorem4a__empty,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ( ine @ P @ E )
% 3.15/1.89 | ( ine @ Q @ E ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( ( loc @ PQ )
% 3.15/1.89 = bot_bo443197316chanID )
% 3.15/1.89 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_173_know_Osimps_I1_J,axiom,
% 3.15/1.89 ! [A2: secrecy_specID,M2: secrecy_Keys] :
% 3.15/1.89 ( ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 = ( ( ine @ A2 @ ( secrecy_kE @ M2 ) )
% 3.15/1.89 | ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_174_correctCompositionKS__exprChannel__k__P,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_175_LocalSecretsComposition__neg__loc__k,axiom,
% 3.15/1.89 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.15/1.89 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 3.15/1.89 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_176_LocalSecretsComposition1,axiom,
% 3.15/1.89 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_177_LocalSecretsComposition__exprChannel__k,axiom,
% 3.15/1.89 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.15/1.89 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 3.15/1.89 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_178_ine__def,axiom,
% 3.15/1.89 ( ine
% 3.15/1.89 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.15/1.89 ? [Ch2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 3.15/1.89 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_179_ine__ins__neg1,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M2: secrecy_Expression,X: secrecy_chanID] :
% 3.15/1.89 ( ~ ( ine @ P @ M2 )
% 3.15/1.89 => ( ( exprChannel @ X @ M2 )
% 3.15/1.89 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_180_ineM__L1,axiom,
% 3.15/1.89 ! [Ch: secrecy_chanID,M: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch @ M )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ E )
% 3.15/1.89 => ( ineM @ P @ M @ E ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_181_ineM__def,axiom,
% 3.15/1.89 ( ineM
% 3.15/1.89 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.15/1.89 ? [Ch2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 3.15/1.89 & ( member1967978193chanID @ Ch2 @ M3 )
% 3.15/1.89 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_182_correctCompositionInLoc__exprChannel,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M2: secrecy_Expression] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ M2 )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 3.15/1.89 => ~ ( exprChannel @ X3 @ M2 ) )
% 3.15/1.89 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_183_TBtheorem4a__PQ,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ( ine @ P @ E )
% 3.15/1.89 | ( ine @ Q @ E ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 3.15/1.89 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_184_TBtheorem4a__P,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( ine @ P @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_185_TBtheorem4b__PQ,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ( ineM @ P @ M @ E )
% 3.15/1.89 | ( ineM @ Q @ M @ E ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 3.15/1.89 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ M )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_186_TBtheorem4b__P,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( ineM @ P @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch3 @ ( ins @ Q ) )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ M ) )
% 3.15/1.89 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_187_correctCompositionKS__exprChannel__k__Qex,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ? [Ch4: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_188_correctCompositionKS__exprChannel__k__Pex,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ? [Ch4: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_189_correctCompositionKS__exprChannel__k__Q,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_190_TBtheorem4b__notP1,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ineM @ P @ M @ E )
% 3.15/1.89 => ( ~ ( ineM @ Q @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ M )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_191_TBtheorem4a__notP1,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ine @ P @ E )
% 3.15/1.89 => ( ~ ( ine @ Q @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_192_LocalSecretsComposition__neg1__k,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_193_LocalSecretsComposition__ine2__k,axiom,
% 3.15/1.89 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.15/1.89 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_194_LocalSecretsComposition__ine1__k,axiom,
% 3.15/1.89 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.15/1.89 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_195_TBtheorem4b__notPQ,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.15/1.89 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetP )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_196_TBtheorem4b__notP2,axiom,
% 3.15/1.89 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( ineM @ Q @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSet )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_197_ine__exprChannelSingle__Set,axiom,
% 3.15/1.89 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 3.15/1.89 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_198_ine__exprChannelSet__Single,axiom,
% 3.15/1.89 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 3.15/1.89 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_199_ine__exprChannelSet__def,axiom,
% 3.15/1.89 ( ine_exprChannelSet
% 3.15/1.89 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.15/1.89 ( ! [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 3.15/1.89 => ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 3.15/1.89 & ( exprChannel @ X2 @ E2 ) ) )
% 3.15/1.89 & ! [X2: secrecy_chanID] :
% 3.15/1.89 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 3.15/1.89 & ( member1967978193chanID @ X2 @ ( ins @ SP ) ) )
% 3.15/1.89 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_200_ine__empty__exprChannelSet,axiom,
% 3.15/1.89 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.15/1.89 => ( ( ChSet = bot_bo443197316chanID )
% 3.15/1.89 => ~ ( ine @ P @ E ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_201_ine__nonempty__exprChannelSet,axiom,
% 3.15/1.89 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.15/1.89 => ( ( ChSet != bot_bo443197316chanID )
% 3.15/1.89 => ( ine @ P @ E ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_202_ine__exprChannelSingle__def,axiom,
% 3.15/1.89 ( ine_ex1303305700Single
% 3.15/1.89 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 3.15/1.89 & ( exprChannel @ Ch2 @ E2 )
% 3.15/1.89 & ! [X2: secrecy_chanID,T: nat] :
% 3.15/1.89 ( ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 3.15/1.89 & ( X2 != Ch2 ) )
% 3.15/1.89 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_203_TBtheorem4a__notP2,axiom,
% 3.15/1.89 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( ine @ Q @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSet )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_204_TBtheorem4a__notPQ,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.15/1.89 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetP )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_205_subcomponents__loc,axiom,
% 3.15/1.89 ! [X: secrecy_specID] :
% 3.15/1.89 ( ( correc965049635ionLoc @ X )
% 3.15/1.89 => ( ( ( subcomponents @ X )
% 3.15/1.89 = bot_bo1785112429specID )
% 3.15/1.89 => ( ( loc @ X )
% 3.15/1.89 = bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_206_LocalSecretsComposition__neg__k,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Keys] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_kE @ M2 ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_207_correctCompositionKS__exprChannel__s__P,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_208_correctCompositionKS__exprChannel__s__Q,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_209_correctCompositionKS__exprChannel__s__Pex,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ? [Ch4: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_210_UnCI,axiom,
% 3.15/1.89 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( ~ ( member740727610specID @ C @ B )
% 3.15/1.89 => ( member740727610specID @ C @ A2 ) )
% 3.15/1.89 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_211_UnCI,axiom,
% 3.15/1.89 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( ~ ( member2138796287ecrets @ C @ B )
% 3.15/1.89 => ( member2138796287ecrets @ C @ A2 ) )
% 3.15/1.89 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_212_UnCI,axiom,
% 3.15/1.89 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 3.15/1.89 => ( member_Secrecy_Keys @ C @ A2 ) )
% 3.15/1.89 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_213_UnCI,axiom,
% 3.15/1.89 ! [C: secrecy_KS,B: set_Secrecy_KS,A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 3.15/1.89 => ( member_Secrecy_KS @ C @ A2 ) )
% 3.15/1.89 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_214_UnCI,axiom,
% 3.15/1.89 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ~ ( member1967978193chanID @ C @ B )
% 3.15/1.89 => ( member1967978193chanID @ C @ A2 ) )
% 3.15/1.89 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_215_Un__iff,axiom,
% 3.15/1.89 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 3.15/1.89 = ( ( member740727610specID @ C @ A2 )
% 3.15/1.89 | ( member740727610specID @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_216_Un__iff,axiom,
% 3.15/1.89 ! [C: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) )
% 3.15/1.89 = ( ( member2138796287ecrets @ C @ A2 )
% 3.15/1.89 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_217_Un__iff,axiom,
% 3.15/1.89 ! [C: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) )
% 3.15/1.89 = ( ( member_Secrecy_Keys @ C @ A2 )
% 3.15/1.89 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_218_Un__iff,axiom,
% 3.15/1.89 ! [C: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 3.15/1.89 = ( ( member_Secrecy_KS @ C @ A2 )
% 3.15/1.89 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_219_Un__iff,axiom,
% 3.15/1.89 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 3.15/1.89 = ( ( member1967978193chanID @ C @ A2 )
% 3.15/1.89 | ( member1967978193chanID @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_220_KS_Oinject_I2_J,axiom,
% 3.15/1.89 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 3.15/1.89 ( ( ( secrecy_sKS @ X22 )
% 3.15/1.89 = ( secrecy_sKS @ Y22 ) )
% 3.15/1.89 = ( X22 = Y22 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_221_Expression_Oinject_I2_J,axiom,
% 3.15/1.89 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 3.15/1.89 ( ( ( secrecy_sE @ X22 )
% 3.15/1.89 = ( secrecy_sE @ Y22 ) )
% 3.15/1.89 = ( X22 = Y22 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_222_Un__empty,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ( ( sup_su1301156759ecy_KS @ A2 @ B )
% 3.15/1.89 = bot_bo1943466239ecy_KS )
% 3.15/1.89 = ( ( A2 = bot_bo1943466239ecy_KS )
% 3.15/1.89 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_223_Un__empty,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ( ( sup_su1712599557specID @ A2 @ B )
% 3.15/1.89 = bot_bo1785112429specID )
% 3.15/1.89 = ( ( A2 = bot_bo1785112429specID )
% 3.15/1.89 & ( B = bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_224_Un__empty,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( sup_su370684444chanID @ A2 @ B )
% 3.15/1.89 = bot_bo443197316chanID )
% 3.15/1.89 = ( ( A2 = bot_bo443197316chanID )
% 3.15/1.89 & ( B = bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_225_Un__insert__right,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID,A: secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 3.15/1.89 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_226_Un__insert__right,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,A: secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ A2 @ ( insert_Secrecy_KS @ A @ B ) )
% 3.15/1.89 = ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_227_Un__insert__right,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,A: secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 3.15/1.89 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_228_Un__insert__left,axiom,
% 3.15/1.89 ! [A: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 3.15/1.89 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_229_Un__insert__left,axiom,
% 3.15/1.89 ! [A: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ B ) @ C3 )
% 3.15/1.89 = ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_230_Un__insert__left,axiom,
% 3.15/1.89 ! [A: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 3.15/1.89 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_231_UnE,axiom,
% 3.15/1.89 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 3.15/1.89 => ( ~ ( member740727610specID @ C @ A2 )
% 3.15/1.89 => ( member740727610specID @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_232_UnE,axiom,
% 3.15/1.89 ! [C: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) )
% 3.15/1.89 => ( ~ ( member2138796287ecrets @ C @ A2 )
% 3.15/1.89 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_233_UnE,axiom,
% 3.15/1.89 ! [C: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_Keys @ C @ A2 )
% 3.15/1.89 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_234_UnE,axiom,
% 3.15/1.89 ! [C: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ C @ A2 )
% 3.15/1.89 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_235_UnE,axiom,
% 3.15/1.89 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 3.15/1.89 => ( ~ ( member1967978193chanID @ C @ A2 )
% 3.15/1.89 => ( member1967978193chanID @ C @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_236_UnI1,axiom,
% 3.15/1.89 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ C @ A2 )
% 3.15/1.89 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_237_UnI1,axiom,
% 3.15/1.89 ! [C: secrecy_Secrets,A2: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ C @ A2 )
% 3.15/1.89 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_238_UnI1,axiom,
% 3.15/1.89 ! [C: secrecy_Keys,A2: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ C @ A2 )
% 3.15/1.89 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_239_UnI1,axiom,
% 3.15/1.89 ! [C: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ C @ A2 )
% 3.15/1.89 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_240_UnI1,axiom,
% 3.15/1.89 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ C @ A2 )
% 3.15/1.89 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_241_UnI2,axiom,
% 3.15/1.89 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ C @ B )
% 3.15/1.89 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_242_UnI2,axiom,
% 3.15/1.89 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A2: set_Secrecy_Secrets] :
% 3.15/1.89 ( ( member2138796287ecrets @ C @ B )
% 3.15/1.89 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_243_UnI2,axiom,
% 3.15/1.89 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A2: set_Secrecy_Keys] :
% 3.15/1.89 ( ( member_Secrecy_Keys @ C @ B )
% 3.15/1.89 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_244_UnI2,axiom,
% 3.15/1.89 ! [C: secrecy_KS,B: set_Secrecy_KS,A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ C @ B )
% 3.15/1.89 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_245_UnI2,axiom,
% 3.15/1.89 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ C @ B )
% 3.15/1.89 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_246_bex__Un,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 3.15/1.89 ( ( ? [X2: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 3.15/1.89 & ( P @ X2 ) ) )
% 3.15/1.89 = ( ? [X2: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X2 @ A2 )
% 3.15/1.89 & ( P @ X2 ) )
% 3.15/1.89 | ? [X2: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X2 @ B )
% 3.15/1.89 & ( P @ X2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_247_bex__Un,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 3.15/1.89 ( ( ? [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 3.15/1.89 & ( P @ X2 ) ) )
% 3.15/1.89 = ( ? [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ A2 )
% 3.15/1.89 & ( P @ X2 ) )
% 3.15/1.89 | ? [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ B )
% 3.15/1.89 & ( P @ X2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_248_ball__Un,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 3.15/1.89 ( ( ! [X2: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 3.15/1.89 => ( P @ X2 ) ) )
% 3.15/1.89 = ( ! [X2: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X2 @ A2 )
% 3.15/1.89 => ( P @ X2 ) )
% 3.15/1.89 & ! [X2: secrecy_KS] :
% 3.15/1.89 ( ( member_Secrecy_KS @ X2 @ B )
% 3.15/1.89 => ( P @ X2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_249_ball__Un,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 3.15/1.89 ( ( ! [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 3.15/1.89 => ( P @ X2 ) ) )
% 3.15/1.89 = ( ! [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ A2 )
% 3.15/1.89 => ( P @ X2 ) )
% 3.15/1.89 & ! [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ B )
% 3.15/1.89 => ( P @ X2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_250_Un__assoc,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A2 @ B ) @ C3 )
% 3.15/1.89 = ( sup_su1301156759ecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_251_Un__assoc,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 )
% 3.15/1.89 = ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_252_Un__absorb,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ A2 @ A2 )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_253_Un__absorb,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ A2 @ A2 )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_254_Un__commute,axiom,
% 3.15/1.89 ( sup_su1301156759ecy_KS
% 3.15/1.89 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_255_Un__commute,axiom,
% 3.15/1.89 ( sup_su370684444chanID
% 3.15/1.89 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_256_Un__left__absorb,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 3.15/1.89 = ( sup_su1301156759ecy_KS @ A2 @ B ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_257_Un__left__absorb,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 3.15/1.89 = ( sup_su370684444chanID @ A2 @ B ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_258_Un__left__commute,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 3.15/1.89 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A2 @ C3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_259_Un__left__commute,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) )
% 3.15/1.89 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A2 @ C3 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_260_KS2Expression_Osimps_I2_J,axiom,
% 3.15/1.89 ! [M2: secrecy_Secrets] :
% 3.15/1.89 ( ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 = ( secrecy_sE @ M2 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_261_Un__empty__right,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_262_Un__empty__right,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_263_Un__empty__right,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 3.15/1.89 = A2 ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_264_Un__empty__left,axiom,
% 3.15/1.89 ! [B: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 3.15/1.89 = B ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_265_Un__empty__left,axiom,
% 3.15/1.89 ! [B: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 3.15/1.89 = B ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_266_Un__empty__left,axiom,
% 3.15/1.89 ! [B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 3.15/1.89 = B ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_267_not__know__s__not__ine,axiom,
% 3.15/1.89 ! [A2: secrecy_specID,M2: secrecy_Secrets] :
% 3.15/1.89 ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 => ~ ( ine @ A2 @ ( secrecy_sE @ M2 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_268_KS_Oexhaust,axiom,
% 3.15/1.89 ! [Y2: secrecy_KS] :
% 3.15/1.89 ( ! [X12: secrecy_Keys] :
% 3.15/1.89 ( Y2
% 3.15/1.89 != ( secrecy_kKS @ X12 ) )
% 3.15/1.89 => ~ ! [X23: secrecy_Secrets] :
% 3.15/1.89 ( Y2
% 3.15/1.89 != ( secrecy_sKS @ X23 ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_269_KS_Oinduct,axiom,
% 3.15/1.89 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 3.15/1.89 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 3.15/1.89 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 3.15/1.89 => ( P @ KS ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_270_KS_Odistinct_I1_J,axiom,
% 3.15/1.89 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 3.15/1.89 ( ( secrecy_kKS @ X1 )
% 3.15/1.89 != ( secrecy_sKS @ X22 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_271_Expression_Odistinct_I1_J,axiom,
% 3.15/1.89 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 3.15/1.89 ( ( secrecy_kE @ X1 )
% 3.15/1.89 != ( secrecy_sE @ X22 ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_272_know_Osimps_I2_J,axiom,
% 3.15/1.89 ! [A2: secrecy_specID,M2: secrecy_Secrets] :
% 3.15/1.89 ( ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 = ( ( ine @ A2 @ ( secrecy_sE @ M2 ) )
% 3.15/1.89 | ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_273_singleton__Un__iff,axiom,
% 3.15/1.89 ! [X: secrecy_KS,A2: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.15/1.89 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 3.15/1.89 = ( sup_su1301156759ecy_KS @ A2 @ B ) )
% 3.15/1.89 = ( ( ( A2 = bot_bo1943466239ecy_KS )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.15/1.89 & ( B = bot_bo1943466239ecy_KS ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_274_singleton__Un__iff,axiom,
% 3.15/1.89 ! [X: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.15/1.89 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 3.15/1.89 = ( sup_su1712599557specID @ A2 @ B ) )
% 3.15/1.89 = ( ( ( A2 = bot_bo1785112429specID )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.15/1.89 & ( B = bot_bo1785112429specID ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_275_singleton__Un__iff,axiom,
% 3.15/1.89 ! [X: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 3.15/1.89 = ( sup_su370684444chanID @ A2 @ B ) )
% 3.15/1.89 = ( ( ( A2 = bot_bo443197316chanID )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.15/1.89 & ( B = bot_bo443197316chanID ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_276_Un__singleton__iff,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 3.15/1.89 ( ( ( sup_su1301156759ecy_KS @ A2 @ B )
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.15/1.89 = ( ( ( A2 = bot_bo1943466239ecy_KS )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.15/1.89 & ( B = bot_bo1943466239ecy_KS ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_277_Un__singleton__iff,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 3.15/1.89 ( ( ( sup_su1712599557specID @ A2 @ B )
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.15/1.89 = ( ( ( A2 = bot_bo1785112429specID )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.15/1.89 & ( B = bot_bo1785112429specID ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_278_Un__singleton__iff,axiom,
% 3.15/1.89 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 3.15/1.89 ( ( ( sup_su370684444chanID @ A2 @ B )
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.15/1.89 = ( ( ( A2 = bot_bo443197316chanID )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.15/1.89 & ( B = bot_bo443197316chanID ) )
% 3.15/1.89 | ( ( A2
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.15/1.89 & ( B
% 3.15/1.89 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_279_insert__is__Un,axiom,
% 3.15/1.89 ( insert_Secrecy_KS
% 3.15/1.89 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_280_insert__is__Un,axiom,
% 3.15/1.89 ( insert1671894227specID
% 3.15/1.89 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_281_insert__is__Un,axiom,
% 3.15/1.89 ( insert751661162chanID
% 3.15/1.89 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_282_LocalSecretsComposition__neg__loc__s,axiom,
% 3.15/1.89 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.15/1.89 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 3.15/1.89 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_283_LocalSecretsComposition__neg__s,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Secrets] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_sE @ M2 ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_284_LocalSecretsComposition__ine1__s,axiom,
% 3.15/1.89 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.15/1.89 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_285_LocalSecretsComposition__ine2__s,axiom,
% 3.15/1.89 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.15/1.89 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_286_LocalSecretsComposition__neg1__s,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_287_LocalSecretsComposition__exprChannel__s,axiom,
% 3.15/1.89 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 3.15/1.89 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 3.15/1.89 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 3.15/1.89 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_288_LocalSecretsComposition__neg,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.15/1.89 => ( ! [M4: secrecy_Keys] :
% 3.15/1.89 ( ( Ks
% 3.15/1.89 = ( secrecy_kKS @ M4 ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.15/1.89 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.15/1.89 => ( ! [M4: secrecy_Secrets] :
% 3.15/1.89 ( ( Ks
% 3.15/1.89 = ( secrecy_sKS @ M4 ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.15/1.89 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_289_LocalSecretsComposition__neg1,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc965049635ionLoc @ PQ )
% 3.15/1.89 => ( ! [M4: secrecy_Keys] :
% 3.15/1.89 ( ( Ks
% 3.15/1.89 = ( secrecy_kKS @ M4 ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.15/1.89 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.15/1.89 => ( ! [M4: secrecy_Secrets] :
% 3.15/1.89 ( ( Ks
% 3.15/1.89 = ( secrecy_sKS @ M4 ) )
% 3.15/1.89 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.15/1.89 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_290_correctCompositionKS__exprChannel__s__Qex,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correctCompositionKS @ PQ )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.15/1.89 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.15/1.89 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.15/1.89 => ( ( correctCompositionIn @ PQ )
% 3.15/1.89 => ? [Ch4: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.15/1.89 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_291_sup__bot_Oright__neutral,axiom,
% 3.15/1.89 ! [A: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 3.15/1.89 = A ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_292_sup__bot_Oright__neutral,axiom,
% 3.15/1.89 ! [A: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 3.15/1.89 = A ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_293_sup__bot_Oright__neutral,axiom,
% 3.15/1.89 ! [A: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 3.15/1.89 = A ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_294_sup__bot_Oneutr__eq__iff,axiom,
% 3.15/1.89 ! [A: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 3.15/1.89 ( ( bot_bo1943466239ecy_KS
% 3.15/1.89 = ( sup_su1301156759ecy_KS @ A @ B2 ) )
% 3.15/1.89 = ( ( A = bot_bo1943466239ecy_KS )
% 3.15/1.89 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_295_sup__bot_Oneutr__eq__iff,axiom,
% 3.15/1.89 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 3.15/1.89 ( ( bot_bo1785112429specID
% 3.15/1.89 = ( sup_su1712599557specID @ A @ B2 ) )
% 3.15/1.89 = ( ( A = bot_bo1785112429specID )
% 3.15/1.89 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_296_sup__bot_Oneutr__eq__iff,axiom,
% 3.15/1.89 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( bot_bo443197316chanID
% 3.15/1.89 = ( sup_su370684444chanID @ A @ B2 ) )
% 3.15/1.89 = ( ( A = bot_bo443197316chanID )
% 3.15/1.89 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_297_sup__bot_Oleft__neutral,axiom,
% 3.15/1.89 ! [A: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
% 3.15/1.89 = A ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_298_sup__bot_Oleft__neutral,axiom,
% 3.15/1.89 ! [A: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
% 3.15/1.89 = A ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_299_sup__bot_Oleft__neutral,axiom,
% 3.15/1.89 ! [A: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
% 3.15/1.89 = A ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_300_sup__bot_Oeq__neutr__iff,axiom,
% 3.15/1.89 ! [A: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 3.15/1.89 ( ( ( sup_su1301156759ecy_KS @ A @ B2 )
% 3.15/1.89 = bot_bo1943466239ecy_KS )
% 3.15/1.89 = ( ( A = bot_bo1943466239ecy_KS )
% 3.15/1.89 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_301_sup__bot_Oeq__neutr__iff,axiom,
% 3.15/1.89 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 3.15/1.89 ( ( ( sup_su1712599557specID @ A @ B2 )
% 3.15/1.89 = bot_bo1785112429specID )
% 3.15/1.89 = ( ( A = bot_bo1785112429specID )
% 3.15/1.89 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_302_sup__bot_Oeq__neutr__iff,axiom,
% 3.15/1.89 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( sup_su370684444chanID @ A @ B2 )
% 3.15/1.89 = bot_bo443197316chanID )
% 3.15/1.89 = ( ( A = bot_bo443197316chanID )
% 3.15/1.89 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_303_sup__eq__bot__iff,axiom,
% 3.15/1.89 ! [X: set_Secrecy_KS,Y2: set_Secrecy_KS] :
% 3.15/1.89 ( ( ( sup_su1301156759ecy_KS @ X @ Y2 )
% 3.15/1.89 = bot_bo1943466239ecy_KS )
% 3.15/1.89 = ( ( X = bot_bo1943466239ecy_KS )
% 3.15/1.89 & ( Y2 = bot_bo1943466239ecy_KS ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_304_sup__eq__bot__iff,axiom,
% 3.15/1.89 ! [X: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 3.15/1.89 ( ( ( sup_su1712599557specID @ X @ Y2 )
% 3.15/1.89 = bot_bo1785112429specID )
% 3.15/1.89 = ( ( X = bot_bo1785112429specID )
% 3.15/1.89 & ( Y2 = bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_305_sup__eq__bot__iff,axiom,
% 3.15/1.89 ! [X: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( sup_su370684444chanID @ X @ Y2 )
% 3.15/1.89 = bot_bo443197316chanID )
% 3.15/1.89 = ( ( X = bot_bo443197316chanID )
% 3.15/1.89 & ( Y2 = bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_306_sup__bot__left,axiom,
% 3.15/1.89 ! [X: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_307_sup__bot__left,axiom,
% 3.15/1.89 ! [X: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_308_sup__bot__left,axiom,
% 3.15/1.89 ! [X: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_309_sup__bot__right,axiom,
% 3.15/1.89 ! [X: set_Secrecy_KS] :
% 3.15/1.89 ( ( sup_su1301156759ecy_KS @ X @ bot_bo1943466239ecy_KS )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_310_sup__bot__right,axiom,
% 3.15/1.89 ! [X: set_Secrecy_specID] :
% 3.15/1.89 ( ( sup_su1712599557specID @ X @ bot_bo1785112429specID )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_311_sup__bot__right,axiom,
% 3.15/1.89 ! [X: set_Secrecy_chanID] :
% 3.15/1.89 ( ( sup_su370684444chanID @ X @ bot_bo443197316chanID )
% 3.15/1.89 = X ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_312_bot__eq__sup__iff,axiom,
% 3.15/1.89 ! [X: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 3.15/1.89 ( ( bot_bo1785112429specID
% 3.15/1.89 = ( sup_su1712599557specID @ X @ Y2 ) )
% 3.15/1.89 = ( ( X = bot_bo1785112429specID )
% 3.15/1.89 & ( Y2 = bot_bo1785112429specID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_313_bot__eq__sup__iff,axiom,
% 3.15/1.89 ! [X: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 3.15/1.89 ( ( bot_bo443197316chanID
% 3.15/1.89 = ( sup_su370684444chanID @ X @ Y2 ) )
% 3.15/1.89 = ( ( X = bot_bo443197316chanID )
% 3.15/1.89 & ( Y2 = bot_bo443197316chanID ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_314_ineM__Un1,axiom,
% 3.15/1.89 ! [P: secrecy_specID,A2: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ineM @ P @ A2 @ E )
% 3.15/1.89 => ( ineM @ P @ ( sup_su370684444chanID @ A2 @ B ) @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_315_locStream__def,axiom,
% 3.15/1.89 ( locStream
% 3.15/1.89 = ( ^ [X2: secrecy_specID] :
% 3.15/1.89 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 3.15/1.89 @ ( loc @ X2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_316_inStream__def,axiom,
% 3.15/1.89 ( inStream
% 3.15/1.89 = ( ^ [X2: secrecy_specID] :
% 3.15/1.89 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 3.15/1.89 @ ( ins @ X2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_317_notSpecKeysSecretsExpr__def,axiom,
% 3.15/1.89 ( notSpe1586871396tsExpr
% 3.15/1.89 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 3.15/1.89 ( ! [X2: secrecy_Keys] :
% 3.15/1.89 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X2 ) @ E3 )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 3.15/1.89 & ! [Y4: secrecy_Secrets] :
% 3.15/1.89 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y4 ) @ E3 )
% 3.15/1.89 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_318_TBtheorem5a__empty,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ( eout @ P @ E )
% 3.15/1.89 | ( eout @ Q @ E ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( ( loc @ PQ )
% 3.15/1.89 = bot_bo443197316chanID )
% 3.15/1.89 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_319_correctCompositionKS__subcomp4,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.15/1.89 ( ( correctCompositionKS @ C3 )
% 3.15/1.89 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.15/1.89 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 3.15/1.89 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_320_correctCompositionKS__subcomp3,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.15/1.89 ( ( correctCompositionKS @ C3 )
% 3.15/1.89 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.15/1.89 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 3.15/1.89 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_321_TBtheorem2a,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( eout @ PQ @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( eout @ P @ E )
% 3.15/1.89 | ( eout @ Q @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_322_correctCompositionKS__subcomp1,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.15/1.89 ( ( correctCompositionKS @ C3 )
% 3.15/1.89 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.15/1.89 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 3.15/1.89 => ? [X3: secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 3.15/1.89 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_323_correctCompositionKS__subcomp2,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.15/1.89 ( ( correctCompositionKS @ C3 )
% 3.15/1.89 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.15/1.89 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 3.15/1.89 => ? [X3: secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 3.15/1.89 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_324_TBtheorem5a__notP1,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( eout @ P @ E )
% 3.15/1.89 => ( ~ ( eout @ Q @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_325_TBtheorem5a__notP2,axiom,
% 3.15/1.89 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( eout @ Q @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSet )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_326_TBtheorem5a__notPQ,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.15/1.89 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetP )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_327_out__exprChannelSet__Single,axiom,
% 3.15/1.89 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 3.15/1.89 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_328_out__exprChannelSingle__Set,axiom,
% 3.15/1.89 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( out_ex985543062Single @ P @ Ch @ E )
% 3.15/1.89 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_329_TBtheorem5b__notPQ,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.15/1.89 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.15/1.89 => ( ( M
% 3.15/1.89 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetP )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_330_eout__know__s,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,M2: secrecy_Secrets] :
% 3.15/1.89 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 = ( ( eout @ C3 @ ( secrecy_sE @ M2 ) )
% 3.15/1.89 = ( ( member2138796287ecrets @ M2 @ ( specSecrets @ C3 ) )
% 3.15/1.89 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_331_not__know__s__not__eout,axiom,
% 3.15/1.89 ! [M2: secrecy_Secrets,A2: secrecy_specID] :
% 3.15/1.89 ( ~ ( member2138796287ecrets @ M2 @ ( specSecrets @ A2 ) )
% 3.15/1.89 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 => ( ( knowle233900195orrect @ A2 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 => ~ ( eout @ A2 @ ( secrecy_sE @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_332_not__eout__eoutM,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( eout @ P @ E )
% 3.15/1.89 => ~ ( eoutM @ P @ M @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_333_eoutM__eout,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.15/1.89 ( ( eoutM @ P @ M @ E )
% 3.15/1.89 => ( eout @ P @ E ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_334_TBtheorem2b,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( eoutM @ PQ @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( eoutM @ P @ M @ E )
% 3.15/1.89 | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_335_TBtheorem5b__notP2,axiom,
% 3.15/1.89 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.15/1.89 ( ~ ( eoutM @ Q @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.15/1.89 => ( ! [X3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X3 @ ChSet )
% 3.15/1.89 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_336_TBtheorem5b__notP1,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( eoutM @ P @ M @ E )
% 3.15/1.89 => ( ~ ( eoutM @ Q @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ M )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_337_eout__know__k,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,M2: secrecy_Keys] :
% 3.15/1.89 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 = ( ( eout @ C3 @ ( secrecy_kE @ M2 ) )
% 3.15/1.89 = ( ( member_Secrecy_Keys @ M2 @ ( specKeys @ C3 ) )
% 3.15/1.89 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_338_not__know__k__not__eout,axiom,
% 3.15/1.89 ! [M2: secrecy_Keys,A2: secrecy_specID] :
% 3.15/1.89 ( ~ ( member_Secrecy_Keys @ M2 @ ( specKeys @ A2 ) )
% 3.15/1.89 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 => ( ( knowle233900195orrect @ A2 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 => ~ ( eout @ A2 @ ( secrecy_kE @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_339_eoutKnowCorrect__L1k,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,M2: secrecy_Keys] :
% 3.15/1.89 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 => ( ( eout @ C3 @ ( secrecy_kE @ M2 ) )
% 3.15/1.89 => ( ( member_Secrecy_Keys @ M2 @ ( specKeys @ C3 ) )
% 3.15/1.89 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_340_eout__know__nonKS__k,axiom,
% 3.15/1.89 ! [M2: secrecy_Keys,A2: secrecy_specID] :
% 3.15/1.89 ( ~ ( member_Secrecy_Keys @ M2 @ ( specKeys @ A2 ) )
% 3.15/1.89 => ( ( eout @ A2 @ ( secrecy_kE @ M2 ) )
% 3.15/1.89 => ( ( knowle233900195orrect @ A2 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 => ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_341_eout__know__nonKS__s,axiom,
% 3.15/1.89 ! [M2: secrecy_Secrets,A2: secrecy_specID] :
% 3.15/1.89 ( ~ ( member2138796287ecrets @ M2 @ ( specSecrets @ A2 ) )
% 3.15/1.89 => ( ( eout @ A2 @ ( secrecy_sE @ M2 ) )
% 3.15/1.89 => ( ( knowle233900195orrect @ A2 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 => ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_342_eoutKnowCorrect__L1s,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,M2: secrecy_Secrets] :
% 3.15/1.89 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 => ( ( eout @ C3 @ ( secrecy_sE @ M2 ) )
% 3.15/1.89 => ( ( member2138796287ecrets @ M2 @ ( specSecrets @ C3 ) )
% 3.15/1.89 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_343_TBtheorem5b__PQ,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ( eoutM @ P @ M @ E )
% 3.15/1.89 | ( eoutM @ Q @ M @ E ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 3.15/1.89 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ M )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_344_TBtheore54b__P,axiom,
% 3.15/1.89 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( eoutM @ P @ M @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch3 @ ( out @ Q ) )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 3.15/1.89 & ( member1967978193chanID @ Ch3 @ M ) )
% 3.15/1.89 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_345_TBtheorem5a__PQ,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.15/1.89 ( ( ( eout @ P @ E )
% 3.15/1.89 | ( eout @ Q @ E ) )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 3.15/1.89 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_346_eout__def,axiom,
% 3.15/1.89 ( eout
% 3.15/1.89 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.15/1.89 ? [Ch2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 3.15/1.89 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_347_eoutM__def,axiom,
% 3.15/1.89 ( eoutM
% 3.15/1.89 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.15/1.89 ? [Ch2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 3.15/1.89 & ( member1967978193chanID @ Ch2 @ M3 )
% 3.15/1.89 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_348_out__exprChannelSet__def,axiom,
% 3.15/1.89 ( out_exprChannelSet
% 3.15/1.89 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.15/1.89 ( ! [X2: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 3.15/1.89 => ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 3.15/1.89 & ( exprChannel @ X2 @ E2 ) ) )
% 3.15/1.89 & ! [X2: secrecy_chanID] :
% 3.15/1.89 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 3.15/1.89 & ( member1967978193chanID @ X2 @ ( out @ SP ) ) )
% 3.15/1.89 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_349_out__exprChannelSingle__def,axiom,
% 3.15/1.89 ( out_ex985543062Single
% 3.15/1.89 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 3.15/1.89 & ( exprChannel @ Ch2 @ E2 )
% 3.15/1.89 & ! [X2: secrecy_chanID,T: nat] :
% 3.15/1.89 ( ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 3.15/1.89 & ( X2 != Ch2 ) )
% 3.15/1.89 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_350_correctCompositionOut__prop1,axiom,
% 3.15/1.89 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.15/1.89 ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 3.15/1.89 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 3.15/1.89 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_351_TBtheorem45a__P,axiom,
% 3.15/1.89 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.15/1.89 ( ( eout @ P @ E )
% 3.15/1.89 => ( ( ( subcomponents @ PQ )
% 3.15/1.89 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.15/1.89 => ( ( correc990227761ionOut @ PQ )
% 3.15/1.89 => ( ? [Ch3: secrecy_chanID] :
% 3.15/1.89 ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 3.15/1.89 & ( exprChannel @ Ch3 @ E )
% 3.15/1.89 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.15/1.89 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_352_adv__not__know2,axiom,
% 3.15/1.89 ! [P: secrecy_specID,A2: secrecy_specID,M2: secrecy_Secrets] :
% 3.15/1.89 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A2 ) )
% 3.15/1.89 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_sKS @ M2 ) )
% 3.15/1.89 => ~ ( eout @ P @ ( secrecy_sE @ M2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_353_adv__not__know1,axiom,
% 3.15/1.89 ! [P: secrecy_specID,A2: secrecy_specID,M2: secrecy_Keys] :
% 3.15/1.89 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A2 ) )
% 3.15/1.89 => ( ~ ( knowle945212990e_know @ A2 @ ( secrecy_kKS @ M2 ) )
% 3.15/1.89 => ~ ( eout @ P @ ( secrecy_kE @ M2 ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(fact_354_correctCompositionKeys__subcomp1,axiom,
% 3.15/1.89 ! [C3: secrecy_specID,X: secrecy_specID,Xb: secrecy_Keys] :
% 3.15/1.89 ( ( correc17873122onKeys @ C3 )
% 3.15/1.89 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.15/1.89 => ( ( member_Secrecy_Keys @ Xb @ ( specKeys @ C3 ) )
% 3.15/1.89 => ? [X3: secrecy_specID] :
% 3.15/1.89 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 3.15/1.89 & ( member_Secrecy_Keys @ Xb @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 3.15/1.89
% 3.15/1.89 thf(conj_0,conjecture,
% 3.15/1.89 ~ ( member_Secrecy_KS @ m @ ( specKeysSecrets @ pq ) ) ).
% 3.15/1.89 ------------------------
% 3.35/1.93 % (18279)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_18108 for (2999ds/4Mi)
% 3.35/1.93 % (18281)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/2Mi)
% 3.35/1.93 % (18280)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_18108 for (2999ds/27Mi)
% 3.35/1.93 % (18282)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_18108 for (2999ds/2Mi)
% 3.35/1.93 % (18285)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/18Mi)
% 3.35/1.93 % (18281)Instruction limit reached!
% 3.35/1.93 % (18281)------------------------------
% 3.35/1.93 % (18281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.93 % (18281)Termination reason: Unknown
% 3.35/1.93 % (18281)Termination phase: shuffling
% 3.35/1.93
% 3.35/1.93 % (18281)Memory used [KB]: 1407
% 3.35/1.93 % (18281)Time elapsed: 0.002 s
% 3.35/1.93 % (18281)Instructions burned: 2 (million)
% 3.35/1.93 % (18281)------------------------------
% 3.35/1.93 % (18281)------------------------------
% 3.35/1.93 % (18282)Instruction limit reached!
% 3.35/1.93 % (18282)------------------------------
% 3.35/1.93 % (18282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.93 % (18282)Termination reason: Unknown
% 3.35/1.93 % (18282)Termination phase: shuffling
% 3.35/1.93
% 3.35/1.93 % (18282)Memory used [KB]: 1407
% 3.35/1.93 % (18282)Time elapsed: 0.002 s
% 3.35/1.93 % (18282)Instructions burned: 2 (million)
% 3.35/1.93 % (18282)------------------------------
% 3.35/1.93 % (18282)------------------------------
% 3.35/1.93 % (18279)Instruction limit reached!
% 3.35/1.93 % (18279)------------------------------
% 3.35/1.93 % (18279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.93 % (18279)Termination reason: Unknown
% 3.35/1.93 % (18279)Termination phase: shuffling
% 3.35/1.93
% 3.35/1.93 % (18279)Memory used [KB]: 1535
% 3.35/1.93 % (18279)Time elapsed: 0.003 s
% 3.35/1.93 % (18279)Instructions burned: 5 (million)
% 3.35/1.93 % (18279)------------------------------
% 3.35/1.93 % (18279)------------------------------
% 3.35/1.93 % (18283)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_18108 for (2999ds/275Mi)
% 3.35/1.93 % (18285)Instruction limit reached!
% 3.35/1.93 % (18285)------------------------------
% 3.35/1.93 % (18285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.93 % (18285)Termination reason: Unknown
% 3.35/1.93 % (18285)Termination phase: shuffling
% 3.35/1.93
% 3.35/1.93 % (18285)Memory used [KB]: 1663
% 3.35/1.93 % (18285)Time elapsed: 0.007 s
% 3.35/1.93 % (18285)Instructions burned: 18 (million)
% 3.35/1.93 % (18285)------------------------------
% 3.35/1.93 % (18285)------------------------------
% 3.35/1.93 % (18278)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/183Mi)
% 3.35/1.94 % (18280)Instruction limit reached!
% 3.35/1.94 % (18280)------------------------------
% 3.35/1.94 % (18280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.94 % (18280)Termination reason: Unknown
% 3.35/1.94 % (18280)Termination phase: shuffling
% 3.35/1.94
% 3.35/1.94 % (18280)Memory used [KB]: 1918
% 3.35/1.94 % (18280)Time elapsed: 0.010 s
% 3.35/1.94 % (18280)Instructions burned: 27 (million)
% 3.35/1.94 % (18280)------------------------------
% 3.35/1.94 % (18280)------------------------------
% 3.35/1.94 % (18287)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/3Mi)
% 3.35/1.94 % (18288)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_18108 for (2999ds/37Mi)
% 3.35/1.94 % (18289)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_18108 for (2999ds/15Mi)
% 3.35/1.94 % (18287)Instruction limit reached!
% 3.35/1.94 % (18287)------------------------------
% 3.35/1.94 % (18287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.94 % (18287)Termination reason: Unknown
% 3.35/1.94 % (18287)Termination phase: shuffling
% 3.35/1.94
% 3.35/1.94 % (18287)Memory used [KB]: 1407
% 3.35/1.94 % (18287)Time elapsed: 0.002 s
% 3.35/1.94 % (18287)Instructions burned: 3 (million)
% 3.35/1.94 % (18287)------------------------------
% 3.35/1.94 % (18287)------------------------------
% 3.35/1.94 % (18290)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_18108 for (2999ds/3Mi)
% 3.35/1.94 % (18289)Instruction limit reached!
% 3.35/1.94 % (18289)------------------------------
% 3.35/1.94 % (18289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.94 % (18289)Termination reason: Unknown
% 3.35/1.94 % (18289)Termination phase: shuffling
% 3.35/1.94
% 3.35/1.94 % (18289)Memory used [KB]: 1663
% 3.35/1.94 % (18289)Time elapsed: 0.006 s
% 3.35/1.94 % (18289)Instructions burned: 15 (million)
% 3.35/1.94 % (18289)------------------------------
% 3.35/1.94 % (18289)------------------------------
% 3.35/1.94 % (18290)Instruction limit reached!
% 3.35/1.94 % (18290)------------------------------
% 3.35/1.94 % (18290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.94 % (18290)Termination reason: Unknown
% 3.35/1.94 % (18290)Termination phase: shuffling
% 3.35/1.94
% 3.35/1.94 % (18290)Memory used [KB]: 1535
% 3.35/1.94 % (18290)Time elapsed: 0.003 s
% 3.35/1.94 % (18290)Instructions burned: 6 (million)
% 3.35/1.94 % (18290)------------------------------
% 3.35/1.94 % (18290)------------------------------
% 3.35/1.95 % (18291)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_18108 for (2999ds/1041Mi)
% 3.35/1.95 % (18288)Instruction limit reached!
% 3.35/1.95 % (18288)------------------------------
% 3.35/1.95 % (18288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.95 % (18288)Termination reason: Unknown
% 3.35/1.95 % (18288)Termination phase: shuffling
% 3.35/1.95
% 3.35/1.95 % (18288)Memory used [KB]: 2174
% 3.35/1.95 % (18288)Time elapsed: 0.011 s
% 3.35/1.95 % (18288)Instructions burned: 37 (million)
% 3.35/1.95 % (18288)------------------------------
% 3.35/1.95 % (18288)------------------------------
% 3.35/1.95 % (18294)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/7Mi)
% 3.35/1.95 % (18294)Instruction limit reached!
% 3.35/1.95 % (18294)------------------------------
% 3.35/1.95 % (18294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.95 % (18294)Termination reason: Unknown
% 3.35/1.95 % (18294)Termination phase: shuffling
% 3.35/1.95
% 3.35/1.95 % (18294)Memory used [KB]: 1535
% 3.35/1.95 % (18294)Time elapsed: 0.004 s
% 3.35/1.95 % (18294)Instructions burned: 9 (million)
% 3.35/1.95 % (18294)------------------------------
% 3.35/1.95 % (18294)------------------------------
% 3.35/1.95 % (18301)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/16Mi)
% 3.35/1.95 % (18304)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_18108 for (2999ds/3Mi)
% 3.35/1.96 % (18304)Instruction limit reached!
% 3.35/1.96 % (18304)------------------------------
% 3.35/1.96 % (18304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.96 % (18304)Termination reason: Unknown
% 3.35/1.96 % (18304)Termination phase: shuffling
% 3.35/1.96
% 3.35/1.96 % (18304)Memory used [KB]: 1535
% 3.35/1.96 % (18304)Time elapsed: 0.003 s
% 3.35/1.96 % (18304)Instructions burned: 6 (million)
% 3.35/1.96 % (18304)------------------------------
% 3.35/1.96 % (18304)------------------------------
% 3.35/1.96 % (18306)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_18108 for (2999ds/3Mi)
% 3.35/1.96 % (18301)Instruction limit reached!
% 3.35/1.96 % (18301)------------------------------
% 3.35/1.96 % (18301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.96 % (18301)Termination reason: Unknown
% 3.35/1.96 % (18301)Termination phase: shuffling
% 3.35/1.96
% 3.35/1.96 % (18301)Memory used [KB]: 1663
% 3.35/1.96 % (18301)Time elapsed: 0.006 s
% 3.35/1.96 % (18301)Instructions burned: 16 (million)
% 3.35/1.96 % (18301)------------------------------
% 3.35/1.96 % (18301)------------------------------
% 3.35/1.96 % (18306)Instruction limit reached!
% 3.35/1.96 % (18306)------------------------------
% 3.35/1.96 % (18306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.96 % (18306)Termination reason: Unknown
% 3.35/1.96 % (18306)Termination phase: shuffling
% 3.35/1.96
% 3.35/1.96 % (18306)Memory used [KB]: 1407
% 3.35/1.96 % (18306)Time elapsed: 0.002 s
% 3.35/1.96 % (18306)Instructions burned: 3 (million)
% 3.35/1.96 % (18306)------------------------------
% 3.35/1.96 % (18306)------------------------------
% 3.35/1.96 % (18308)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/7Mi)
% 3.35/1.96 % (18283)Refutation not found, incomplete strategy
% 3.35/1.96 % (18283)------------------------------
% 3.35/1.96 % (18283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.96 % (18283)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.96
% 3.35/1.96
% 3.35/1.96 % (18283)Memory used [KB]: 6652
% 3.35/1.96 % (18283)Time elapsed: 0.031 s
% 3.35/1.96 % (18283)Instructions burned: 71 (million)
% 3.35/1.96 % (18283)------------------------------
% 3.35/1.96 % (18283)------------------------------
% 3.35/1.96 % (18308)Instruction limit reached!
% 3.35/1.96 % (18308)------------------------------
% 3.35/1.96 % (18308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.96 % (18308)Termination reason: Unknown
% 3.35/1.96 % (18308)Termination phase: shuffling
% 3.35/1.96
% 3.35/1.96 % (18308)Memory used [KB]: 1535
% 3.35/1.96 % (18308)Time elapsed: 0.004 s
% 3.35/1.96 % (18308)Instructions burned: 10 (million)
% 3.35/1.96 % (18308)------------------------------
% 3.35/1.96 % (18308)------------------------------
% 3.35/1.96 % (18311)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/3Mi)
% 3.35/1.97 % (18311)Instruction limit reached!
% 3.35/1.97 % (18311)------------------------------
% 3.35/1.97 % (18311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.97 % (18311)Termination reason: Unknown
% 3.35/1.97 % (18311)Termination phase: shuffling
% 3.35/1.97
% 3.35/1.97 % (18311)Memory used [KB]: 1407
% 3.35/1.97 % (18311)Time elapsed: 0.002 s
% 3.35/1.97 % (18311)Instructions burned: 4 (million)
% 3.35/1.97 % (18311)------------------------------
% 3.35/1.97 % (18311)------------------------------
% 3.35/1.97 % (18313)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/4Mi)
% 3.35/1.97 % (18314)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/18Mi)
% 3.35/1.97 % (18313)Instruction limit reached!
% 3.35/1.97 % (18313)------------------------------
% 3.35/1.97 % (18313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.97 % (18313)Termination reason: Unknown
% 3.35/1.97 % (18313)Termination phase: shuffling
% 3.35/1.97
% 3.35/1.97 % (18313)Memory used [KB]: 1535
% 3.35/1.97 % (18313)Time elapsed: 0.003 s
% 3.35/1.97 % (18313)Instructions burned: 6 (million)
% 3.35/1.97 % (18313)------------------------------
% 3.35/1.97 % (18313)------------------------------
% 3.35/1.97 % (18318)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/710Mi)
% 3.35/1.97 % (18320)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/6Mi)
% 3.35/1.97 % (18314)Instruction limit reached!
% 3.35/1.97 % (18314)------------------------------
% 3.35/1.97 % (18314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.97 % (18314)Termination reason: Unknown
% 3.35/1.97 % (18314)Termination phase: shuffling
% 3.35/1.97
% 3.35/1.97 % (18314)Memory used [KB]: 1791
% 3.35/1.97 % (18314)Time elapsed: 0.007 s
% 3.35/1.97 % (18314)Instructions burned: 19 (million)
% 3.35/1.97 % (18314)------------------------------
% 3.35/1.97 % (18314)------------------------------
% 3.35/1.97 % (18320)Instruction limit reached!
% 3.35/1.97 % (18320)------------------------------
% 3.35/1.97 % (18320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.97 % (18320)Termination reason: Unknown
% 3.35/1.97 % (18320)Termination phase: shuffling
% 3.35/1.97
% 3.35/1.97 % (18320)Memory used [KB]: 1535
% 3.35/1.97 % (18320)Time elapsed: 0.003 s
% 3.35/1.97 % (18320)Instructions burned: 6 (million)
% 3.35/1.97 % (18320)------------------------------
% 3.35/1.97 % (18320)------------------------------
% 3.35/1.98 % (18322)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_18108 for (2999ds/902Mi)
% 3.35/1.98 % (18323)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_18108 for (2999ds/21Mi)
% 3.35/1.98 % (18324)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/5Mi)
% 3.35/1.98 % (18325)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_18108 for (2999ds/6Mi)
% 3.35/1.98 % (18324)Instruction limit reached!
% 3.35/1.98 % (18324)------------------------------
% 3.35/1.98 % (18324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.98 % (18324)Termination reason: Unknown
% 3.35/1.98 % (18324)Termination phase: shuffling
% 3.35/1.98
% 3.35/1.98 % (18324)Memory used [KB]: 1535
% 3.35/1.98 % (18324)Time elapsed: 0.003 s
% 3.35/1.98 % (18324)Instructions burned: 6 (million)
% 3.35/1.98 % (18324)------------------------------
% 3.35/1.98 % (18324)------------------------------
% 3.35/1.98 % (18323)Instruction limit reached!
% 3.35/1.98 % (18323)------------------------------
% 3.35/1.98 % (18323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.98 % (18323)Termination reason: Unknown
% 3.35/1.98 % (18323)Termination phase: shuffling
% 3.35/1.98
% 3.35/1.98 % (18323)Memory used [KB]: 1791
% 3.35/1.98 % (18323)Time elapsed: 0.008 s
% 3.35/1.98 % (18323)Instructions burned: 21 (million)
% 3.35/1.98 % (18323)------------------------------
% 3.35/1.98 % (18323)------------------------------
% 3.35/1.99 % (18325)Instruction limit reached!
% 3.35/1.99 % (18325)------------------------------
% 3.35/1.99 % (18325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.99 % (18325)Termination reason: Unknown
% 3.35/1.99 % (18325)Termination phase: shuffling
% 3.35/1.99
% 3.35/1.99 % (18325)Memory used [KB]: 1535
% 3.35/1.99 % (18325)Time elapsed: 0.003 s
% 3.35/1.99 % (18325)Instructions burned: 6 (million)
% 3.35/1.99 % (18325)------------------------------
% 3.35/1.99 % (18325)------------------------------
% 3.35/1.99 % (18318)Refutation not found, incomplete strategy
% 3.35/1.99 % (18318)------------------------------
% 3.35/1.99 % (18318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/1.99 % (18318)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.99
% 3.35/1.99
% 3.35/1.99 % (18318)Memory used [KB]: 6524
% 3.35/1.99 % (18318)Time elapsed: 0.018 s
% 3.35/1.99 % (18318)Instructions burned: 55 (million)
% 3.35/1.99 % (18318)------------------------------
% 3.35/1.99 % (18318)------------------------------
% 3.35/1.99 % (18331)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/377Mi)
% 3.35/1.99 % (18332)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_18108 for (2999ds/779Mi)
% 3.35/1.99 % (18333)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_18108 for (2999ds/19Mi)
% 3.35/2.00 % (18339)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/879Mi)
% 3.35/2.00 % (18333)Instruction limit reached!
% 3.35/2.00 % (18333)------------------------------
% 3.35/2.00 % (18333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/2.00 % (18333)Termination reason: Unknown
% 3.35/2.00 % (18333)Termination phase: shuffling
% 3.35/2.00
% 3.35/2.00 % (18333)Memory used [KB]: 1791
% 3.35/2.00 % (18333)Time elapsed: 0.007 s
% 3.35/2.00 % (18333)Instructions burned: 22 (million)
% 3.35/2.00 % (18333)------------------------------
% 3.35/2.00 % (18333)------------------------------
% 3.35/2.00 % (18278)Instruction limit reached!
% 3.35/2.00 % (18278)------------------------------
% 3.35/2.00 % (18278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/2.00 % (18278)Termination reason: Unknown
% 3.35/2.00 % (18278)Termination phase: Saturation
% 3.35/2.00
% 3.35/2.00 % (18278)Memory used [KB]: 7419
% 3.35/2.00 % (18278)Time elapsed: 0.071 s
% 3.35/2.00 % (18278)Instructions burned: 185 (million)
% 3.35/2.00 % (18278)------------------------------
% 3.35/2.00 % (18278)------------------------------
% 3.35/2.01 % (18346)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/17Mi)
% 3.35/2.01 % (18349)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18108 for (2999ds/3Mi)
% 3.35/2.01 % (18349)Instruction limit reached!
% 3.35/2.01 % (18349)------------------------------
% 3.35/2.01 % (18349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/2.01 % (18349)Termination reason: Unknown
% 3.35/2.01 % (18349)Termination phase: shuffling
% 3.35/2.01
% 3.35/2.01 % (18349)Memory used [KB]: 1407
% 3.35/2.01 % (18349)Time elapsed: 0.002 s
% 3.35/2.01 % (18349)Instructions burned: 3 (million)
% 3.35/2.01 % (18349)------------------------------
% 3.35/2.01 % (18349)------------------------------
% 3.35/2.02 % (18346)Instruction limit reached!
% 3.35/2.02 % (18346)------------------------------
% 3.35/2.02 % (18346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.35/2.02 % (18346)Termination reason: Unknown
% 3.35/2.02 % (18346)Termination phase: shuffling
% 3.35/2.02
% 3.35/2.02 % (18346)Memory used [KB]: 1791
% 3.35/2.02 % (18346)Time elapsed: 0.007 s
% 3.35/2.02 % (18346)Instructions burned: 19 (million)
% 3.35/2.02 % (18346)------------------------------
% 3.35/2.02 % (18346)------------------------------
% 3.35/2.02 % (18356)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18108 for (2998ds/30Mi)
% 4.05/2.03 % (18322)Refutation not found, incomplete strategy
% 4.05/2.03 % (18322)------------------------------
% 4.05/2.03 % (18322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.03 % (18322)Termination reason: Refutation not found, incomplete strategy
% 4.05/2.03
% 4.05/2.03
% 4.05/2.03 % (18322)Memory used [KB]: 7803
% 4.05/2.03 % (18322)Time elapsed: 0.050 s
% 4.05/2.03 % (18322)Instructions burned: 174 (million)
% 4.05/2.03 % (18322)------------------------------
% 4.05/2.03 % (18322)------------------------------
% 4.05/2.03 % (18357)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18108 for (2998ds/127Mi)
% 4.05/2.03 % (18339)First to succeed.
% 4.05/2.03 % (18339)Refutation found. Thanks to Tanya!
% 4.05/2.03 % SZS status Theorem for DTF2THF_18108
% 4.05/2.03 % SZS output start Proof for DTF2THF_18108
% 4.05/2.03 thf(type_def_5, type, secrecy_specID: $tType).
% 4.05/2.03 thf(type_def_6, type, set_Secrecy_KS: $tType).
% 4.05/2.03 thf(type_def_8, type, secrecy_KS: $tType).
% 4.05/2.03 thf(type_def_9, type, set_Secrecy_Keys: $tType).
% 4.05/2.03 thf(type_def_10, type, set_Secrecy_Secrets: $tType).
% 4.05/2.03 thf(type_def_11, type, set_Secrecy_chanID: $tType).
% 4.05/2.03 thf(type_def_12, type, set_Secrecy_specID: $tType).
% 4.05/2.03 thf(type_def_13, type, secrecy_Expression: $tType).
% 4.05/2.03 thf(type_def_14, type, list_S529945141ession: $tType).
% 4.05/2.03 thf(type_def_15, type, secrecy_Keys: $tType).
% 4.05/2.03 thf(type_def_16, type, secrecy_Secrets: $tType).
% 4.05/2.03 thf(type_def_17, type, secrecy_chanID: $tType).
% 4.05/2.03 thf(type_def_18, type, nat: $tType).
% 4.05/2.03 thf(func_def_0, type, list_S529945141ession: $tType).
% 4.05/2.03 thf(func_def_1, type, set_Secrecy_Secrets: $tType).
% 4.05/2.03 thf(func_def_2, type, set_Secrecy_specID: $tType).
% 4.05/2.03 thf(func_def_3, type, set_Secrecy_chanID: $tType).
% 4.05/2.03 thf(func_def_4, type, set_Secrecy_Keys: $tType).
% 4.05/2.03 thf(func_def_5, type, set_Secrecy_KS: $tType).
% 4.05/2.03 thf(func_def_6, type, secrecy_Expression: $tType).
% 4.05/2.03 thf(func_def_7, type, secrecy_Secrets: $tType).
% 4.05/2.03 thf(func_def_8, type, secrecy_specID: $tType).
% 4.05/2.03 thf(func_def_9, type, secrecy_chanID: $tType).
% 4.05/2.03 thf(func_def_10, type, secrecy_Keys: $tType).
% 4.05/2.03 thf(func_def_11, type, secrecy_KS: $tType).
% 4.05/2.03 thf(func_def_12, type, nat: $tType).
% 4.05/2.03 thf(func_def_13, type, localSecrets: secrecy_specID > set_Secrecy_KS).
% 4.05/2.03 thf(func_def_14, type, knowle233900195orrect: secrecy_specID > secrecy_KS > $o).
% 4.05/2.03 thf(func_def_15, type, knowle945212990e_know: secrecy_specID > secrecy_KS > $o).
% 4.05/2.03 thf(func_def_16, type, sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 4.05/2.03 thf(func_def_17, type, sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 4.05/2.03 thf(func_def_18, type, sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 4.05/2.03 thf(func_def_19, type, sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 4.05/2.03 thf(func_def_20, type, sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 4.05/2.03 thf(func_def_21, type, mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o).
% 4.05/2.03 thf(func_def_22, type, bot_bot_Secrecy_KS_o: secrecy_KS > $o).
% 4.05/2.03 thf(func_def_23, type, bot_bo2072920570Keys_o: secrecy_Keys > $o).
% 4.05/2.03 thf(func_def_24, type, bot_bo1909946299rets_o: secrecy_Secrets > $o).
% 4.05/2.03 thf(func_def_25, type, bot_bo1012329985anID_o: secrecy_chanID > $o).
% 4.05/2.03 thf(func_def_26, type, bot_bo1767780696ecID_o: secrecy_specID > $o).
% 4.05/2.03 thf(func_def_27, type, bot_bo1943466239ecy_KS: set_Secrecy_KS).
% 4.05/2.03 thf(func_def_28, type, bot_bo701486667y_Keys: set_Secrecy_Keys).
% 4.05/2.03 thf(func_def_29, type, bot_bo1124690338ecrets: set_Secrecy_Secrets).
% 4.05/2.03 thf(func_def_30, type, bot_bo443197316chanID: set_Secrecy_chanID).
% 4.05/2.03 thf(func_def_31, type, bot_bo1785112429specID: set_Secrecy_specID).
% 4.05/2.03 thf(func_def_32, type, ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o).
% 4.05/2.03 thf(func_def_33, type, correctCompositionKS: secrecy_specID > $o).
% 4.05/2.03 thf(func_def_34, type, correc17873122onKeys: secrecy_specID > $o).
% 4.05/2.03 thf(func_def_35, type, eout: secrecy_specID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_36, type, eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_37, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_38, type, ine: secrecy_specID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_39, type, ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_40, type, ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_41, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_42, type, notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o).
% 4.05/2.03 thf(func_def_43, type, out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_44, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 4.05/2.03 thf(func_def_45, type, specKeys: secrecy_specID > set_Secrecy_Keys).
% 4.05/2.03 thf(func_def_46, type, specKeysSecrets: secrecy_specID > set_Secrecy_KS).
% 4.05/2.03 thf(func_def_47, type, specSecrets: secrecy_specID > set_Secrecy_Secrets).
% 4.05/2.03 thf(func_def_48, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 4.05/2.03 thf(func_def_49, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 4.05/2.03 thf(func_def_50, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 4.05/2.03 thf(func_def_51, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 4.05/2.03 thf(func_def_52, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 4.05/2.03 thf(func_def_53, type, collect_Secrecy_KS: (secrecy_KS > $o) > set_Secrecy_KS).
% 4.05/2.03 thf(func_def_54, type, collect_Secrecy_Keys: (secrecy_Keys > $o) > set_Secrecy_Keys).
% 4.05/2.03 thf(func_def_55, type, collec836099393ecrets: (secrecy_Secrets > $o) > set_Secrecy_Secrets).
% 4.05/2.03 thf(func_def_56, type, collec625564175chanID: (secrecy_chanID > $o) > set_Secrecy_chanID).
% 4.05/2.03 thf(func_def_57, type, collec1545797240specID: (secrecy_specID > $o) > set_Secrecy_specID).
% 4.05/2.03 thf(func_def_58, type, insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 4.05/2.03 thf(func_def_59, type, insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 4.05/2.03 thf(func_def_60, type, insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 4.05/2.03 thf(func_def_61, type, insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 4.05/2.03 thf(func_def_62, type, insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 4.05/2.03 thf(func_def_63, type, is_emp928984296chanID: set_Secrecy_chanID > $o).
% 4.05/2.03 thf(func_def_64, type, is_emp1849217361specID: set_Secrecy_specID > $o).
% 4.05/2.03 thf(func_def_65, type, is_sin1442426433ecy_KS: set_Secrecy_KS > $o).
% 4.05/2.03 thf(func_def_66, type, is_sin1096471309y_Keys: set_Secrecy_Keys > $o).
% 4.05/2.03 thf(func_def_67, type, is_sin1002224330ecrets: set_Secrecy_Secrets > $o).
% 4.05/2.03 thf(func_def_68, type, is_sin581274182chanID: set_Secrecy_chanID > $o).
% 4.05/2.03 thf(func_def_69, type, is_sin1501507247specID: set_Secrecy_specID > $o).
% 4.05/2.03 thf(func_def_70, type, the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID).
% 4.05/2.03 thf(func_def_71, type, the_el827131246specID: set_Secrecy_specID > secrecy_specID).
% 4.05/2.03 thf(func_def_72, type, correctCompositionIn: secrecy_specID > $o).
% 4.05/2.03 thf(func_def_73, type, correc965049635ionLoc: secrecy_specID > $o).
% 4.05/2.03 thf(func_def_74, type, correc990227761ionOut: secrecy_specID > $o).
% 4.05/2.03 thf(func_def_75, type, inStream: secrecy_specID > set_Secrecy_chanID > $o).
% 4.05/2.03 thf(func_def_76, type, ins: secrecy_specID > set_Secrecy_chanID).
% 4.05/2.03 thf(func_def_77, type, loc: secrecy_specID > set_Secrecy_chanID).
% 4.05/2.03 thf(func_def_78, type, locStream: secrecy_specID > set_Secrecy_chanID > $o).
% 4.05/2.03 thf(func_def_79, type, out: secrecy_specID > set_Secrecy_chanID).
% 4.05/2.03 thf(func_def_80, type, subcomponents: secrecy_specID > set_Secrecy_specID).
% 4.05/2.03 thf(func_def_81, type, member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o).
% 4.05/2.03 thf(func_def_82, type, member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o).
% 4.05/2.03 thf(func_def_83, type, member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o).
% 4.05/2.03 thf(func_def_84, type, member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o).
% 4.05/2.03 thf(func_def_85, type, member740727610specID: secrecy_specID > set_Secrecy_specID > $o).
% 4.05/2.03 thf(func_def_86, type, p: secrecy_specID).
% 4.05/2.03 thf(func_def_87, type, pq: secrecy_specID).
% 4.05/2.03 thf(func_def_88, type, q: secrecy_specID).
% 4.05/2.03 thf(func_def_89, type, key: secrecy_Keys).
% 4.05/2.03 thf(func_def_90, type, m: secrecy_KS).
% 4.05/2.03 thf(func_def_106, type, sK0: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 4.05/2.03 thf(func_def_107, type, sK1: secrecy_specID > secrecy_Secrets > secrecy_chanID).
% 4.05/2.03 thf(func_def_108, type, sK2: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets).
% 4.05/2.03 thf(func_def_109, type, sK3: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys).
% 4.05/2.03 thf(func_def_110, type, sK4: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 4.05/2.03 thf(func_def_111, type, sK5: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 4.05/2.03 thf(f1072,plain,(
% 4.05/2.03 $false),
% 4.05/2.03 inference(subsumption_resolution,[status(thm)],[f1071,f1063])).
% 4.05/2.03 thf(f1063,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)) != $true)),
% 4.05/2.03 inference(definition_unfolding,[status(thm)],[f1026,f1049])).
% 4.05/2.03 thf(f1049,plain,(
% 4.05/2.03 (m = (secrecy_kKS @ key))),
% 4.05/2.03 inference(cnf_transformation,[status(thm)],[f7])).
% 4.05/2.03 thf(f7,axiom,(
% 4.05/2.03 (m = (secrecy_kKS @ key))),
% 4.05/2.03 file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_6_a1)).
% 4.05/2.03 thf(f1026,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ m @ (specKeysSecrets @ p)) != $true)),
% 4.05/2.03 inference(cnf_transformation,[status(thm)],[f961])).
% 4.05/2.03 thf(f961,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ m @ (specKeysSecrets @ p)) != $true)),
% 4.05/2.03 inference(flattening,[status(thm)],[f912])).
% 4.05/2.03 thf(f912,plain,(
% 4.05/2.03 ~((member_Secrecy_KS @ m @ (specKeysSecrets @ p)) = $true)),
% 4.05/2.03 inference(fool_elimination,[status(thm)],[f911])).
% 4.05/2.03 thf(f911,plain,(
% 4.05/2.03 ~(member_Secrecy_KS @ m @ (specKeysSecrets @ p))),
% 4.05/2.03 inference(rectify,[status(thm)],[f3])).
% 4.05/2.03 thf(f3,axiom,(
% 4.05/2.03 ~(member_Secrecy_KS @ m @ (specKeysSecrets @ p))),
% 4.05/2.03 file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_2_notKSP)).
% 4.05/2.03 thf(f1071,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)) = $true)),
% 4.05/2.03 inference(subsumption_resolution,[status(thm)],[f1070,f1056])).
% 4.05/2.03 thf(f1056,plain,(
% 4.05/2.03 ((correctCompositionKS @ pq) = $true)),
% 4.05/2.03 inference(cnf_transformation,[status(thm)],[f480])).
% 4.05/2.03 thf(f480,plain,(
% 4.05/2.03 ((correctCompositionKS @ pq) = $true)),
% 4.05/2.03 inference(fool_elimination,[status(thm)],[f479])).
% 4.05/2.03 thf(f479,plain,(
% 4.05/2.03 (correctCompositionKS @ pq)),
% 4.05/2.03 inference(rectify,[status(thm)],[f1])).
% 4.05/2.03 thf(f1,axiom,(
% 4.05/2.03 (correctCompositionKS @ pq)),
% 4.05/2.03 file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_0_cCompKS)).
% 4.05/2.03 thf(f1070,plain,(
% 4.05/2.03 ((correctCompositionKS @ pq) != $true) | ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)) = $true)),
% 4.05/2.03 inference(subsumption_resolution,[status(thm)],[f1069,f1061])).
% 4.05/2.03 thf(f1061,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ q)) != $true)),
% 4.05/2.03 inference(definition_unfolding,[status(thm)],[f1024,f1049])).
% 4.05/2.03 thf(f1024,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ m @ (specKeysSecrets @ q)) != $true)),
% 4.05/2.03 inference(cnf_transformation,[status(thm)],[f970])).
% 4.05/2.03 thf(f970,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ m @ (specKeysSecrets @ q)) != $true)),
% 4.05/2.03 inference(flattening,[status(thm)],[f570])).
% 4.05/2.03 thf(f570,plain,(
% 4.05/2.03 ~((member_Secrecy_KS @ m @ (specKeysSecrets @ q)) = $true)),
% 4.05/2.03 inference(fool_elimination,[status(thm)],[f569])).
% 4.05/2.03 thf(f569,plain,(
% 4.05/2.03 ~(member_Secrecy_KS @ m @ (specKeysSecrets @ q))),
% 4.05/2.03 inference(rectify,[status(thm)],[f2])).
% 4.05/2.03 thf(f2,axiom,(
% 4.05/2.03 ~(member_Secrecy_KS @ m @ (specKeysSecrets @ q))),
% 4.05/2.03 file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_1_notKSQ)).
% 4.05/2.03 thf(f1069,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ q)) = $true) | ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)) = $true) | ((correctCompositionKS @ pq) != $true)),
% 4.05/2.03 inference(trivial_inequality_removal,[status(thm)],[f1068])).
% 4.05/2.03 thf(f1068,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ q)) = $true) | ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)) = $true) | ($true != $true) | ((correctCompositionKS @ pq) != $true) | ((subcomponents @ pq) != (subcomponents @ pq))),
% 4.05/2.03 inference(superposition,[status(thm)],[f1067,f1064])).
% 4.05/2.03 thf(f1064,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ pq)) = $true)),
% 4.05/2.03 inference(definition_unfolding,[status(thm)],[f1050,f1049])).
% 4.05/2.03 thf(f1050,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ m @ (specKeysSecrets @ pq)) = $true)),
% 4.05/2.03 inference(cnf_transformation,[status(thm)],[f959])).
% 4.05/2.03 thf(f959,plain,(
% 4.05/2.03 ((member_Secrecy_KS @ m @ (specKeysSecrets @ pq)) = $true)),
% 4.05/2.03 inference(flattening,[status(thm)],[f878])).
% 4.05/2.03 thf(f878,plain,(
% 4.05/2.03 ~~((member_Secrecy_KS @ m @ (specKeysSecrets @ pq)) = $true)),
% 4.05/2.03 inference(fool_elimination,[status(thm)],[f877])).
% 4.05/2.03 thf(f877,plain,(
% 4.05/2.03 ~~(member_Secrecy_KS @ m @ (specKeysSecrets @ pq))),
% 4.05/2.03 inference(rectify,[status(thm)],[f357])).
% 4.05/2.03 thf(f357,negated_conjecture,(
% 4.05/2.03 ~~(member_Secrecy_KS @ m @ (specKeysSecrets @ pq))),
% 4.05/2.03 inference(negated_conjecture,[status(cth)],[f356])).
% 4.05/2.03 thf(f356,conjecture,(
% 4.05/2.03 ~(member_Secrecy_KS @ m @ (specKeysSecrets @ pq))),
% 4.05/2.03 file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',conj_0)).
% 4.05/2.03 thf(f1067,plain,(
% 4.05/2.03 ( ! [X0 : secrecy_specID,X1 : secrecy_KS] : (($true != (member_Secrecy_KS @ X1 @ (specKeysSecrets @ X0))) | ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ q)) = $true) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true = (member_Secrecy_KS @ X1 @ (specKeysSecrets @ p))) | ((correctCompositionKS @ X0) != $true)) )),
% 4.05/2.03 inference(superposition,[status(thm)],[f1052,f1051])).
% 4.05/2.03 thf(f1051,plain,(
% 4.05/2.03 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 4.05/2.03 inference(cnf_transformation,[status(thm)],[f4])).
% 4.05/2.03 thf(f4,axiom,(
% 4.05/2.03 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 4.05/2.03 file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_3_subPQ)).
% 4.05/2.03 thf(f1052,plain,(
% 4.05/2.03 ( ! [X2 : secrecy_specID,X3 : secrecy_specID,X0 : secrecy_specID,X1 : secrecy_KS] : (((subcomponents @ X2) != (insert1671894227specID @ X3 @ (insert1671894227specID @ X0 @ bot_bo1785112429specID))) | ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X2)) != $true) | ((correctCompositionKS @ X2) != $true) | ($true = (member_Secrecy_KS @ X1 @ (specKeysSecrets @ X0))) | ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X3)) = $true)) )),
% 4.05/2.03 inference(cnf_transformation,[status(thm)],[f1009])).
% 4.05/2.03 thf(f1009,plain,(
% 4.05/2.03 ! [X0 : secrecy_specID,X1 : secrecy_KS,X2 : secrecy_specID,X3 : secrecy_specID] : (((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X3)) = $true) | ((subcomponents @ X2) != (insert1671894227specID @ X3 @ (insert1671894227specID @ X0 @ bot_bo1785112429specID))) | ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X2)) != $true) | ($true = (member_Secrecy_KS @ X1 @ (specKeysSecrets @ X0))) | ((correctCompositionKS @ X2) != $true))),
% 4.05/2.03 inference(flattening,[status(thm)],[f1008])).
% 4.05/2.03 thf(f1008,plain,(
% 4.05/2.03 ! [X0 : secrecy_specID,X1 : secrecy_KS,X2 : secrecy_specID,X3 : secrecy_specID] : ((((($true = (member_Secrecy_KS @ X1 @ (specKeysSecrets @ X0))) | ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X3)) = $true)) | ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X2)) != $true)) | ((correctCompositionKS @ X2) != $true)) | ((subcomponents @ X2) != (insert1671894227specID @ X3 @ (insert1671894227specID @ X0 @ bot_bo1785112429specID))))),
% 4.05/2.03 inference(ennf_transformation,[status(thm)],[f448])).
% 4.05/2.03 thf(f448,plain,(
% 4.05/2.03 ! [X0 : secrecy_specID,X1 : secrecy_KS,X2 : secrecy_specID,X3 : secrecy_specID] : (((subcomponents @ X2) = (insert1671894227specID @ X3 @ (insert1671894227specID @ X0 @ bot_bo1785112429specID))) => (((correctCompositionKS @ X2) = $true) => (((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X2)) = $true) => (($true = (member_Secrecy_KS @ X1 @ (specKeysSecrets @ X0))) | ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X3)) = $true)))))),
% 4.05/2.03 inference(fool_elimination,[status(thm)],[f447])).
% 4.05/2.03 thf(f447,plain,(
% 4.05/2.03 ! [X0 : secrecy_specID,X1 : secrecy_KS,X2 : secrecy_specID,X3 : secrecy_specID] : (((subcomponents @ X2) = (insert1671894227specID @ X3 @ (insert1671894227specID @ X0 @ bot_bo1785112429specID))) => ((correctCompositionKS @ X2) => ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X2)) => ((member_Secrecy_KS @ X1 @ (specKeysSecrets @ X0)) | (member_Secrecy_KS @ X1 @ (specKeysSecrets @ X3))))))),
% 4.05/2.03 inference(rectify,[status(thm)],[f8])).
% 4.05/2.03 thf(f8,axiom,(
% 4.05/2.03 ! [X2 : secrecy_specID,X3 : secrecy_KS,X0 : secrecy_specID,X1 : secrecy_specID] : (((subcomponents @ X0) = (insert1671894227specID @ X1 @ (insert1671894227specID @ X2 @ bot_bo1785112429specID))) => ((correctCompositionKS @ X0) => ((member_Secrecy_KS @ X3 @ (specKeysSecrets @ X0)) => ((member_Secrecy_KS @ X3 @ (specKeysSecrets @ X2)) | (member_Secrecy_KS @ X3 @ (specKeysSecrets @ X1))))))),
% 4.05/2.03 file('/export/starexec/sandbox/tmp/tmp.uhT4Iu5bWm/DTF2THF_18108.p',fact_7_correctCompositionKS__PQ)).
% 4.05/2.03 % SZS output end Proof for DTF2THF_18108
% 4.05/2.03 % (18339)------------------------------
% 4.05/2.03 % (18339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.05/2.03 % (18339)Termination reason: Refutation
% 4.05/2.03
% 4.05/2.03 % (18339)Memory used [KB]: 6780
% 4.05/2.03 % (18339)Time elapsed: 0.033 s
% 4.05/2.03 % (18339)Instructions burned: 106 (million)
% 4.05/2.03 % (18339)------------------------------
% 4.05/2.03 % (18339)------------------------------
% 4.05/2.03 % (18268)Success in time 0.119 s
%------------------------------------------------------------------------------