%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP088^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:27 AM UTC 2026
% Result : Theorem 6.52s 2.26s
% Output : Refutation 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 206 ( 70 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 325 ( 59 ~; 34 |; 0 &; 219 @)
% ( 0 <=>; 13 =>; 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 : 96 ( 93 usr; 11 con; 0-4 aty)
% Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
secrecy_specID: $tType ).
thf(type_def_6,type,
set_Secrecy_KS: $tType ).
thf(type_def_8,type,
secrecy_KS: $tType ).
thf(type_def_9,type,
set_Secrecy_Keys: $tType ).
thf(type_def_10,type,
set_Secrecy_Secrets: $tType ).
thf(type_def_11,type,
set_Secrecy_chanID: $tType ).
thf(type_def_12,type,
set_Secrecy_specID: $tType ).
thf(type_def_13,type,
secrecy_Expression: $tType ).
thf(type_def_14,type,
list_S529945141ession: $tType ).
thf(type_def_15,type,
secrecy_Keys: $tType ).
thf(type_def_16,type,
secrecy_Secrets: $tType ).
thf(type_def_17,type,
secrecy_chanID: $tType ).
thf(type_def_18,type,
nat: $tType ).
thf(func_def_0,type,
list_S529945141ession: $tType ).
thf(func_def_1,type,
set_Secrecy_Secrets: $tType ).
thf(func_def_2,type,
set_Secrecy_specID: $tType ).
thf(func_def_3,type,
set_Secrecy_chanID: $tType ).
thf(func_def_4,type,
set_Secrecy_Keys: $tType ).
thf(func_def_5,type,
set_Secrecy_KS: $tType ).
thf(func_def_6,type,
secrecy_Expression: $tType ).
thf(func_def_7,type,
secrecy_Secrets: $tType ).
thf(func_def_8,type,
secrecy_specID: $tType ).
thf(func_def_9,type,
secrecy_chanID: $tType ).
thf(func_def_10,type,
secrecy_Keys: $tType ).
thf(func_def_11,type,
secrecy_KS: $tType ).
thf(func_def_12,type,
nat: $tType ).
thf(func_def_13,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_14,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(func_def_15,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(func_def_16,type,
sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_17,type,
sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_18,type,
sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_19,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_20,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_21,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_22,type,
bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
thf(func_def_23,type,
bot_bo2072920570Keys_o: secrecy_Keys > $o ).
thf(func_def_24,type,
bot_bo1909946299rets_o: secrecy_Secrets > $o ).
thf(func_def_25,type,
bot_bo1012329985anID_o: secrecy_chanID > $o ).
thf(func_def_26,type,
bot_bo1767780696ecID_o: secrecy_specID > $o ).
thf(func_def_27,type,
bot_bo1943466239ecy_KS: set_Secrecy_KS ).
thf(func_def_28,type,
bot_bo701486667y_Keys: set_Secrecy_Keys ).
thf(func_def_29,type,
bot_bo1124690338ecrets: set_Secrecy_Secrets ).
thf(func_def_30,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(func_def_31,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(func_def_32,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_33,type,
correctCompositionKS: secrecy_specID > $o ).
thf(func_def_34,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_35,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_36,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_37,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_38,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_39,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_40,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_41,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_42,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_43,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_44,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_45,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_46,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_47,type,
secrecy_dE: nat > secrecy_Expression ).
thf(func_def_48,type,
secrecy_idE: secrecy_specID > secrecy_Expression ).
thf(func_def_49,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_50,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_51,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_52,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_53,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_54,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_55,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_56,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_57,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(func_def_58,type,
collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
thf(func_def_59,type,
insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_60,type,
insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_61,type,
insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_62,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_63,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_64,type,
is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
thf(func_def_65,type,
is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
thf(func_def_66,type,
is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
thf(func_def_67,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(func_def_68,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(func_def_69,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_70,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(func_def_71,type,
correctCompositionIn: secrecy_specID > $o ).
thf(func_def_72,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(func_def_73,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(func_def_74,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_75,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_76,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_77,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_78,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_79,type,
outStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_80,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(func_def_81,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(func_def_82,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(func_def_83,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(func_def_84,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_85,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(func_def_86,type,
p: secrecy_specID ).
thf(func_def_87,type,
pq: secrecy_specID ).
thf(func_def_88,type,
q: secrecy_specID ).
thf(func_def_89,type,
key: secrecy_Keys ).
thf(func_def_104,type,
sP0: secrecy_specID > secrecy_specID > secrecy_specID > secrecy_Expression > $o ).
thf(func_def_105,type,
sP1: secrecy_KS > secrecy_specID > secrecy_specID > $o ).
thf(func_def_106,type,
sP2: secrecy_specID > secrecy_specID > secrecy_specID > secrecy_specID > $o ).
thf(func_def_107,type,
sP3: secrecy_specID > secrecy_specID > secrecy_specID > secrecy_specID > $o ).
thf(func_def_108,type,
sP4: secrecy_specID > secrecy_specID > secrecy_KS > $o ).
thf(func_def_109,type,
sK5: secrecy_specID > secrecy_Keys > secrecy_chanID ).
thf(func_def_110,type,
sK6: secrecy_KS > secrecy_Keys ).
thf(func_def_111,type,
sK7: secrecy_KS > secrecy_Secrets ).
thf(func_def_112,type,
sK8: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets ).
thf(func_def_113,type,
sK9: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys ).
thf(func_def_114,type,
sK10: ( secrecy_KS > $o ) > secrecy_Keys ).
thf(func_def_115,type,
sK11: ( secrecy_KS > $o ) > secrecy_Secrets ).
thf(func_def_116,type,
sK12: secrecy_Keys > secrecy_specID > secrecy_chanID ).
thf(func_def_117,type,
sK13: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys ).
thf(func_def_118,type,
sK14: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets ).
thf(func_def_120,type,
ph16:
!>[X0: $tType] : X0 ).
thf(f2049,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f2045,f1147]) ).
thf(f1147,plain,
( ( correctCompositionIn @ pq )
= $true ),
inference(cnf_transformation,[status(thm)],[f879]) ).
thf(f879,plain,
( ( correctCompositionIn @ pq )
= $true ),
inference(fool_elimination,[status(thm)],[f878]) ).
thf(f878,plain,
correctCompositionIn @ pq,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
correctCompositionIn @ pq,
file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_0_assms_I4_J) ).
thf(f2045,plain,
( ( correctCompositionIn @ pq )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2039]) ).
thf(f2039,plain,
( ( ( correctCompositionIn @ pq )
!= $true )
| ( $true != $true )
| ( ( subcomponents @ pq )
!= ( subcomponents @ pq ) ) ),
inference(superposition,[status(thm)],[f2038,f1120]) ).
thf(f1120,plain,
( ( ine @ pq @ ( secrecy_kE @ key ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f947]) ).
thf(f947,plain,
( ( ine @ pq @ ( secrecy_kE @ key ) )
= $true ),
inference(flattening,[status(thm)],[f699]) ).
thf(f699,plain,
~ ( ( ( ine @ pq @ ( secrecy_kE @ key ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f698]) ).
thf(f698,plain,
~ ~ ( ine @ pq @ ( secrecy_kE @ key ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ~ ( ine @ pq @ ( secrecy_kE @ key ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
~ ( ine @ pq @ ( secrecy_kE @ key ) ),
file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',conj_0) ).
thf(f2038,plain,
! [X0: secrecy_specID] :
( ( $true
!= ( ine @ X0 @ ( secrecy_kE @ key ) ) )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f2037,f1183]) ).
thf(f1183,plain,
( $true
!= ( ine @ p @ ( secrecy_kE @ key ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1181]) ).
thf(f1181,plain,
( ( $true
!= ( ine @ p @ ( secrecy_kE @ key ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1082,f1089]) ).
thf(f1089,plain,
! [X0: secrecy_Keys,X1: secrecy_specID] :
( ( ( knowle945212990e_know @ X1 @ ( secrecy_kKS @ X0 ) )
= $true )
| ( $true
!= ( ine @ X1 @ ( secrecy_kE @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f991]) ).
thf(f991,plain,
! [X0: secrecy_Keys,X1: secrecy_specID] :
( ( $true
!= ( ine @ X1 @ ( secrecy_kE @ X0 ) ) )
| ( ( knowle945212990e_know @ X1 @ ( secrecy_kKS @ X0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f969]) ).
thf(f969,plain,
! [X0: secrecy_Keys,X1: secrecy_specID] :
( ( ( knowle945212990e_know @ X1 @ ( secrecy_kKS @ X0 ) )
!= $true )
=> ( $true
!= ( ine @ X1 @ ( secrecy_kE @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f585]) ).
thf(f585,plain,
! [X0: secrecy_Keys,X1: secrecy_specID] :
( ( ( knowle945212990e_know @ X1 @ ( secrecy_kKS @ X0 ) )
!= $true )
=> ( $true
!= ( ine @ X1 @ ( secrecy_kE @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f584]) ).
thf(f584,plain,
! [X0: secrecy_Keys,X1: secrecy_specID] :
( ~ ( knowle945212990e_know @ X1 @ ( secrecy_kKS @ X0 ) )
=> ~ ( ine @ X1 @ ( secrecy_kE @ X0 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X3: secrecy_Keys,X2: secrecy_specID] :
( ~ ( knowle945212990e_know @ X2 @ ( secrecy_kKS @ X3 ) )
=> ~ ( ine @ X2 @ ( secrecy_kE @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_5_not__know__k__not__ine) ).
thf(f1082,plain,
( ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f979]) ).
thf(f979,plain,
( ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) )
!= $true ),
inference(flattening,[status(thm)],[f803]) ).
thf(f803,plain,
( ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f802]) ).
thf(f802,plain,
~ ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
~ ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) ),
file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_2_assms_I1_J) ).
thf(f2037,plain,
! [X0: secrecy_specID] :
( ( $true
= ( ine @ p @ ( secrecy_kE @ key ) ) )
| ( $true
!= ( ine @ X0 @ ( secrecy_kE @ key ) ) )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
!= ( correctCompositionIn @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2034]) ).
thf(f2034,plain,
! [X0: secrecy_specID] :
( ( $true != $true )
| ( $true
!= ( ine @ X0 @ ( secrecy_kE @ key ) ) )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( $true
= ( ine @ p @ ( secrecy_kE @ key ) ) ) ),
inference(superposition,[status(thm)],[f1184,f1366]) ).
thf(f1366,plain,
! [X0: secrecy_specID,X1: secrecy_Expression] :
( ( ( ine @ q @ X1 )
= $true )
| ( ( ine @ p @ X1 )
= $true )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( $true
!= ( ine @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f1127,f1134]) ).
thf(f1134,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/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_3_assms_I3_J) ).
thf(f1127,plain,
! [X2: secrecy_Expression,X3: secrecy_specID,X0: secrecy_specID,X1: secrecy_specID] :
( ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X1 @ bot_bo1785112429specID ) )
!= ( subcomponents @ X0 ) )
| ( $true
= ( ine @ X1 @ X2 ) )
| ( ( ine @ X3 @ X2 )
= $true )
| ( $true
!= ( ine @ X0 @ X2 ) )
| ( $true
!= ( correctCompositionIn @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
thf(f1034,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_Expression,X3: secrecy_specID] :
( ( ( ine @ X3 @ X2 )
= $true )
| ( $true
!= ( ine @ X0 @ X2 ) )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( $true
= ( ine @ X1 @ X2 ) )
| ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X1 @ bot_bo1785112429specID ) )
!= ( subcomponents @ X0 ) ) ),
inference(flattening,[status(thm)],[f1033]) ).
thf(f1033,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_Expression,X3: secrecy_specID] :
( ( $true
= ( ine @ X1 @ X2 ) )
| ( ( ine @ X3 @ X2 )
= $true )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X1 @ bot_bo1785112429specID ) )
!= ( subcomponents @ X0 ) )
| ( $true
!= ( ine @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f785]) ).
thf(f785,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_Expression,X3: secrecy_specID] :
( ( $true
= ( ine @ X0 @ X2 ) )
=> ( ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X1 @ bot_bo1785112429specID ) )
= ( subcomponents @ X0 ) )
=> ( ( $true
= ( correctCompositionIn @ X0 ) )
=> ( ( $true
= ( ine @ X1 @ X2 ) )
| ( ( ine @ X3 @ X2 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f784]) ).
thf(f784,plain,
! [X0: secrecy_specID,X1: secrecy_specID,X2: secrecy_Expression,X3: secrecy_specID] :
( ( ine @ X0 @ X2 )
=> ( ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X1 @ bot_bo1785112429specID ) )
= ( subcomponents @ X0 ) )
=> ( ( correctCompositionIn @ X0 )
=> ( ( ine @ X3 @ X2 )
| ( ine @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,axiom,
! [X21: secrecy_specID,X11: secrecy_specID,X8: secrecy_Expression,X6: secrecy_specID] :
( ( ine @ X21 @ X8 )
=> ( ( ( subcomponents @ X21 )
= ( insert1671894227specID @ X6 @ ( insert1671894227specID @ X11 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ X21 )
=> ( ( ine @ X6 @ X8 )
| ( ine @ X11 @ X8 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_35_TBtheorem1a) ).
thf(f1184,plain,
( $true
!= ( ine @ q @ ( secrecy_kE @ key ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1182]) ).
thf(f1182,plain,
( ( $true != $true )
| ( $true
!= ( ine @ q @ ( secrecy_kE @ key ) ) ) ),
inference(superposition,[status(thm)],[f1128,f1089]) ).
thf(f1128,plain,
( ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f980]) ).
thf(f980,plain,
( ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) )
!= $true ),
inference(flattening,[status(thm)],[f362]) ).
thf(f362,plain,
( ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f361]) ).
thf(f361,plain,
~ ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
~ ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ),
file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_1_assms_I2_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP088^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:26:09 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP088^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_351__3295008_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : KnowledgeKeysSecrets/prob_351__3295008_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 446 ( 177 unt; 90 typ; 0 def)
% 0.31/0.46 % Number of atoms : 1268 ( 469 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.31/0.46 % Number of connectives : 3855 ( 291 ~; 51 |; 128 &;2832 @)
% 0.31/0.46 % ( 0 <=>; 553 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 19 ( 7 avg)
% 0.31/0.46 % Number of types : 14 ( 13 usr)
% 0.31/0.46 % Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 78 ( 77 usr; 9 con; 0-3 aty)
% 0.31/0.46 % Number of variables : 1014 ( 54 ^; 915 !; 45 ?;1014 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:59.423
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (13)
% 0.31/0.46 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.31/0.46 list_S529945141ession: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.31/0.46 set_Secrecy_Secrets: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.31/0.46 set_Secrecy_specID: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.46 set_Secrecy_chanID: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.31/0.46 set_Secrecy_Keys: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.31/0.46 set_Secrecy_KS: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.31/0.46 secrecy_Expression: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.31/0.46 secrecy_Secrets: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.31/0.46 secrecy_specID: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Secrecy____types__OchanID,type,
% 0.31/0.46 secrecy_chanID: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.31/0.46 secrecy_Keys: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.31/0.46 secrecy_KS: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.31/0.46 nat: $tType ).
% 0.31/0.46
% 0.31/0.46 % Explicit typings (77)
% 0.31/0.46 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.31/0.46 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.31/0.46 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.31/0.46 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.31/0.46 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.31/0.46 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.31/0.46 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.46 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.31/0.46 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.31/0.46 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 0.31/0.46 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 0.31/0.46 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 0.31/0.46 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 0.31/0.46 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 0.31/0.46 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.31/0.46 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.31/0.46 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.31/0.46 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.46 bot_bo443197316chanID: set_Secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.31/0.46 bot_bo1785112429specID: set_Secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.31/0.46 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.31/0.46 correctCompositionKS: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oeout,type,
% 0.31/0.46 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OeoutM,type,
% 0.31/0.46 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OexprChannel,type,
% 0.31/0.46 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.31/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OineM,type,
% 0.31/0.46 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.31/0.46 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.31/0.46 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.31/0.46 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.31/0.46 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.31/0.46 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.31/0.46 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.31/0.46 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.31/0.46 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OdE,type,
% 0.31/0.46 secrecy_dE: nat > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OidE,type,
% 0.31/0.46 secrecy_idE: secrecy_specID > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.31/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.31/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.31/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.31/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.31/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.31/0.46 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.31/0.46 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.31/0.46 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 0.31/0.46 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 0.31/0.46 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 0.31/0.46 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 0.31/0.46 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 0.31/0.46 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 0.31/0.46 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 0.31/0.46 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 0.31/0.46 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 0.31/0.46 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 0.31/0.46 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 0.31/0.46 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 0.31/0.46 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 0.31/0.46 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 0.31/0.46 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.31/0.46 correctCompositionIn: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.31/0.46 correc965049635ionLoc: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.31/0.46 correc990227761ionOut: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OinStream,type,
% 0.31/0.46 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Oins,type,
% 0.31/0.46 ins: secrecy_specID > set_Secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Oloc,type,
% 0.31/0.46 loc: secrecy_specID > set_Secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OlocStream,type,
% 0.31/0.46 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Oout,type,
% 0.31/0.46 out: secrecy_specID > set_Secrecy_chanID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OoutStream,type,
% 0.31/0.46 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Osubcomponents,type,
% 0.31/0.46 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.31/0.46 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.31/0.46 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.31/0.46 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 0.31/0.46 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 0.31/0.46 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_P,type,
% 0.31/0.46 p: secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_PQ,type,
% 0.31/0.46 pq: secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_Q,type,
% 0.31/0.46 q: secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_key,type,
% 0.31/0.46 key: secrecy_Keys ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (355)
% 0.31/0.46 thf(fact_0_assms_I4_J,axiom,
% 0.31/0.46 correctCompositionIn @ pq ).
% 0.31/0.46
% 0.31/0.46 % assms(4)
% 0.31/0.46 thf(fact_1_assms_I2_J,axiom,
% 0.31/0.46 ~ ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(2)
% 0.31/0.46 thf(fact_2_assms_I1_J,axiom,
% 0.31/0.46 ~ ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(1)
% 0.31/0.46 thf(fact_3_assms_I3_J,axiom,
% 0.31/0.46 ( ( subcomponents @ pq )
% 0.31/0.46 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(3)
% 0.31/0.46 thf(fact_4_Expression_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.31/0.46 ( ( ( secrecy_kE @ X1 )
% 0.31/0.46 = ( secrecy_kE @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(1)
% 0.31/0.46 thf(fact_5_not__know__k__not__ine,axiom,
% 0.31/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.46 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.46 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_know_k_not_ine
% 0.31/0.46 thf(fact_6_know_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.46 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.31/0.46 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % know.simps(1)
% 0.31/0.46 thf(fact_7_Expression_Odistinct_I5_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrecy_kE @ X1 )
% 0.31/0.46 != ( secrecy_idE @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(5)
% 0.31/0.46 thf(fact_8_Expression_Odistinct_I3_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,X3: nat] :
% 0.31/0.46 ( ( secrecy_kE @ X1 )
% 0.31/0.46 != ( secrecy_dE @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(3)
% 0.31/0.46 thf(fact_9_KS2Expression_Osimps_I1_J,axiom,
% 0.31/0.46 ! [M: secrecy_Keys] :
% 0.31/0.46 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.31/0.46 = ( secrecy_kE @ M ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS2Expression.simps(1)
% 0.31/0.46 thf(fact_10_ineM__ine,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.46 ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ine @ P @ E ) ) ).
% 0.31/0.46
% 0.31/0.46 % ineM_ine
% 0.31/0.46 thf(fact_11_not__ine__ineM,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 0.31/0.46 ( ~ ( ine @ P @ E )
% 0.31/0.46 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_ine_ineM
% 0.31/0.46 thf(fact_12_LocalSecretsComposition__exprChannel__k,axiom,
% 0.31/0.46 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.31/0.46 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_exprChannel_k
% 0.31/0.46 thf(fact_13_Expression_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.31/0.46 ( ( secrecy_kE @ X1 )
% 0.31/0.46 != ( secrecy_sE @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(1)
% 0.31/0.46 thf(fact_14_KS_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.31/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.31/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS.inject(1)
% 0.31/0.46 thf(fact_15_Expression_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.31/0.46 ( ( ( secrecy_sE @ X2 )
% 0.31/0.46 = ( secrecy_sE @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(2)
% 0.31/0.46 thf(fact_16_Expression_Oinject_I4_J,axiom,
% 0.31/0.46 ! [X4: secrecy_specID,Y4: secrecy_specID] :
% 0.31/0.46 ( ( ( secrecy_idE @ X4 )
% 0.31/0.46 = ( secrecy_idE @ Y4 ) )
% 0.31/0.46 = ( X4 = Y4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(4)
% 0.31/0.46 thf(fact_17_Expression_Oinject_I3_J,axiom,
% 0.31/0.46 ! [X3: nat,Y3: nat] :
% 0.31/0.46 ( ( ( secrecy_dE @ X3 )
% 0.31/0.46 = ( secrecy_dE @ Y3 ) )
% 0.31/0.46 = ( X3 = Y3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(3)
% 0.31/0.46 thf(fact_18_Expression_Odistinct_I11_J,axiom,
% 0.31/0.46 ! [X3: nat,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrecy_dE @ X3 )
% 0.31/0.46 != ( secrecy_idE @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(11)
% 0.31/0.46 thf(fact_19_Expression_Odistinct_I9_J,axiom,
% 0.31/0.46 ! [X2: secrecy_Secrets,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrecy_sE @ X2 )
% 0.31/0.46 != ( secrecy_idE @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(9)
% 0.31/0.46 thf(fact_20_Expression_Odistinct_I7_J,axiom,
% 0.31/0.46 ! [X2: secrecy_Secrets,X3: nat] :
% 0.31/0.46 ( ( secrecy_sE @ X2 )
% 0.31/0.46 != ( secrecy_dE @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(7)
% 0.31/0.46 thf(fact_21_ineM__L1,axiom,
% 0.31/0.46 ! [Ch: secrecy_chanID,M2: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.31/0.46 ( ( member1967978193chanID @ Ch @ M2 )
% 0.31/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ E )
% 0.31/0.46 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ineM_L1
% 0.31/0.46 thf(fact_22_ine__def,axiom,
% 0.31/0.46 ( ine
% 0.31/0.46 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.31/0.46 ? [Ch2: secrecy_chanID] :
% 0.31/0.46 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 0.31/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_def
% 0.31/0.46 thf(fact_23_ineM__def,axiom,
% 0.31/0.46 ( ineM
% 0.31/0.46 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.46 ? [Ch2: secrecy_chanID] :
% 0.31/0.46 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 0.31/0.46 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.31/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ineM_def
% 0.31/0.46 thf(fact_24_TBlemma3b,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.46 ( ~ ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member1967978193chanID @ Ch @ M2 )
% 0.31/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBlemma3b
% 0.31/0.46 thf(fact_25_TBtheorem1b,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ineM @ PQ @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem1b
% 0.31/0.46 thf(fact_26_TBtheorem3b,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ~ ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem3b
% 0.31/0.46 thf(fact_27_ine__ins__neg1,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 0.31/0.46 ( ~ ( ine @ P @ M )
% 0.31/0.46 => ( ( exprChannel @ X @ M )
% 0.31/0.46 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_ins_neg1
% 0.31/0.46 thf(fact_28_correctCompositionIn__L2,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionIn_L2
% 0.31/0.46 thf(fact_29_Expression_Oinduct,axiom,
% 0.31/0.46 ! [P: secrecy_Expression > $o,Expression: secrecy_Expression] :
% 0.31/0.46 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kE @ X5 ) )
% 0.31/0.46 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sE @ X5 ) )
% 0.31/0.46 => ( ! [X5: nat] : ( P @ ( secrecy_dE @ X5 ) )
% 0.31/0.46 => ( ! [X5: secrecy_specID] : ( P @ ( secrecy_idE @ X5 ) )
% 0.31/0.46 => ( P @ Expression ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.induct
% 0.31/0.46 thf(fact_30_Expression_Oexhaust,axiom,
% 0.31/0.46 ! [Y: secrecy_Expression] :
% 0.31/0.46 ( ! [X12: secrecy_Keys] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_kE @ X12 ) )
% 0.31/0.46 => ( ! [X22: secrecy_Secrets] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_sE @ X22 ) )
% 0.31/0.46 => ( ! [X32: nat] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_dE @ X32 ) )
% 0.31/0.46 => ~ ! [X42: secrecy_specID] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_idE @ X42 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.exhaust
% 0.31/0.46 thf(fact_31_correctCompositionIn__prop1,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 0.31/0.46 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.31/0.46 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionIn_prop1
% 0.31/0.46 thf(fact_32_LocalSecretsComposition1,axiom,
% 0.31/0.46 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition1
% 0.31/0.46 thf(fact_33_LocalSecretsComposition__exprChannel__s,axiom,
% 0.31/0.46 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.31/0.46 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.31/0.46 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_exprChannel_s
% 0.31/0.46 thf(fact_34_TBtheorem3a,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ~ ( ine @ P @ E )
% 0.31/0.46 => ( ~ ( ine @ Q @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem3a
% 0.31/0.46 thf(fact_35_TBtheorem1a,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ine @ PQ @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ine @ P @ E )
% 0.31/0.46 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem1a
% 0.31/0.46 thf(fact_36_singletonI,axiom,
% 0.31/0.46 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_37_singletonI,axiom,
% 0.31/0.46 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_38_singletonI,axiom,
% 0.31/0.46 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_39_singletonI,axiom,
% 0.31/0.46 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_40_singletonI,axiom,
% 0.31/0.46 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_41_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 0.31/0.46 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 0.31/0.46 = ( P @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_42_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 0.31/0.46 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 0.31/0.46 = ( P @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_43_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 0.31/0.46 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 0.31/0.46 = ( P @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_44_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.31/0.46 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 0.31/0.46 = ( P @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.31/0.46 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 0.31/0.46 = ( P @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: set_Secrecy_KS] :
% 0.31/0.46 ( ( collect_Secrecy_KS
% 0.31/0.46 @ ^ [X6: secrecy_KS] : ( member_Secrecy_KS @ X6 @ A ) )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_47_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: set_Secrecy_chanID] :
% 0.31/0.46 ( ( collec625564175chanID
% 0.31/0.46 @ ^ [X6: secrecy_chanID] : ( member1967978193chanID @ X6 @ A ) )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_48_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: set_Secrecy_specID] :
% 0.31/0.46 ( ( collec1545797240specID
% 0.31/0.46 @ ^ [X6: secrecy_specID] : ( member740727610specID @ X6 @ A ) )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_49_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: set_Secrecy_Keys] :
% 0.31/0.46 ( ( collect_Secrecy_Keys
% 0.31/0.46 @ ^ [X6: secrecy_Keys] : ( member_Secrecy_Keys @ X6 @ A ) )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_50_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: set_Secrecy_Secrets] :
% 0.31/0.46 ( ( collec836099393ecrets
% 0.31/0.46 @ ^ [X6: secrecy_Secrets] : ( member2138796287ecrets @ X6 @ A ) )
% 0.31/0.46 = A ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_51_LocalSecretsComposition__neg1__k,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_neg1_k
% 0.31/0.46 thf(fact_52_LocalSecretsComposition__ine2__k,axiom,
% 0.31/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.31/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_ine2_k
% 0.31/0.46 thf(fact_53_LocalSecretsComposition__ine1__k,axiom,
% 0.31/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.31/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_ine1_k
% 0.31/0.46 thf(fact_54_TBtheorem4b__P,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( member1967978193chanID @ Ch3 @ ( ins @ Q ) )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 0.31/0.46 & ( member1967978193chanID @ Ch3 @ M2 ) )
% 0.31/0.46 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4b_P
% 0.31/0.46 thf(fact_55_TBtheorem4b__PQ,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 | ( ineM @ Q @ M2 @ E ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 0.31/0.46 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.31/0.46 & ( member1967978193chanID @ Ch3 @ M2 )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4b_PQ
% 0.31/0.46 thf(fact_56_TBtheorem4a__P,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ine @ P @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_P
% 0.31/0.46 thf(fact_57_TBtheorem4a__PQ,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ( ( ine @ P @ E )
% 0.31/0.46 | ( ine @ Q @ E ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 0.31/0.46 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_PQ
% 0.31/0.47 thf(fact_58_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.31/0.47 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_59_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.31/0.47 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_60_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.31/0.47 ( ( ~ ( member740727610specID @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_61_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.31/0.47 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_62_insertCI,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.31/0.47 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 0.31/0.47 => ( A2 = B2 ) )
% 0.31/0.47 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_63_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_64_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_65_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member740727610specID @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_66_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_67_insert__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.31/0.47 = ( ( A2 = B2 )
% 0.31/0.47 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_68_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P: secrecy_specID > $o] :
% 0.31/0.47 ( ( bot_bo1785112429specID
% 0.31/0.47 = ( collec1545797240specID @ P ) )
% 0.31/0.47 = ( ! [X6: secrecy_specID] :
% 0.31/0.47 ~ ( P @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_69_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P: secrecy_chanID > $o] :
% 0.31/0.47 ( ( bot_bo443197316chanID
% 0.31/0.47 = ( collec625564175chanID @ P ) )
% 0.31/0.47 = ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ~ ( P @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_70_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P: secrecy_specID > $o] :
% 0.31/0.47 ( ( ( collec1545797240specID @ P )
% 0.31/0.47 = bot_bo1785112429specID )
% 0.31/0.47 = ( ! [X6: secrecy_specID] :
% 0.31/0.47 ~ ( P @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_71_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P: secrecy_chanID > $o] :
% 0.31/0.47 ( ( ( collec625564175chanID @ P )
% 0.31/0.47 = bot_bo443197316chanID )
% 0.31/0.47 = ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ~ ( P @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_72_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ( ! [X6: secrecy_KS] :
% 0.31/0.47 ~ ( member_Secrecy_KS @ X6 @ A ) )
% 0.31/0.47 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_73_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( ! [X6: secrecy_Keys] :
% 0.31/0.47 ~ ( member_Secrecy_Keys @ X6 @ A ) )
% 0.31/0.47 = ( A = bot_bo701486667y_Keys ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_74_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( ! [X6: secrecy_Secrets] :
% 0.31/0.47 ~ ( member2138796287ecrets @ X6 @ A ) )
% 0.31/0.47 = ( A = bot_bo1124690338ecrets ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_75_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ( ! [X6: secrecy_specID] :
% 0.31/0.47 ~ ( member740727610specID @ X6 @ A ) )
% 0.31/0.47 = ( A = bot_bo1785112429specID ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_76_all__not__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ~ ( member1967978193chanID @ X6 @ A ) )
% 0.31/0.47 = ( A = bot_bo443197316chanID ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_77_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_KS] :
% 0.31/0.47 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_78_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_Keys] :
% 0.31/0.47 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_79_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_Secrets] :
% 0.31/0.47 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_80_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_specID] :
% 0.31/0.47 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_81_empty__iff,axiom,
% 0.31/0.47 ! [C: secrecy_chanID] :
% 0.31/0.47 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_82_insert__absorb2,axiom,
% 0.31/0.47 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A ) )
% 0.31/0.47 = ( insert1671894227specID @ X @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb2
% 0.31/0.47 thf(fact_83_insert__absorb2,axiom,
% 0.31/0.47 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A ) )
% 0.31/0.47 = ( insert751661162chanID @ X @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb2
% 0.31/0.47 thf(fact_84_TBtheorem4a__empty,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ( ine @ P @ E )
% 0.31/0.47 | ( ine @ Q @ E ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( ( loc @ PQ )
% 0.31/0.47 = bot_bo443197316chanID )
% 0.31/0.47 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem4a_empty
% 0.31/0.47 thf(fact_85_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ( ? [X6: secrecy_KS] : ( member_Secrecy_KS @ X6 @ A ) )
% 0.31/0.47 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_86_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( ? [X6: secrecy_Keys] : ( member_Secrecy_Keys @ X6 @ A ) )
% 0.31/0.47 = ( A != bot_bo701486667y_Keys ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_87_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( ? [X6: secrecy_Secrets] : ( member2138796287ecrets @ X6 @ A ) )
% 0.31/0.47 = ( A != bot_bo1124690338ecrets ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_88_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ( ? [X6: secrecy_specID] : ( member740727610specID @ X6 @ A ) )
% 0.31/0.47 = ( A != bot_bo1785112429specID ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_89_ex__in__conv,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ? [X6: secrecy_chanID] : ( member1967978193chanID @ X6 @ A ) )
% 0.31/0.47 = ( A != bot_bo443197316chanID ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_90_equals0I,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ! [Y5: secrecy_KS] :
% 0.31/0.47 ~ ( member_Secrecy_KS @ Y5 @ A )
% 0.31/0.47 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_91_equals0I,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Keys] :
% 0.31/0.47 ( ! [Y5: secrecy_Keys] :
% 0.31/0.47 ~ ( member_Secrecy_Keys @ Y5 @ A )
% 0.31/0.47 => ( A = bot_bo701486667y_Keys ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_92_equals0I,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ! [Y5: secrecy_Secrets] :
% 0.31/0.47 ~ ( member2138796287ecrets @ Y5 @ A )
% 0.31/0.47 => ( A = bot_bo1124690338ecrets ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_93_equals0I,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ! [Y5: secrecy_specID] :
% 0.31/0.47 ~ ( member740727610specID @ Y5 @ A )
% 0.31/0.47 => ( A = bot_bo1785112429specID ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_94_equals0I,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ! [Y5: secrecy_chanID] :
% 0.31/0.47 ~ ( member1967978193chanID @ Y5 @ A )
% 0.31/0.47 => ( A = bot_bo443197316chanID ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_95_equals0D,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 0.31/0.47 ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_96_equals0D,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 0.31/0.47 ( ( A = bot_bo701486667y_Keys )
% 0.31/0.47 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_97_equals0D,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 0.31/0.47 ( ( A = bot_bo1124690338ecrets )
% 0.31/0.47 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_98_equals0D,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 0.31/0.47 ( ( A = bot_bo1785112429specID )
% 0.31/0.47 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_99_equals0D,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 0.31/0.47 ( ( A = bot_bo443197316chanID )
% 0.31/0.47 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_100_emptyE,axiom,
% 0.31/0.47 ! [A2: secrecy_KS] :
% 0.31/0.47 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_101_emptyE,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys] :
% 0.31/0.47 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_102_emptyE,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets] :
% 0.31/0.47 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_103_emptyE,axiom,
% 0.31/0.47 ! [A2: secrecy_specID] :
% 0.31/0.47 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_104_emptyE,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID] :
% 0.31/0.47 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_105_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ A2 @ A )
% 0.31/0.47 => ? [B3: set_Secrecy_KS] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 0.31/0.47 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_106_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ A2 @ A )
% 0.31/0.47 => ? [B3: set_Secrecy_chanID] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert751661162chanID @ A2 @ B3 ) )
% 0.31/0.47 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_107_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ A2 @ A )
% 0.31/0.47 => ? [B3: set_Secrecy_specID] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert1671894227specID @ A2 @ B3 ) )
% 0.31/0.47 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_108_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.31/0.47 => ? [B3: set_Secrecy_Keys] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 0.31/0.47 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_109_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ A2 @ A )
% 0.31/0.47 => ? [B3: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert565337510ecrets @ A2 @ B3 ) )
% 0.31/0.47 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_110_insert__commute,axiom,
% 0.31/0.47 ! [X: secrecy_specID,Y: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y @ A ) )
% 0.31/0.47 = ( insert1671894227specID @ Y @ ( insert1671894227specID @ X @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_commute
% 0.31/0.47 thf(fact_111_insert__commute,axiom,
% 0.31/0.47 ! [X: secrecy_chanID,Y: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y @ A ) )
% 0.31/0.47 = ( insert751661162chanID @ Y @ ( insert751661162chanID @ X @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_commute
% 0.31/0.47 thf(fact_112_insert__eq__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 0.31/0.47 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 0.31/0.47 = ( insert_Secrecy_KS @ B2 @ B ) )
% 0.31/0.47 = ( ( ( A2 = B2 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 & ( ( A2 != B2 )
% 0.31/0.47 => ? [C2: set_Secrecy_KS] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 0.31/0.47 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 0.31/0.47 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_113_insert__eq__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ~ ( member1967978193chanID @ A2 @ A )
% 0.31/0.47 => ( ~ ( member1967978193chanID @ B2 @ B )
% 0.31/0.47 => ( ( ( insert751661162chanID @ A2 @ A )
% 0.31/0.47 = ( insert751661162chanID @ B2 @ B ) )
% 0.31/0.47 = ( ( ( A2 = B2 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 & ( ( A2 != B2 )
% 0.31/0.47 => ? [C2: set_Secrecy_chanID] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert751661162chanID @ B2 @ C2 ) )
% 0.31/0.47 & ~ ( member1967978193chanID @ B2 @ C2 )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert751661162chanID @ A2 @ C2 ) )
% 0.31/0.47 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_114_insert__eq__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ~ ( member740727610specID @ A2 @ A )
% 0.31/0.47 => ( ~ ( member740727610specID @ B2 @ B )
% 0.31/0.47 => ( ( ( insert1671894227specID @ A2 @ A )
% 0.31/0.47 = ( insert1671894227specID @ B2 @ B ) )
% 0.31/0.47 = ( ( ( A2 = B2 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 & ( ( A2 != B2 )
% 0.31/0.47 => ? [C2: set_Secrecy_specID] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert1671894227specID @ B2 @ C2 ) )
% 0.31/0.47 & ~ ( member740727610specID @ B2 @ C2 )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert1671894227specID @ A2 @ C2 ) )
% 0.31/0.47 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_115_insert__eq__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.47 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 0.31/0.47 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 0.31/0.47 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.31/0.47 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 0.31/0.47 = ( ( ( A2 = B2 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 & ( ( A2 != B2 )
% 0.31/0.47 => ? [C2: set_Secrecy_Keys] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 0.31/0.47 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 0.31/0.47 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_116_insert__eq__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.47 ( ~ ( member2138796287ecrets @ A2 @ A )
% 0.31/0.47 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 0.31/0.47 => ( ( ( insert565337510ecrets @ A2 @ A )
% 0.31/0.47 = ( insert565337510ecrets @ B2 @ B ) )
% 0.31/0.47 = ( ( ( A2 = B2 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 & ( ( A2 != B2 )
% 0.31/0.47 => ? [C2: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert565337510ecrets @ B2 @ C2 ) )
% 0.31/0.47 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert565337510ecrets @ A2 @ C2 ) )
% 0.31/0.47 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_117_insert__absorb,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ A2 @ A )
% 0.31/0.47 => ( ( insert_Secrecy_KS @ A2 @ A )
% 0.31/0.47 = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_118_insert__absorb,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ A2 @ A )
% 0.31/0.47 => ( ( insert751661162chanID @ A2 @ A )
% 0.31/0.47 = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_119_insert__absorb,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ A2 @ A )
% 0.31/0.47 => ( ( insert1671894227specID @ A2 @ A )
% 0.31/0.47 = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_120_insert__absorb,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.31/0.47 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.31/0.47 = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_121_insert__absorb,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ A2 @ A )
% 0.31/0.47 => ( ( insert565337510ecrets @ A2 @ A )
% 0.31/0.47 = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_122_insert__ident,axiom,
% 0.31/0.47 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ~ ( member_Secrecy_KS @ X @ A )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ X @ B )
% 0.31/0.47 => ( ( ( insert_Secrecy_KS @ X @ A )
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ B ) )
% 0.31/0.47 = ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_123_insert__ident,axiom,
% 0.31/0.47 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ~ ( member1967978193chanID @ X @ A )
% 0.31/0.47 => ( ~ ( member1967978193chanID @ X @ B )
% 0.31/0.47 => ( ( ( insert751661162chanID @ X @ A )
% 0.31/0.47 = ( insert751661162chanID @ X @ B ) )
% 0.31/0.47 = ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_124_insert__ident,axiom,
% 0.31/0.47 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ~ ( member740727610specID @ X @ A )
% 0.31/0.47 => ( ~ ( member740727610specID @ X @ B )
% 0.31/0.47 => ( ( ( insert1671894227specID @ X @ A )
% 0.31/0.47 = ( insert1671894227specID @ X @ B ) )
% 0.31/0.47 = ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_125_insert__ident,axiom,
% 0.31/0.47 ! [X: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.47 ( ~ ( member_Secrecy_Keys @ X @ A )
% 0.31/0.47 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 0.31/0.47 => ( ( ( insert_Secrecy_Keys @ X @ A )
% 0.31/0.47 = ( insert_Secrecy_Keys @ X @ B ) )
% 0.31/0.47 = ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_126_insert__ident,axiom,
% 0.31/0.47 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.47 ( ~ ( member2138796287ecrets @ X @ A )
% 0.31/0.47 => ( ~ ( member2138796287ecrets @ X @ B )
% 0.31/0.47 => ( ( ( insert565337510ecrets @ X @ A )
% 0.31/0.47 = ( insert565337510ecrets @ X @ B ) )
% 0.31/0.47 = ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_127_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X @ A )
% 0.31/0.47 => ~ ! [B3: set_Secrecy_KS] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ B3 ) )
% 0.31/0.47 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_128_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X @ A )
% 0.31/0.47 => ~ ! [B3: set_Secrecy_chanID] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert751661162chanID @ X @ B3 ) )
% 0.31/0.47 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_129_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ X @ A )
% 0.31/0.47 => ~ ! [B3: set_Secrecy_specID] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert1671894227specID @ X @ B3 ) )
% 0.31/0.47 => ( member740727610specID @ X @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_130_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ X @ A )
% 0.31/0.47 => ~ ! [B3: set_Secrecy_Keys] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 0.31/0.47 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_131_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ X @ A )
% 0.31/0.47 => ~ ! [B3: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( insert565337510ecrets @ X @ B3 ) )
% 0.31/0.47 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_132_insertI2,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ A2 @ B )
% 0.31/0.47 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_133_insertI2,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ A2 @ B )
% 0.31/0.47 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_134_insertI2,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ A2 @ B )
% 0.31/0.47 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_135_insertI2,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ A2 @ B )
% 0.31/0.47 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_136_insertI2,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ A2 @ B )
% 0.31/0.47 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_137_insertI1,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_138_insertI1,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_139_insertI1,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_140_insertI1,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_141_insertI1,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_142_insertE,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.31/0.47 => ( ( A2 != B2 )
% 0.31/0.47 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_143_insertE,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.31/0.47 => ( ( A2 != B2 )
% 0.31/0.47 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_144_insertE,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.31/0.47 => ( ( A2 != B2 )
% 0.31/0.47 => ( member740727610specID @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_145_insertE,axiom,
% 0.31/0.47 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.31/0.47 => ( ( A2 != B2 )
% 0.31/0.47 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_146_insertE,axiom,
% 0.31/0.47 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.31/0.47 => ( ( A2 != B2 )
% 0.31/0.47 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_147_correctCompositionIn__L1,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.47 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionIn_L1
% 0.31/0.47 thf(fact_148_singleton__inject,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 0.31/0.47 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 0.31/0.47 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.31/0.47 => ( A2 = B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_inject
% 0.31/0.47 thf(fact_149_singleton__inject,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 0.31/0.47 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 0.31/0.47 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.31/0.47 => ( A2 = B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_inject
% 0.31/0.47 thf(fact_150_insert__not__empty,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( insert1671894227specID @ A2 @ A )
% 0.31/0.47 != bot_bo1785112429specID ) ).
% 0.31/0.47
% 0.31/0.47 % insert_not_empty
% 0.31/0.47 thf(fact_151_insert__not__empty,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( insert751661162chanID @ A2 @ A )
% 0.31/0.47 != bot_bo443197316chanID ) ).
% 0.31/0.47
% 0.31/0.47 % insert_not_empty
% 0.31/0.47 thf(fact_152_doubleton__eq__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 0.31/0.47 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.31/0.47 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 0.31/0.47 = ( ( ( A2 = C )
% 0.31/0.47 & ( B2 = D ) )
% 0.31/0.47 | ( ( A2 = D )
% 0.31/0.47 & ( B2 = C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % doubleton_eq_iff
% 0.31/0.47 thf(fact_153_doubleton__eq__iff,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 0.31/0.47 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.31/0.47 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 0.31/0.47 = ( ( ( A2 = C )
% 0.31/0.47 & ( B2 = D ) )
% 0.31/0.47 | ( ( A2 = D )
% 0.31/0.47 & ( B2 = C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % doubleton_eq_iff
% 0.31/0.47 thf(fact_154_singleton__iff,axiom,
% 0.31/0.47 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.31/0.47 = ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_155_singleton__iff,axiom,
% 0.31/0.47 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.31/0.47 = ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_156_singleton__iff,axiom,
% 0.31/0.47 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.31/0.47 = ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_157_singleton__iff,axiom,
% 0.31/0.47 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.31/0.47 = ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_158_singleton__iff,axiom,
% 0.31/0.47 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.31/0.47 = ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_159_singletonD,axiom,
% 0.31/0.47 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.31/0.47 => ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_160_singletonD,axiom,
% 0.31/0.47 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.31/0.47 => ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_161_singletonD,axiom,
% 0.31/0.47 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.31/0.47 => ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_162_singletonD,axiom,
% 0.31/0.47 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.31/0.47 => ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_163_singletonD,axiom,
% 0.31/0.47 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.31/0.47 => ( B2 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_164_correctCompositionInLoc__exprChannel,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ M )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ( ins @ PQ ) )
% 0.31/0.47 => ~ ( exprChannel @ X5 @ M ) )
% 0.31/0.47 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionInLoc_exprChannel
% 0.31/0.47 thf(fact_165_subcomponents__loc,axiom,
% 0.31/0.47 ! [X: secrecy_specID] :
% 0.31/0.47 ( ( correc965049635ionLoc @ X )
% 0.31/0.47 => ( ( ( subcomponents @ X )
% 0.31/0.47 = bot_bo1785112429specID )
% 0.31/0.47 => ( ( loc @ X )
% 0.31/0.47 = bot_bo443197316chanID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subcomponents_loc
% 0.31/0.47 thf(fact_166_TBtheorem4b__notP1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ineM @ P @ M2 @ E )
% 0.31/0.47 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ M2 )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem4b_notP1
% 0.31/0.47 thf(fact_167_TBtheorem4a__notP1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ine @ P @ E )
% 0.31/0.47 => ( ~ ( ine @ Q @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem4a_notP1
% 0.31/0.47 thf(fact_168_TBtheorem4b__notPQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.47 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetP )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem4b_notPQ
% 0.31/0.47 thf(fact_169_TBtheorem4b__notP2,axiom,
% 0.31/0.47 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.47 ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSet )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem4b_notP2
% 0.31/0.47 thf(fact_170_TBtheorem4a__notPQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.47 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetP )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem4a_notPQ
% 0.31/0.47 thf(fact_171_TBtheorem4a__notP2,axiom,
% 0.31/0.47 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.47 ( ~ ( ine @ Q @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSet )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem4a_notP2
% 0.31/0.47 thf(fact_172_ine__exprChannelSet__Single,axiom,
% 0.31/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.31/0.47 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % ine_exprChannelSet_Single
% 0.31/0.47 thf(fact_173_ine__exprChannelSingle__Set,axiom,
% 0.31/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.31/0.47 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % ine_exprChannelSingle_Set
% 0.31/0.47 thf(fact_174_ine__nonempty__exprChannelSet,axiom,
% 0.31/0.47 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ( ChSet != bot_bo443197316chanID )
% 0.31/0.47 => ( ine @ P @ E ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ine_nonempty_exprChannelSet
% 0.31/0.47 thf(fact_175_ine__empty__exprChannelSet,axiom,
% 0.31/0.47 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ( ChSet = bot_bo443197316chanID )
% 0.31/0.47 => ~ ( ine @ P @ E ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ine_empty_exprChannelSet
% 0.31/0.47 thf(fact_176_ine__exprChannelSet__def,axiom,
% 0.31/0.47 ( ine_exprChannelSet
% 0.31/0.47 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ ChSet2 )
% 0.31/0.47 => ( ( member1967978193chanID @ X6 @ ( ins @ SP ) )
% 0.31/0.47 & ( exprChannel @ X6 @ E2 ) ) )
% 0.31/0.47 & ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( ~ ( member1967978193chanID @ X6 @ ChSet2 )
% 0.31/0.47 & ( member1967978193chanID @ X6 @ ( ins @ SP ) ) )
% 0.31/0.47 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ine_exprChannelSet_def
% 0.31/0.47 thf(fact_177_ine__exprChannelSingle__def,axiom,
% 0.31/0.47 ( ine_ex1303305700Single
% 0.31/0.47 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 0.31/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.31/0.47 & ! [X6: secrecy_chanID,T: nat] :
% 0.31/0.47 ( ( ( member1967978193chanID @ X6 @ ( ins @ SP ) )
% 0.31/0.47 & ( X6 != Ch2 ) )
% 0.31/0.47 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ine_exprChannelSingle_def
% 0.31/0.47 thf(fact_178_LocalSecretsComposition__neg1,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ! [M4: secrecy_Keys] :
% 0.31/0.47 ( ( Ks
% 0.31/0.47 = ( secrecy_kKS @ M4 ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.31/0.47 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.31/0.47 => ( ! [M4: secrecy_Secrets] :
% 0.31/0.47 ( ( Ks
% 0.31/0.47 = ( secrecy_sKS @ M4 ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.31/0.47 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg1
% 0.31/0.47 thf(fact_179_locStream__def,axiom,
% 0.31/0.47 ( locStream
% 0.31/0.47 = ( ^ [X6: secrecy_specID] :
% 0.31/0.47 ( ^ [Y6: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y6 = Z )
% 0.31/0.47 @ ( loc @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % locStream_def
% 0.31/0.47 thf(fact_180_inStream__def,axiom,
% 0.31/0.47 ( inStream
% 0.31/0.47 = ( ^ [X6: secrecy_specID] :
% 0.31/0.47 ( ^ [Y6: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y6 = Z )
% 0.31/0.47 @ ( ins @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % inStream_def
% 0.31/0.47 thf(fact_181_the__elem__eq,axiom,
% 0.31/0.47 ! [X: secrecy_specID] :
% 0.31/0.47 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % the_elem_eq
% 0.31/0.47 thf(fact_182_the__elem__eq,axiom,
% 0.31/0.47 ! [X: secrecy_chanID] :
% 0.31/0.47 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % the_elem_eq
% 0.31/0.47 thf(fact_183_LocalSecretsComposition__ine1__s,axiom,
% 0.31/0.47 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.47 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_ine1_s
% 0.31/0.47 thf(fact_184_KS_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.31/0.47 ( ( ( secrecy_sKS @ X2 )
% 0.31/0.47 = ( secrecy_sKS @ Y2 ) )
% 0.31/0.47 = ( X2 = Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % KS.inject(2)
% 0.31/0.47 thf(fact_185_bot__set__def,axiom,
% 0.31/0.47 ( bot_bo1785112429specID
% 0.31/0.47 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_set_def
% 0.31/0.47 thf(fact_186_bot__set__def,axiom,
% 0.31/0.47 ( bot_bo443197316chanID
% 0.31/0.47 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_set_def
% 0.31/0.47 thf(fact_187_KS_Oexhaust,axiom,
% 0.31/0.47 ! [Y: secrecy_KS] :
% 0.31/0.47 ( ! [X12: secrecy_Keys] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( secrecy_kKS @ X12 ) )
% 0.31/0.47 => ~ ! [X22: secrecy_Secrets] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % KS.exhaust
% 0.31/0.47 thf(fact_188_KS_Oinduct,axiom,
% 0.31/0.47 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.31/0.47 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kKS @ X5 ) )
% 0.31/0.47 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X5 ) )
% 0.31/0.47 => ( P @ KS ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % KS.induct
% 0.31/0.47 thf(fact_189_KS_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.31/0.47 ( ( secrecy_kKS @ X1 )
% 0.31/0.47 != ( secrecy_sKS @ X2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % KS.distinct(1)
% 0.31/0.47 thf(fact_190_KS2Expression_Osimps_I2_J,axiom,
% 0.31/0.47 ! [M: secrecy_Secrets] :
% 0.31/0.47 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.31/0.47 = ( secrecy_sE @ M ) ) ).
% 0.31/0.47
% 0.31/0.47 % KS2Expression.simps(2)
% 0.31/0.47 thf(fact_191_not__know__s__not__ine,axiom,
% 0.31/0.47 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_know_s_not_ine
% 0.31/0.47 thf(fact_192_know_Osimps_I2_J,axiom,
% 0.31/0.47 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.31/0.47 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % know.simps(2)
% 0.31/0.47 thf(fact_193_LocalSecretsComposition__neg1__s,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg1_s
% 0.31/0.47 thf(fact_194_LocalSecretsComposition__ine2__s,axiom,
% 0.31/0.47 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.47 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_ine2_s
% 0.31/0.47 thf(fact_195_is__singleton__the__elem,axiom,
% 0.31/0.47 ( is_sin1501507247specID
% 0.31/0.47 = ( ^ [A3: set_Secrecy_specID] :
% 0.31/0.47 ( A3
% 0.31/0.47 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singleton_the_elem
% 0.31/0.47 thf(fact_196_is__singleton__the__elem,axiom,
% 0.31/0.47 ( is_sin581274182chanID
% 0.31/0.47 = ( ^ [A3: set_Secrecy_chanID] :
% 0.31/0.47 ( A3
% 0.31/0.47 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singleton_the_elem
% 0.31/0.47 thf(fact_197_is__singletonI,axiom,
% 0.31/0.47 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonI
% 0.31/0.47 thf(fact_198_is__singletonI,axiom,
% 0.31/0.47 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonI
% 0.31/0.47 thf(fact_199_LocalSecretsComposition__neg__loc__s,axiom,
% 0.31/0.47 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.47 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg_loc_s
% 0.31/0.47 thf(fact_200_LocalSecretsComposition__neg__loc__k,axiom,
% 0.31/0.47 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.47 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg_loc_k
% 0.31/0.47 thf(fact_201_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ? [Ch4: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_s_Qex
% 0.31/0.47 thf(fact_202_correctCompositionKS__PQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.47 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_PQ
% 0.31/0.47 thf(fact_203_correctCompositionKS__neg1,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_neg1
% 0.31/0.47 thf(fact_204_correctCompositionKS__negP,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_negP
% 0.31/0.47 thf(fact_205_correctCompositionKS__negQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_negQ
% 0.31/0.47 thf(fact_206_is__singletonI_H,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ( A != bot_bo1943466239ecy_KS )
% 0.31/0.47 => ( ! [X5: secrecy_KS,Y5: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X5 @ A )
% 0.31/0.47 => ( ( member_Secrecy_KS @ Y5 @ A )
% 0.31/0.47 => ( X5 = Y5 ) ) )
% 0.31/0.47 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonI'
% 0.31/0.47 thf(fact_207_is__singletonI_H,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( A != bot_bo701486667y_Keys )
% 0.31/0.47 => ( ! [X5: secrecy_Keys,Y5: secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ X5 @ A )
% 0.31/0.47 => ( ( member_Secrecy_Keys @ Y5 @ A )
% 0.31/0.47 => ( X5 = Y5 ) ) )
% 0.31/0.47 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonI'
% 0.31/0.47 thf(fact_208_is__singletonI_H,axiom,
% 0.31/0.47 ! [A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( A != bot_bo1124690338ecrets )
% 0.31/0.47 => ( ! [X5: secrecy_Secrets,Y5: secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ X5 @ A )
% 0.31/0.47 => ( ( member2138796287ecrets @ Y5 @ A )
% 0.31/0.47 => ( X5 = Y5 ) ) )
% 0.31/0.47 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonI'
% 0.31/0.47 thf(fact_209_is__singletonI_H,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ( A != bot_bo1785112429specID )
% 0.31/0.47 => ( ! [X5: secrecy_specID,Y5: secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ X5 @ A )
% 0.31/0.47 => ( ( member740727610specID @ Y5 @ A )
% 0.31/0.47 => ( X5 = Y5 ) ) )
% 0.31/0.47 => ( is_sin1501507247specID @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonI'
% 0.31/0.47 thf(fact_210_is__singletonI_H,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( A != bot_bo443197316chanID )
% 0.31/0.47 => ( ! [X5: secrecy_chanID,Y5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ A )
% 0.31/0.47 => ( ( member1967978193chanID @ Y5 @ A )
% 0.31/0.47 => ( X5 = Y5 ) ) )
% 0.31/0.47 => ( is_sin581274182chanID @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonI'
% 0.31/0.47 thf(fact_211_know__composition,axiom,
% 0.31/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ( ( knowle945212990e_know @ P @ M )
% 0.31/0.47 | ( knowle945212990e_know @ Q @ M ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % know_composition
% 0.31/0.47 thf(fact_212_know__composition1,axiom,
% 0.31/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ( knowle945212990e_know @ P @ M )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % know_composition1
% 0.31/0.47 thf(fact_213_know__composition2,axiom,
% 0.31/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ( knowle945212990e_know @ Q @ M )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % know_composition2
% 0.31/0.47 thf(fact_214_is__singletonE,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ( is_sin1501507247specID @ A )
% 0.31/0.47 => ~ ! [X5: secrecy_specID] :
% 0.31/0.47 ( A
% 0.31/0.47 != ( insert1671894227specID @ X5 @ bot_bo1785112429specID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonE
% 0.31/0.47 thf(fact_215_is__singletonE,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( is_sin581274182chanID @ A )
% 0.31/0.47 => ~ ! [X5: secrecy_chanID] :
% 0.31/0.47 ( A
% 0.31/0.47 != ( insert751661162chanID @ X5 @ bot_bo443197316chanID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singletonE
% 0.31/0.47 thf(fact_216_is__singleton__def,axiom,
% 0.31/0.47 ( is_sin1501507247specID
% 0.31/0.47 = ( ^ [A3: set_Secrecy_specID] :
% 0.31/0.47 ? [X6: secrecy_specID] :
% 0.31/0.47 ( A3
% 0.31/0.47 = ( insert1671894227specID @ X6 @ bot_bo1785112429specID ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singleton_def
% 0.31/0.47 thf(fact_217_is__singleton__def,axiom,
% 0.31/0.47 ( is_sin581274182chanID
% 0.31/0.47 = ( ^ [A3: set_Secrecy_chanID] :
% 0.31/0.47 ? [X6: secrecy_chanID] :
% 0.31/0.47 ( A3
% 0.31/0.47 = ( insert751661162chanID @ X6 @ bot_bo443197316chanID ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_singleton_def
% 0.31/0.47 thf(fact_218_correctCompositionKS__exprChannel__k__P,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_k_P
% 0.31/0.47 thf(fact_219_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_k_Q
% 0.31/0.47 thf(fact_220_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ? [Ch4: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_k_Pex
% 0.31/0.47 thf(fact_221_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ? [Ch4: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_k_Qex
% 0.31/0.47 thf(fact_222_correctCompositionKS__exprChannel__s__P,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_s_P
% 0.31/0.47 thf(fact_223_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_s_Q
% 0.31/0.47 thf(fact_224_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.31/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.47 => ( ( correctCompositionIn @ PQ )
% 0.31/0.47 => ? [Ch4: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.47 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_exprChannel_s_Pex
% 0.31/0.47 thf(fact_225_LocalSecretsComposition__neg,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ! [M4: secrecy_Keys] :
% 0.31/0.47 ( ( Ks
% 0.31/0.47 = ( secrecy_kKS @ M4 ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.31/0.47 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.31/0.47 => ( ! [M4: secrecy_Secrets] :
% 0.31/0.47 ( ( Ks
% 0.31/0.47 = ( secrecy_sKS @ M4 ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.31/0.47 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg
% 0.31/0.47 thf(fact_226_LocalSecretsComposition__neg__s,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg_s
% 0.31/0.47 thf(fact_227_LocalSecretsComposition__neg__k,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg_k
% 0.31/0.47 thf(fact_228_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bot_Secrecy_KS_o
% 0.31/0.47 = ( ^ [X6: secrecy_KS] : ( member_Secrecy_KS @ X6 @ bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_229_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bo2072920570Keys_o
% 0.31/0.47 = ( ^ [X6: secrecy_Keys] : ( member_Secrecy_Keys @ X6 @ bot_bo701486667y_Keys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_230_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bo1909946299rets_o
% 0.31/0.47 = ( ^ [X6: secrecy_Secrets] : ( member2138796287ecrets @ X6 @ bot_bo1124690338ecrets ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_231_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bo1767780696ecID_o
% 0.31/0.47 = ( ^ [X6: secrecy_specID] : ( member740727610specID @ X6 @ bot_bo1785112429specID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_232_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bo1012329985anID_o
% 0.31/0.47 = ( ^ [X6: secrecy_chanID] : ( member1967978193chanID @ X6 @ bot_bo443197316chanID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_233_UnCI,axiom,
% 0.31/0.47 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( ~ ( member740727610specID @ C @ B )
% 0.31/0.47 => ( member740727610specID @ C @ A ) )
% 0.31/0.47 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_234_UnCI,axiom,
% 0.31/0.47 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 0.31/0.47 => ( member_Secrecy_Keys @ C @ A ) )
% 0.31/0.47 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_235_UnCI,axiom,
% 0.31/0.47 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( ~ ( member2138796287ecrets @ C @ B )
% 0.31/0.47 => ( member2138796287ecrets @ C @ A ) )
% 0.31/0.47 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_236_UnCI,axiom,
% 0.31/0.47 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 0.31/0.47 => ( member_Secrecy_KS @ C @ A ) )
% 0.31/0.47 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_237_UnCI,axiom,
% 0.31/0.47 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ~ ( member1967978193chanID @ C @ B )
% 0.31/0.47 => ( member1967978193chanID @ C @ A ) )
% 0.31/0.47 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_238_Un__iff,axiom,
% 0.31/0.47 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.31/0.47 = ( ( member740727610specID @ C @ A )
% 0.31/0.47 | ( member740727610specID @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_239_Un__iff,axiom,
% 0.31/0.47 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.31/0.47 = ( ( member_Secrecy_Keys @ C @ A )
% 0.31/0.47 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_240_Un__iff,axiom,
% 0.31/0.47 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.31/0.47 = ( ( member2138796287ecrets @ C @ A )
% 0.31/0.47 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_241_Un__iff,axiom,
% 0.31/0.47 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.47 = ( ( member_Secrecy_KS @ C @ A )
% 0.31/0.47 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_242_Un__iff,axiom,
% 0.31/0.47 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.47 = ( ( member1967978193chanID @ C @ A )
% 0.31/0.47 | ( member1967978193chanID @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_243_Un__empty,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.31/0.47 = bot_bo1943466239ecy_KS )
% 0.31/0.47 = ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.47 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty
% 0.31/0.47 thf(fact_244_Un__empty,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ( ( sup_su1712599557specID @ A @ B )
% 0.31/0.47 = bot_bo1785112429specID )
% 0.31/0.47 = ( ( A = bot_bo1785112429specID )
% 0.31/0.47 & ( B = bot_bo1785112429specID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty
% 0.31/0.47 thf(fact_245_Un__empty,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ( sup_su370684444chanID @ A @ B )
% 0.31/0.47 = bot_bo443197316chanID )
% 0.31/0.47 = ( ( A = bot_bo443197316chanID )
% 0.31/0.47 & ( B = bot_bo443197316chanID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty
% 0.31/0.47 thf(fact_246_Un__insert__right,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 0.31/0.47 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_right
% 0.31/0.47 thf(fact_247_Un__insert__right,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 0.31/0.47 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_right
% 0.31/0.47 thf(fact_248_Un__insert__right,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 0.31/0.47 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_right
% 0.31/0.47 thf(fact_249_Un__insert__left,axiom,
% 0.31/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 0.31/0.47 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_left
% 0.31/0.47 thf(fact_250_Un__insert__left,axiom,
% 0.31/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 0.31/0.47 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_left
% 0.31/0.47 thf(fact_251_Un__insert__left,axiom,
% 0.31/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 0.31/0.47 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_left
% 0.31/0.47 thf(fact_252_Un__empty__right,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_right
% 0.31/0.47 thf(fact_253_Un__empty__right,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_right
% 0.31/0.47 thf(fact_254_Un__empty__right,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_right
% 0.31/0.47 thf(fact_255_Un__empty__left,axiom,
% 0.31/0.47 ! [B: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 0.31/0.47 = B ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_left
% 0.31/0.47 thf(fact_256_Un__empty__left,axiom,
% 0.31/0.47 ! [B: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 0.31/0.47 = B ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_left
% 0.31/0.47 thf(fact_257_Un__empty__left,axiom,
% 0.31/0.47 ! [B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 0.31/0.47 = B ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_left
% 0.31/0.47 thf(fact_258_UnE,axiom,
% 0.31/0.47 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.31/0.47 => ( ~ ( member740727610specID @ C @ A )
% 0.31/0.47 => ( member740727610specID @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_259_UnE,axiom,
% 0.31/0.47 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 0.31/0.47 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_260_UnE,axiom,
% 0.31/0.47 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.31/0.47 => ( ~ ( member2138796287ecrets @ C @ A )
% 0.31/0.47 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_261_UnE,axiom,
% 0.31/0.47 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.47 => ( ~ ( member_Secrecy_KS @ C @ A )
% 0.31/0.47 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_262_UnE,axiom,
% 0.31/0.47 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.47 => ( ~ ( member1967978193chanID @ C @ A )
% 0.31/0.47 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_263_UnI1,axiom,
% 0.31/0.47 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ C @ A )
% 0.31/0.47 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_264_UnI1,axiom,
% 0.31/0.47 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ C @ A )
% 0.31/0.47 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_265_UnI1,axiom,
% 0.31/0.47 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ C @ A )
% 0.31/0.47 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_266_UnI1,axiom,
% 0.31/0.47 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ C @ A )
% 0.31/0.47 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_267_UnI1,axiom,
% 0.31/0.47 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ C @ A )
% 0.31/0.47 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_268_UnI2,axiom,
% 0.31/0.47 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ C @ B )
% 0.31/0.47 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_269_UnI2,axiom,
% 0.31/0.47 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.31/0.47 ( ( member_Secrecy_Keys @ C @ B )
% 0.31/0.47 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_270_UnI2,axiom,
% 0.31/0.47 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.31/0.47 ( ( member2138796287ecrets @ C @ B )
% 0.31/0.47 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_271_UnI2,axiom,
% 0.31/0.47 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ C @ B )
% 0.31/0.47 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_272_UnI2,axiom,
% 0.31/0.47 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ C @ B )
% 0.31/0.47 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_273_bex__Un,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.31/0.47 ( ( ? [X6: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X6 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.47 & ( P @ X6 ) ) )
% 0.31/0.47 = ( ? [X6: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X6 @ A )
% 0.31/0.47 & ( P @ X6 ) )
% 0.31/0.47 | ? [X6: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X6 @ B )
% 0.31/0.47 & ( P @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bex_Un
% 0.31/0.47 thf(fact_274_bex__Un,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.31/0.47 ( ( ? [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.47 & ( P @ X6 ) ) )
% 0.31/0.47 = ( ? [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ A )
% 0.31/0.47 & ( P @ X6 ) )
% 0.31/0.47 | ? [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ B )
% 0.31/0.47 & ( P @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bex_Un
% 0.31/0.47 thf(fact_275_ball__Un,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.31/0.47 ( ( ! [X6: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X6 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.47 => ( P @ X6 ) ) )
% 0.31/0.47 = ( ! [X6: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X6 @ A )
% 0.31/0.47 => ( P @ X6 ) )
% 0.31/0.47 & ! [X6: secrecy_KS] :
% 0.31/0.47 ( ( member_Secrecy_KS @ X6 @ B )
% 0.31/0.47 => ( P @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ball_Un
% 0.31/0.47 thf(fact_276_ball__Un,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.31/0.47 ( ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.47 => ( P @ X6 ) ) )
% 0.31/0.47 = ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ A )
% 0.31/0.47 => ( P @ X6 ) )
% 0.31/0.47 & ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ B )
% 0.31/0.47 => ( P @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ball_Un
% 0.31/0.47 thf(fact_277_Un__assoc,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 0.31/0.47 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_assoc
% 0.31/0.47 thf(fact_278_Un__assoc,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 0.31/0.47 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_assoc
% 0.31/0.47 thf(fact_279_Un__absorb,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ A @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % Un_absorb
% 0.31/0.47 thf(fact_280_Un__absorb,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ A @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % Un_absorb
% 0.31/0.47 thf(fact_281_Un__commute,axiom,
% 0.31/0.47 ( sup_su1301156759ecy_KS
% 0.31/0.47 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_commute
% 0.31/0.47 thf(fact_282_Un__commute,axiom,
% 0.31/0.47 ( sup_su370684444chanID
% 0.31/0.47 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_commute
% 0.31/0.47 thf(fact_283_Un__left__absorb,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.47 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_absorb
% 0.31/0.47 thf(fact_284_Un__left__absorb,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.47 = ( sup_su370684444chanID @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_absorb
% 0.31/0.47 thf(fact_285_Un__left__commute,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 0.31/0.47 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_commute
% 0.31/0.47 thf(fact_286_Un__left__commute,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 0.31/0.47 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_commute
% 0.31/0.47 thf(fact_287_singleton__Un__iff,axiom,
% 0.31/0.47 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.31/0.47 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 0.31/0.47 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.31/0.47 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.47 & ( B = bot_bo1943466239ecy_KS ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_Un_iff
% 0.31/0.47 thf(fact_288_singleton__Un__iff,axiom,
% 0.31/0.47 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.31/0.47 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 0.31/0.47 = ( sup_su1712599557specID @ A @ B ) )
% 0.31/0.47 = ( ( ( A = bot_bo1785112429specID )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.47 & ( B = bot_bo1785112429specID ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_Un_iff
% 0.31/0.47 thf(fact_289_singleton__Un__iff,axiom,
% 0.31/0.47 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 0.31/0.47 = ( sup_su370684444chanID @ A @ B ) )
% 0.31/0.47 = ( ( ( A = bot_bo443197316chanID )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.47 & ( B = bot_bo443197316chanID ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_Un_iff
% 0.31/0.47 thf(fact_290_Un__singleton__iff,axiom,
% 0.31/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 0.31/0.47 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.47 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.47 & ( B = bot_bo1943466239ecy_KS ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_singleton_iff
% 0.31/0.47 thf(fact_291_Un__singleton__iff,axiom,
% 0.31/0.47 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 0.31/0.47 ( ( ( sup_su1712599557specID @ A @ B )
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.47 = ( ( ( A = bot_bo1785112429specID )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.47 & ( B = bot_bo1785112429specID ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_singleton_iff
% 0.31/0.47 thf(fact_292_Un__singleton__iff,axiom,
% 0.31/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 0.31/0.47 ( ( ( sup_su370684444chanID @ A @ B )
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.47 = ( ( ( A = bot_bo443197316chanID )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.47 & ( B = bot_bo443197316chanID ) )
% 0.31/0.47 | ( ( A
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.31/0.47 & ( B
% 0.31/0.47 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_singleton_iff
% 0.31/0.47 thf(fact_293_insert__is__Un,axiom,
% 0.31/0.47 ( insert_Secrecy_KS
% 0.31/0.47 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_is_Un
% 0.31/0.47 thf(fact_294_insert__is__Un,axiom,
% 0.31/0.47 ( insert1671894227specID
% 0.31/0.47 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_is_Un
% 0.31/0.47 thf(fact_295_insert__is__Un,axiom,
% 0.31/0.47 ( insert751661162chanID
% 0.31/0.47 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_is_Un
% 0.31/0.47 thf(fact_296_sup__bot_Oright__neutral,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.right_neutral
% 0.31/0.47 thf(fact_297_sup__bot_Oright__neutral,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.right_neutral
% 0.31/0.47 thf(fact_298_sup__bot_Oright__neutral,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.right_neutral
% 0.31/0.47 thf(fact_299_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.31/0.47 ( ( bot_bo1943466239ecy_KS
% 0.31/0.47 = ( sup_su1301156759ecy_KS @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.31/0.47 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.neutr_eq_iff
% 0.31/0.47 thf(fact_300_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.31/0.47 ( ( bot_bo1785112429specID
% 0.31/0.47 = ( sup_su1712599557specID @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A2 = bot_bo1785112429specID )
% 0.31/0.47 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.neutr_eq_iff
% 0.31/0.47 thf(fact_301_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.31/0.47 ( ( bot_bo443197316chanID
% 0.31/0.47 = ( sup_su370684444chanID @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A2 = bot_bo443197316chanID )
% 0.31/0.47 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.neutr_eq_iff
% 0.31/0.47 thf(fact_302_sup__bot_Oleft__neutral,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A2 )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.left_neutral
% 0.31/0.47 thf(fact_303_sup__bot_Oleft__neutral,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A2 )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.left_neutral
% 0.31/0.47 thf(fact_304_sup__bot_Oleft__neutral,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A2 )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.left_neutral
% 0.31/0.47 thf(fact_305_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.31/0.47 ( ( ( sup_su1301156759ecy_KS @ A2 @ B2 )
% 0.31/0.47 = bot_bo1943466239ecy_KS )
% 0.31/0.47 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.31/0.47 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.eq_neutr_iff
% 0.31/0.47 thf(fact_306_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.31/0.47 ( ( ( sup_su1712599557specID @ A2 @ B2 )
% 0.31/0.47 = bot_bo1785112429specID )
% 0.31/0.47 = ( ( A2 = bot_bo1785112429specID )
% 0.31/0.47 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.eq_neutr_iff
% 0.31/0.47 thf(fact_307_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.47 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ( sup_su370684444chanID @ A2 @ B2 )
% 0.31/0.47 = bot_bo443197316chanID )
% 0.31/0.47 = ( ( A2 = bot_bo443197316chanID )
% 0.31/0.47 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.eq_neutr_iff
% 0.31/0.47 thf(fact_308_sup__bot__left,axiom,
% 0.31/0.47 ! [X: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_left
% 0.31/0.47 thf(fact_309_sup__bot__left,axiom,
% 0.31/0.47 ! [X: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_left
% 0.31/0.47 thf(fact_310_sup__bot__left,axiom,
% 0.31/0.47 ! [X: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_left
% 0.31/0.47 thf(fact_311_sup__bot__right,axiom,
% 0.31/0.47 ! [X: set_Secrecy_KS] :
% 0.31/0.47 ( ( sup_su1301156759ecy_KS @ X @ bot_bo1943466239ecy_KS )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_right
% 0.31/0.47 thf(fact_312_sup__bot__right,axiom,
% 0.31/0.47 ! [X: set_Secrecy_specID] :
% 0.31/0.47 ( ( sup_su1712599557specID @ X @ bot_bo1785112429specID )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_right
% 0.31/0.47 thf(fact_313_sup__bot__right,axiom,
% 0.31/0.47 ! [X: set_Secrecy_chanID] :
% 0.31/0.47 ( ( sup_su370684444chanID @ X @ bot_bo443197316chanID )
% 0.31/0.47 = X ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_right
% 0.31/0.47 thf(fact_314_bot__eq__sup__iff,axiom,
% 0.31/0.47 ! [X: set_Secrecy_KS,Y: set_Secrecy_KS] :
% 0.31/0.47 ( ( bot_bo1943466239ecy_KS
% 0.31/0.47 = ( sup_su1301156759ecy_KS @ X @ Y ) )
% 0.31/0.47 = ( ( X = bot_bo1943466239ecy_KS )
% 0.31/0.47 & ( Y = bot_bo1943466239ecy_KS ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_eq_sup_iff
% 0.31/0.47 thf(fact_315_bot__eq__sup__iff,axiom,
% 0.31/0.47 ! [X: set_Secrecy_specID,Y: set_Secrecy_specID] :
% 0.31/0.47 ( ( bot_bo1785112429specID
% 0.31/0.47 = ( sup_su1712599557specID @ X @ Y ) )
% 0.31/0.47 = ( ( X = bot_bo1785112429specID )
% 0.31/0.47 & ( Y = bot_bo1785112429specID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_eq_sup_iff
% 0.31/0.47 thf(fact_316_bot__eq__sup__iff,axiom,
% 0.31/0.47 ! [X: set_Secrecy_chanID,Y: set_Secrecy_chanID] :
% 0.31/0.47 ( ( bot_bo443197316chanID
% 0.31/0.47 = ( sup_su370684444chanID @ X @ Y ) )
% 0.31/0.47 = ( ( X = bot_bo443197316chanID )
% 0.31/0.47 & ( Y = bot_bo443197316chanID ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_eq_sup_iff
% 0.31/0.47 thf(fact_317_ineM__Un1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,A: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ineM @ P @ A @ E )
% 0.31/0.47 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % ineM_Un1
% 0.31/0.47 thf(fact_318_notSpecKeysSecretsExpr__def,axiom,
% 0.31/0.47 ( notSpe1586871396tsExpr
% 0.31/0.47 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 0.31/0.47 ( ! [X6: secrecy_Keys] :
% 0.31/0.47 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X6 ) @ E3 )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X6 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.31/0.47 & ! [Y7: secrecy_Secrets] :
% 0.31/0.47 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y7 ) @ E3 )
% 0.31/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y7 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % notSpecKeysSecretsExpr_def
% 0.31/0.47 thf(fact_319_TBtheorem5a__empty,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ( eout @ P @ E )
% 0.31/0.47 | ( eout @ Q @ E ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( ( loc @ PQ )
% 0.31/0.47 = bot_bo443197316chanID )
% 0.31/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_empty
% 0.31/0.47 thf(fact_320_correctCompositionKS__subcomp1,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.31/0.47 ( ( correctCompositionKS @ C3 )
% 0.31/0.47 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.47 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 0.31/0.47 => ? [X5: secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ X5 @ ( subcomponents @ C3 ) )
% 0.31/0.47 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X5 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp1
% 0.31/0.47 thf(fact_321_correctCompositionKS__subcomp2,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.31/0.47 ( ( correctCompositionKS @ C3 )
% 0.31/0.47 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.47 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 0.31/0.47 => ? [X5: secrecy_specID] :
% 0.31/0.47 ( ( member740727610specID @ X5 @ ( subcomponents @ C3 ) )
% 0.31/0.47 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X5 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp2
% 0.31/0.47 thf(fact_322_TBtheorem2a,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eout @ PQ @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( eout @ P @ E )
% 0.31/0.47 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem2a
% 0.31/0.47 thf(fact_323_correctCompositionKS__subcomp4,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.31/0.47 ( ( correctCompositionKS @ C3 )
% 0.31/0.47 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.47 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 0.31/0.47 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp4
% 0.31/0.47 thf(fact_324_correctCompositionKS__subcomp3,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.31/0.47 ( ( correctCompositionKS @ C3 )
% 0.31/0.47 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.31/0.47 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.31/0.47 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp3
% 0.31/0.47 thf(fact_325_TBtheorem5a__notP1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( eout @ P @ E )
% 0.31/0.47 => ( ~ ( eout @ Q @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_notP1
% 0.31/0.47 thf(fact_326_TBtheorem5a__notP2,axiom,
% 0.31/0.47 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.47 ( ~ ( eout @ Q @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSet )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_notP2
% 0.31/0.47 thf(fact_327_TBtheorem5a__notPQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetP )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_notPQ
% 0.31/0.47 thf(fact_328_out__exprChannelSingle__Set,axiom,
% 0.31/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.31/0.47 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSingle_Set
% 0.31/0.47 thf(fact_329_out__exprChannelSet__Single,axiom,
% 0.31/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.31/0.47 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSet_Single
% 0.31/0.47 thf(fact_330_TBtheorem5b__notPQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.47 => ( ( M2
% 0.31/0.47 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetP )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_notPQ
% 0.31/0.47 thf(fact_331_eout__know__s,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.31/0.47 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.31/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_s
% 0.31/0.47 thf(fact_332_not__know__s__not__eout,axiom,
% 0.31/0.47 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.31/0.47 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.31/0.47 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_know_s_not_eout
% 0.31/0.47 thf(fact_333_eoutM__eout,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 => ( eout @ P @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutM_eout
% 0.31/0.47 thf(fact_334_not__eout__eoutM,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 0.31/0.47 ( ~ ( eout @ P @ E )
% 0.31/0.47 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_eout_eoutM
% 0.31/0.47 thf(fact_335_TBtheorem2b,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eoutM @ PQ @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem2b
% 0.31/0.47 thf(fact_336_TBtheorem5b__notP2,axiom,
% 0.31/0.47 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.31/0.47 ( ~ ( eoutM @ Q @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X5 @ ChSet )
% 0.31/0.47 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_notP2
% 0.31/0.47 thf(fact_337_TBtheorem5b__notP1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 => ( ~ ( eoutM @ Q @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ M2 )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_notP1
% 0.31/0.47 thf(fact_338_eout__know__nonKS__k,axiom,
% 0.31/0.47 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.31/0.47 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.31/0.47 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_nonKS_k
% 0.31/0.47 thf(fact_339_eoutKnowCorrect__L1k,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.31/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutKnowCorrect_L1k
% 0.31/0.47 thf(fact_340_not__know__k__not__eout,axiom,
% 0.31/0.47 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.31/0.47 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.31/0.47 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_know_k_not_eout
% 0.31/0.47 thf(fact_341_eout__know__k,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.31/0.47 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.31/0.47 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.31/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_k
% 0.31/0.47 thf(fact_342_eout__know__nonKS__s,axiom,
% 0.31/0.47 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.31/0.47 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.31/0.47 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_nonKS_s
% 0.31/0.47 thf(fact_343_eoutKnowCorrect__L1s,axiom,
% 0.31/0.47 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.31/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutKnowCorrect_L1s
% 0.31/0.47 thf(fact_344_TBtheore54b__P,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch3 @ ( out @ Q ) )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ M2 ) )
% 0.31/0.47 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheore54b_P
% 0.31/0.47 thf(fact_345_TBtheorem5b__PQ,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 | ( eoutM @ Q @ M2 @ E ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 0.31/0.47 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 0.31/0.47 & ( member1967978193chanID @ Ch3 @ M2 )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_PQ
% 0.31/0.47 thf(fact_346_TBtheorem45a__P,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eout @ P @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem45a_P
% 0.31/0.47 thf(fact_347_eout__def,axiom,
% 0.31/0.47 ( eout
% 0.31/0.47 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.31/0.47 ? [Ch2: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 0.31/0.47 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_def
% 0.31/0.47 thf(fact_348_eoutM__def,axiom,
% 0.31/0.47 ( eoutM
% 0.31/0.47 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ? [Ch2: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 0.31/0.47 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.31/0.47 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutM_def
% 0.31/0.47 thf(fact_349_out__exprChannelSet__def,axiom,
% 0.31/0.47 ( out_exprChannelSet
% 0.31/0.47 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member1967978193chanID @ X6 @ ChSet2 )
% 0.31/0.47 => ( ( member1967978193chanID @ X6 @ ( out @ SP ) )
% 0.31/0.47 & ( exprChannel @ X6 @ E2 ) ) )
% 0.31/0.47 & ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( ~ ( member1967978193chanID @ X6 @ ChSet2 )
% 0.31/0.47 & ( member1967978193chanID @ X6 @ ( out @ SP ) ) )
% 0.31/0.47 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSet_def
% 0.31/0.47 thf(fact_350_out__exprChannelSingle__def,axiom,
% 0.31/0.47 ( out_ex985543062Single
% 0.31/0.47 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 0.31/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.31/0.47 & ! [X6: secrecy_chanID,T: nat] :
% 0.31/0.47 ( ( ( member1967978193chanID @ X6 @ ( out @ SP ) )
% 0.31/0.47 & ( X6 != Ch2 ) )
% 0.31/0.47 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSingle_def
% 0.31/0.47 thf(fact_351_correctCompositionOut__prop1,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 0.31/0.47 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 0.31/0.47 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionOut_prop1
% 0.31/0.47 thf(fact_352_TBtheorem5a__PQ,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ( eout @ P @ E )
% 0.31/0.47 | ( eout @ Q @ E ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 0.31/0.47 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_PQ
% 0.31/0.47 thf(fact_353_outStream__def,axiom,
% 0.31/0.47 ( outStream
% 0.31/0.47 = ( ^ [X6: secrecy_specID] :
% 0.31/0.47 ( ^ [Y6: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y6 = Z )
% 0.31/0.47 @ ( out @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % outStream_def
% 0.31/0.47 thf(fact_354_adv__not__know2,axiom,
% 0.31/0.47 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 0.31/0.47 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % adv_not_know2
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.91/1.59 ---- Embedded in THF ---
% 2.91/1.59 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.91/1.59 %%% Generated on Tue Feb 24 08:26:10 EST 2026
% 2.91/1.59 %%% using '$$dhol' embedding, version 1.3.0.
% 2.91/1.59 %%% Logic specification used:
% 2.91/1.59 %%% thf(spec, logic, $$dhol).
% 2.91/1.59
% 2.91/1.59 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2DTF6360.p
% See solution above
% 2.91/1.59 ------------------------
% 3.16/1.64 ---- Cleaned THF ---
% 3.16/1.64 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 3.16/1.64 list_S529945141ession: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 3.16/1.64 set_Secrecy_Secrets: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 3.16/1.64 set_Secrecy_specID: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.16/1.64 set_Secrecy_chanID: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 3.16/1.64 set_Secrecy_Keys: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 3.16/1.64 set_Secrecy_KS: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Secrecy____types__OExpression,type,
% 3.16/1.64 secrecy_Expression: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 3.16/1.64 secrecy_Secrets: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Secrecy____types__OspecID,type,
% 3.16/1.64 secrecy_specID: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Secrecy____types__OchanID,type,
% 3.16/1.64 secrecy_chanID: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Secrecy____types__OKeys,type,
% 3.16/1.64 secrecy_Keys: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Secrecy____types__OKS,type,
% 3.16/1.64 secrecy_KS: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(ty_n_t__Nat__Onat,type,
% 3.16/1.64 nat: $tType ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 3.16/1.64 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 3.16/1.64 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 3.16/1.64 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 3.16/1.64 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 3.16/1.64 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 3.16/1.64 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.16/1.64 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 3.16/1.64 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 3.16/1.64 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 3.16/1.64 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 3.16/1.64 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 3.16/1.64 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 3.16/1.64 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 3.16/1.64 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 3.16/1.64 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 3.16/1.64 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 3.16/1.64 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.16/1.64 bot_bo443197316chanID: set_Secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 3.16/1.64 bot_bo1785112429specID: set_Secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 3.16/1.64 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 3.16/1.64 correctCompositionKS: secrecy_specID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_Oeout,type,
% 3.16/1.64 eout: secrecy_specID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OeoutM,type,
% 3.16/1.64 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OexprChannel,type,
% 3.16/1.64 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_Oine,type,
% 3.16/1.64 ine: secrecy_specID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OineM,type,
% 3.16/1.64 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 3.16/1.64 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 3.16/1.64 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 3.16/1.64 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 3.16/1.64 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 3.16/1.64 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OspecKeys,type,
% 3.16/1.64 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 3.16/1.64 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy_OspecSecrets,type,
% 3.16/1.64 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy__types_OExpression_OdE,type,
% 3.16/1.64 secrecy_dE: nat > secrecy_Expression ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy__types_OExpression_OidE,type,
% 3.16/1.64 secrecy_idE: secrecy_specID > secrecy_Expression ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 3.16/1.64 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 3.16/1.64 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 3.16/1.64 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 3.16/1.64 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 3.16/1.64 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 3.16/1.64 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 3.16/1.64 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 3.16/1.64 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 3.16/1.64 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 3.16/1.64 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 3.16/1.64 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 3.16/1.64 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 3.16/1.64 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 3.16/1.64 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 3.16/1.64 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 3.16/1.64 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 3.16/1.64 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 3.16/1.64 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 3.16/1.64 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 3.16/1.64 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 3.16/1.64 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 3.16/1.64 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_OcorrectCompositionIn,type,
% 3.16/1.64 correctCompositionIn: secrecy_specID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 3.16/1.64 correc965049635ionLoc: secrecy_specID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_OcorrectCompositionOut,type,
% 3.16/1.64 correc990227761ionOut: secrecy_specID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_OinStream,type,
% 3.16/1.64 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_Oins,type,
% 3.16/1.64 ins: secrecy_specID > set_Secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_Oloc,type,
% 3.16/1.64 loc: secrecy_specID > set_Secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_OlocStream,type,
% 3.16/1.64 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_Oout,type,
% 3.16/1.64 out: secrecy_specID > set_Secrecy_chanID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_OoutStream,type,
% 3.16/1.64 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_inout_Osubcomponents,type,
% 3.16/1.64 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 3.16/1.64 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 3.16/1.64 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 3.16/1.64 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 3.16/1.64 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 3.16/1.64 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 3.16/1.64
% 3.16/1.64 thf(sy_v_P,type,
% 3.16/1.64 p: secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_v_PQ,type,
% 3.16/1.64 pq: secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_v_Q,type,
% 3.16/1.64 q: secrecy_specID ).
% 3.16/1.64
% 3.16/1.64 thf(sy_v_key,type,
% 3.16/1.64 key: secrecy_Keys ).
% 3.16/1.64
% 3.16/1.64 thf(fact_0_assms_I4_J,axiom,
% 3.16/1.64 correctCompositionIn @ pq ).
% 3.16/1.64
% 3.16/1.64 thf(fact_1_assms_I2_J,axiom,
% 3.16/1.64 ~ ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_2_assms_I1_J,axiom,
% 3.16/1.64 ~ ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_3_assms_I3_J,axiom,
% 3.16/1.64 ( ( subcomponents @ pq )
% 3.16/1.64 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_4_Expression_Oinject_I1_J,axiom,
% 3.16/1.64 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.16/1.64 ( ( ( secrecy_kE @ X1 )
% 3.16/1.64 = ( secrecy_kE @ Y1 ) )
% 3.16/1.64 = ( X1 = Y1 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_5_not__know__k__not__ine,axiom,
% 3.16/1.64 ! [A: secrecy_specID,M: secrecy_Keys] :
% 3.16/1.64 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 3.16/1.64 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_6_know_Osimps_I1_J,axiom,
% 3.16/1.64 ! [A: secrecy_specID,M: secrecy_Keys] :
% 3.16/1.64 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 3.16/1.64 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 3.16/1.64 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_7_Expression_Odistinct_I5_J,axiom,
% 3.16/1.64 ! [X1: secrecy_Keys,X4: secrecy_specID] :
% 3.16/1.64 ( ( secrecy_kE @ X1 )
% 3.16/1.64 != ( secrecy_idE @ X4 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_8_Expression_Odistinct_I3_J,axiom,
% 3.16/1.64 ! [X1: secrecy_Keys,X3: nat] :
% 3.16/1.64 ( ( secrecy_kE @ X1 )
% 3.16/1.64 != ( secrecy_dE @ X3 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_9_KS2Expression_Osimps_I1_J,axiom,
% 3.16/1.64 ! [M: secrecy_Keys] :
% 3.16/1.64 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 3.16/1.64 = ( secrecy_kE @ M ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_10_ineM__ine,axiom,
% 3.16/1.64 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.64 ( ( ineM @ P @ M2 @ E )
% 3.16/1.64 => ( ine @ P @ E ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_11_not__ine__ineM,axiom,
% 3.16/1.64 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 3.16/1.64 ( ~ ( ine @ P @ E )
% 3.16/1.64 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_12_LocalSecretsComposition__exprChannel__k,axiom,
% 3.16/1.64 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.64 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 3.16/1.64 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.16/1.64 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.16/1.64 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 3.16/1.64 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_13_Expression_Odistinct_I1_J,axiom,
% 3.16/1.64 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 3.16/1.64 ( ( secrecy_kE @ X1 )
% 3.16/1.64 != ( secrecy_sE @ X2 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_14_KS_Oinject_I1_J,axiom,
% 3.16/1.64 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.16/1.64 ( ( ( secrecy_kKS @ X1 )
% 3.16/1.64 = ( secrecy_kKS @ Y1 ) )
% 3.16/1.64 = ( X1 = Y1 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_15_Expression_Oinject_I2_J,axiom,
% 3.16/1.64 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 3.16/1.64 ( ( ( secrecy_sE @ X2 )
% 3.16/1.64 = ( secrecy_sE @ Y2 ) )
% 3.16/1.64 = ( X2 = Y2 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_16_Expression_Oinject_I4_J,axiom,
% 3.16/1.64 ! [X4: secrecy_specID,Y4: secrecy_specID] :
% 3.16/1.64 ( ( ( secrecy_idE @ X4 )
% 3.16/1.64 = ( secrecy_idE @ Y4 ) )
% 3.16/1.64 = ( X4 = Y4 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_17_Expression_Oinject_I3_J,axiom,
% 3.16/1.64 ! [X3: nat,Y3: nat] :
% 3.16/1.64 ( ( ( secrecy_dE @ X3 )
% 3.16/1.64 = ( secrecy_dE @ Y3 ) )
% 3.16/1.64 = ( X3 = Y3 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_18_Expression_Odistinct_I11_J,axiom,
% 3.16/1.64 ! [X3: nat,X4: secrecy_specID] :
% 3.16/1.64 ( ( secrecy_dE @ X3 )
% 3.16/1.64 != ( secrecy_idE @ X4 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_19_Expression_Odistinct_I9_J,axiom,
% 3.16/1.64 ! [X2: secrecy_Secrets,X4: secrecy_specID] :
% 3.16/1.64 ( ( secrecy_sE @ X2 )
% 3.16/1.64 != ( secrecy_idE @ X4 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_20_Expression_Odistinct_I7_J,axiom,
% 3.16/1.64 ! [X2: secrecy_Secrets,X3: nat] :
% 3.16/1.64 ( ( secrecy_sE @ X2 )
% 3.16/1.64 != ( secrecy_dE @ X3 ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_21_ineM__L1,axiom,
% 3.16/1.64 ! [Ch: secrecy_chanID,M2: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 3.16/1.64 ( ( member1967978193chanID @ Ch @ M2 )
% 3.16/1.64 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.64 => ( ( exprChannel @ Ch @ E )
% 3.16/1.64 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_22_ine__def,axiom,
% 3.16/1.64 ( ine
% 3.16/1.64 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.16/1.64 ? [Ch2: secrecy_chanID] :
% 3.16/1.64 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 3.16/1.64 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.16/1.64
% 3.16/1.64 thf(fact_23_ineM__def,axiom,
% 3.16/1.64 ( ineM
% 3.16/1.64 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.16/1.64 ? [Ch2: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 3.16/1.65 & ( member1967978193chanID @ Ch2 @ M3 )
% 3.16/1.65 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_24_TBlemma3b,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 3.16/1.65 ( ~ ( ineM @ P @ M2 @ E )
% 3.16/1.65 => ( ~ ( ineM @ Q @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ M2 )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.16/1.65 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_25_TBtheorem1b,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( ineM @ PQ @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( ineM @ P @ M2 @ E )
% 3.16/1.65 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_26_TBtheorem3b,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ~ ( ineM @ P @ M2 @ E )
% 3.16/1.65 => ( ~ ( ineM @ Q @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_27_ine__ins__neg1,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 3.16/1.65 ( ~ ( ine @ P @ M )
% 3.16/1.65 => ( ( exprChannel @ X @ M )
% 3.16/1.65 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_28_correctCompositionIn__L2,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.65 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_29_Expression_Oinduct,axiom,
% 3.16/1.65 ! [P: secrecy_Expression > $o,Expression: secrecy_Expression] :
% 3.16/1.65 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kE @ X5 ) )
% 3.16/1.65 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sE @ X5 ) )
% 3.16/1.65 => ( ! [X5: nat] : ( P @ ( secrecy_dE @ X5 ) )
% 3.16/1.65 => ( ! [X5: secrecy_specID] : ( P @ ( secrecy_idE @ X5 ) )
% 3.16/1.65 => ( P @ Expression ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_30_Expression_Oexhaust,axiom,
% 3.16/1.65 ! [Y: secrecy_Expression] :
% 3.16/1.65 ( ! [X12: secrecy_Keys] :
% 3.16/1.65 ( Y
% 3.16/1.65 != ( secrecy_kE @ X12 ) )
% 3.16/1.65 => ( ! [X22: secrecy_Secrets] :
% 3.16/1.65 ( Y
% 3.16/1.65 != ( secrecy_sE @ X22 ) )
% 3.16/1.65 => ( ! [X32: nat] :
% 3.16/1.65 ( Y
% 3.16/1.65 != ( secrecy_dE @ X32 ) )
% 3.16/1.65 => ~ ! [X42: secrecy_specID] :
% 3.16/1.65 ( Y
% 3.16/1.65 != ( secrecy_idE @ X42 ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_31_correctCompositionIn__prop1,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 3.16/1.65 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_32_LocalSecretsComposition1,axiom,
% 3.16/1.65 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_33_LocalSecretsComposition__exprChannel__s,axiom,
% 3.16/1.65 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 3.16/1.65 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 3.16/1.65 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 3.16/1.65 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_34_TBtheorem3a,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ~ ( ine @ P @ E )
% 3.16/1.65 => ( ~ ( ine @ Q @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_35_TBtheorem1a,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( ine @ PQ @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( ine @ P @ E )
% 3.16/1.65 | ( ine @ Q @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_36_singletonI,axiom,
% 3.16/1.65 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_37_singletonI,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_38_singletonI,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_39_singletonI,axiom,
% 3.16/1.65 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_40_singletonI,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_41_mem__Collect__eq,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 3.16/1.65 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 3.16/1.65 = ( P @ A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_42_mem__Collect__eq,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 3.16/1.65 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 3.16/1.65 = ( P @ A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_43_mem__Collect__eq,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 3.16/1.65 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 3.16/1.65 = ( P @ A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_44_mem__Collect__eq,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 3.16/1.65 = ( P @ A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_45_mem__Collect__eq,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 3.16/1.65 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 3.16/1.65 = ( P @ A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_46_Collect__mem__eq,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS] :
% 3.16/1.65 ( ( collect_Secrecy_KS
% 3.16/1.65 @ ^ [X6: secrecy_KS] : ( member_Secrecy_KS @ X6 @ A ) )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_47_Collect__mem__eq,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( collec625564175chanID
% 3.16/1.65 @ ^ [X6: secrecy_chanID] : ( member1967978193chanID @ X6 @ A ) )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_48_Collect__mem__eq,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID] :
% 3.16/1.65 ( ( collec1545797240specID
% 3.16/1.65 @ ^ [X6: secrecy_specID] : ( member740727610specID @ X6 @ A ) )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_49_Collect__mem__eq,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( collect_Secrecy_Keys
% 3.16/1.65 @ ^ [X6: secrecy_Keys] : ( member_Secrecy_Keys @ X6 @ A ) )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_50_Collect__mem__eq,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( collec836099393ecrets
% 3.16/1.65 @ ^ [X6: secrecy_Secrets] : ( member2138796287ecrets @ X6 @ A ) )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_51_LocalSecretsComposition__neg1__k,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.16/1.65 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_52_LocalSecretsComposition__ine2__k,axiom,
% 3.16/1.65 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.16/1.65 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_53_LocalSecretsComposition__ine1__k,axiom,
% 3.16/1.65 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.16/1.65 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_54_TBtheorem4b__P,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( ineM @ P @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch3 @ ( ins @ Q ) )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ M2 ) )
% 3.16/1.65 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_55_TBtheorem4b__PQ,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ( ineM @ P @ M2 @ E )
% 3.16/1.65 | ( ineM @ Q @ M2 @ E ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 3.16/1.65 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ M2 )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_56_TBtheorem4a__P,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( ine @ P @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_57_TBtheorem4a__PQ,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ( ine @ P @ E )
% 3.16/1.65 | ( ine @ Q @ E ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( ( member1967978193chanID @ Ch3 @ ( ins @ P ) )
% 3.16/1.65 | ( member1967978193chanID @ Ch3 @ ( ins @ Q ) ) )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_58_insertCI,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 3.16/1.65 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 3.16/1.65 => ( A2 = B2 ) )
% 3.16/1.65 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_59_insertCI,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 3.16/1.65 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 3.16/1.65 => ( A2 = B2 ) )
% 3.16/1.65 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_60_insertCI,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 3.16/1.65 ( ( ~ ( member740727610specID @ A2 @ B )
% 3.16/1.65 => ( A2 = B2 ) )
% 3.16/1.65 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_61_insertCI,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 3.16/1.65 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 3.16/1.65 => ( A2 = B2 ) )
% 3.16/1.65 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_62_insertCI,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 3.16/1.65 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 3.16/1.65 => ( A2 = B2 ) )
% 3.16/1.65 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_63_insert__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 3.16/1.65 = ( ( A2 = B2 )
% 3.16/1.65 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_64_insert__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 3.16/1.65 = ( ( A2 = B2 )
% 3.16/1.65 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_65_insert__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 3.16/1.65 = ( ( A2 = B2 )
% 3.16/1.65 | ( member740727610specID @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_66_insert__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 3.16/1.65 = ( ( A2 = B2 )
% 3.16/1.65 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_67_insert__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 3.16/1.65 = ( ( A2 = B2 )
% 3.16/1.65 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_68_empty__Collect__eq,axiom,
% 3.16/1.65 ! [P: secrecy_specID > $o] :
% 3.16/1.65 ( ( bot_bo1785112429specID
% 3.16/1.65 = ( collec1545797240specID @ P ) )
% 3.16/1.65 = ( ! [X6: secrecy_specID] :
% 3.16/1.65 ~ ( P @ X6 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_69_empty__Collect__eq,axiom,
% 3.16/1.65 ! [P: secrecy_chanID > $o] :
% 3.16/1.65 ( ( bot_bo443197316chanID
% 3.16/1.65 = ( collec625564175chanID @ P ) )
% 3.16/1.65 = ( ! [X6: secrecy_chanID] :
% 3.16/1.65 ~ ( P @ X6 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_70_Collect__empty__eq,axiom,
% 3.16/1.65 ! [P: secrecy_specID > $o] :
% 3.16/1.65 ( ( ( collec1545797240specID @ P )
% 3.16/1.65 = bot_bo1785112429specID )
% 3.16/1.65 = ( ! [X6: secrecy_specID] :
% 3.16/1.65 ~ ( P @ X6 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_71_Collect__empty__eq,axiom,
% 3.16/1.65 ! [P: secrecy_chanID > $o] :
% 3.16/1.65 ( ( ( collec625564175chanID @ P )
% 3.16/1.65 = bot_bo443197316chanID )
% 3.16/1.65 = ( ! [X6: secrecy_chanID] :
% 3.16/1.65 ~ ( P @ X6 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_72_all__not__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS] :
% 3.16/1.65 ( ( ! [X6: secrecy_KS] :
% 3.16/1.65 ~ ( member_Secrecy_KS @ X6 @ A ) )
% 3.16/1.65 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_73_all__not__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( ! [X6: secrecy_Keys] :
% 3.16/1.65 ~ ( member_Secrecy_Keys @ X6 @ A ) )
% 3.16/1.65 = ( A = bot_bo701486667y_Keys ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_74_all__not__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( ! [X6: secrecy_Secrets] :
% 3.16/1.65 ~ ( member2138796287ecrets @ X6 @ A ) )
% 3.16/1.65 = ( A = bot_bo1124690338ecrets ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_75_all__not__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID] :
% 3.16/1.65 ( ( ! [X6: secrecy_specID] :
% 3.16/1.65 ~ ( member740727610specID @ X6 @ A ) )
% 3.16/1.65 = ( A = bot_bo1785112429specID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_76_all__not__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ! [X6: secrecy_chanID] :
% 3.16/1.65 ~ ( member1967978193chanID @ X6 @ A ) )
% 3.16/1.65 = ( A = bot_bo443197316chanID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_77_empty__iff,axiom,
% 3.16/1.65 ! [C: secrecy_KS] :
% 3.16/1.65 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_78_empty__iff,axiom,
% 3.16/1.65 ! [C: secrecy_Keys] :
% 3.16/1.65 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_79_empty__iff,axiom,
% 3.16/1.65 ! [C: secrecy_Secrets] :
% 3.16/1.65 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_80_empty__iff,axiom,
% 3.16/1.65 ! [C: secrecy_specID] :
% 3.16/1.65 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_81_empty__iff,axiom,
% 3.16/1.65 ! [C: secrecy_chanID] :
% 3.16/1.65 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_82_insert__absorb2,axiom,
% 3.16/1.65 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A ) )
% 3.16/1.65 = ( insert1671894227specID @ X @ A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_83_insert__absorb2,axiom,
% 3.16/1.65 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A ) )
% 3.16/1.65 = ( insert751661162chanID @ X @ A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_84_TBtheorem4a__empty,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ( ine @ P @ E )
% 3.16/1.65 | ( ine @ Q @ E ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( ( loc @ PQ )
% 3.16/1.65 = bot_bo443197316chanID )
% 3.16/1.65 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_85_ex__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS] :
% 3.16/1.65 ( ( ? [X6: secrecy_KS] : ( member_Secrecy_KS @ X6 @ A ) )
% 3.16/1.65 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_86_ex__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( ? [X6: secrecy_Keys] : ( member_Secrecy_Keys @ X6 @ A ) )
% 3.16/1.65 = ( A != bot_bo701486667y_Keys ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_87_ex__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( ? [X6: secrecy_Secrets] : ( member2138796287ecrets @ X6 @ A ) )
% 3.16/1.65 = ( A != bot_bo1124690338ecrets ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_88_ex__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID] :
% 3.16/1.65 ( ( ? [X6: secrecy_specID] : ( member740727610specID @ X6 @ A ) )
% 3.16/1.65 = ( A != bot_bo1785112429specID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_89_ex__in__conv,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ? [X6: secrecy_chanID] : ( member1967978193chanID @ X6 @ A ) )
% 3.16/1.65 = ( A != bot_bo443197316chanID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_90_equals0I,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS] :
% 3.16/1.65 ( ! [Y5: secrecy_KS] :
% 3.16/1.65 ~ ( member_Secrecy_KS @ Y5 @ A )
% 3.16/1.65 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_91_equals0I,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Keys] :
% 3.16/1.65 ( ! [Y5: secrecy_Keys] :
% 3.16/1.65 ~ ( member_Secrecy_Keys @ Y5 @ A )
% 3.16/1.65 => ( A = bot_bo701486667y_Keys ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_92_equals0I,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ! [Y5: secrecy_Secrets] :
% 3.16/1.65 ~ ( member2138796287ecrets @ Y5 @ A )
% 3.16/1.65 => ( A = bot_bo1124690338ecrets ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_93_equals0I,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID] :
% 3.16/1.65 ( ! [Y5: secrecy_specID] :
% 3.16/1.65 ~ ( member740727610specID @ Y5 @ A )
% 3.16/1.65 => ( A = bot_bo1785112429specID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_94_equals0I,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ! [Y5: secrecy_chanID] :
% 3.16/1.65 ~ ( member1967978193chanID @ Y5 @ A )
% 3.16/1.65 => ( A = bot_bo443197316chanID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_95_equals0D,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 3.16/1.65 ( ( A = bot_bo1943466239ecy_KS )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_96_equals0D,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 3.16/1.65 ( ( A = bot_bo701486667y_Keys )
% 3.16/1.65 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_97_equals0D,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 3.16/1.65 ( ( A = bot_bo1124690338ecrets )
% 3.16/1.65 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_98_equals0D,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 3.16/1.65 ( ( A = bot_bo1785112429specID )
% 3.16/1.65 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_99_equals0D,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 3.16/1.65 ( ( A = bot_bo443197316chanID )
% 3.16/1.65 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_100_emptyE,axiom,
% 3.16/1.65 ! [A2: secrecy_KS] :
% 3.16/1.65 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_101_emptyE,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys] :
% 3.16/1.65 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_102_emptyE,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets] :
% 3.16/1.65 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_103_emptyE,axiom,
% 3.16/1.65 ! [A2: secrecy_specID] :
% 3.16/1.65 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_104_emptyE,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID] :
% 3.16/1.65 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_105_mk__disjoint__insert,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ A2 @ A )
% 3.16/1.65 => ? [B3: set_Secrecy_KS] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 3.16/1.65 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_106_mk__disjoint__insert,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ A2 @ A )
% 3.16/1.65 => ? [B3: set_Secrecy_chanID] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert751661162chanID @ A2 @ B3 ) )
% 3.16/1.65 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_107_mk__disjoint__insert,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ A2 @ A )
% 3.16/1.65 => ? [B3: set_Secrecy_specID] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert1671894227specID @ A2 @ B3 ) )
% 3.16/1.65 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_108_mk__disjoint__insert,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ A2 @ A )
% 3.16/1.65 => ? [B3: set_Secrecy_Keys] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 3.16/1.65 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_109_mk__disjoint__insert,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ A2 @ A )
% 3.16/1.65 => ? [B3: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert565337510ecrets @ A2 @ B3 ) )
% 3.16/1.65 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_110_insert__commute,axiom,
% 3.16/1.65 ! [X: secrecy_specID,Y: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y @ A ) )
% 3.16/1.65 = ( insert1671894227specID @ Y @ ( insert1671894227specID @ X @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_111_insert__commute,axiom,
% 3.16/1.65 ! [X: secrecy_chanID,Y: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y @ A ) )
% 3.16/1.65 = ( insert751661162chanID @ Y @ ( insert751661162chanID @ X @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_112_insert__eq__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 3.16/1.65 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 3.16/1.65 = ( insert_Secrecy_KS @ B2 @ B ) )
% 3.16/1.65 = ( ( ( A2 = B2 )
% 3.16/1.65 => ( A = B ) )
% 3.16/1.65 & ( ( A2 != B2 )
% 3.16/1.65 => ? [C2: set_Secrecy_KS] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 3.16/1.65 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 3.16/1.65 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_113_insert__eq__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ~ ( member1967978193chanID @ A2 @ A )
% 3.16/1.65 => ( ~ ( member1967978193chanID @ B2 @ B )
% 3.16/1.65 => ( ( ( insert751661162chanID @ A2 @ A )
% 3.16/1.65 = ( insert751661162chanID @ B2 @ B ) )
% 3.16/1.65 = ( ( ( A2 = B2 )
% 3.16/1.65 => ( A = B ) )
% 3.16/1.65 & ( ( A2 != B2 )
% 3.16/1.65 => ? [C2: set_Secrecy_chanID] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert751661162chanID @ B2 @ C2 ) )
% 3.16/1.65 & ~ ( member1967978193chanID @ B2 @ C2 )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert751661162chanID @ A2 @ C2 ) )
% 3.16/1.65 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_114_insert__eq__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ~ ( member740727610specID @ A2 @ A )
% 3.16/1.65 => ( ~ ( member740727610specID @ B2 @ B )
% 3.16/1.65 => ( ( ( insert1671894227specID @ A2 @ A )
% 3.16/1.65 = ( insert1671894227specID @ B2 @ B ) )
% 3.16/1.65 = ( ( ( A2 = B2 )
% 3.16/1.65 => ( A = B ) )
% 3.16/1.65 & ( ( A2 != B2 )
% 3.16/1.65 => ? [C2: set_Secrecy_specID] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert1671894227specID @ B2 @ C2 ) )
% 3.16/1.65 & ~ ( member740727610specID @ B2 @ C2 )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert1671894227specID @ A2 @ C2 ) )
% 3.16/1.65 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_115_insert__eq__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 3.16/1.65 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 3.16/1.65 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 3.16/1.65 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 3.16/1.65 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 3.16/1.65 = ( ( ( A2 = B2 )
% 3.16/1.65 => ( A = B ) )
% 3.16/1.65 & ( ( A2 != B2 )
% 3.16/1.65 => ? [C2: set_Secrecy_Keys] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 3.16/1.65 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 3.16/1.65 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_116_insert__eq__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.16/1.65 ( ~ ( member2138796287ecrets @ A2 @ A )
% 3.16/1.65 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 3.16/1.65 => ( ( ( insert565337510ecrets @ A2 @ A )
% 3.16/1.65 = ( insert565337510ecrets @ B2 @ B ) )
% 3.16/1.65 = ( ( ( A2 = B2 )
% 3.16/1.65 => ( A = B ) )
% 3.16/1.65 & ( ( A2 != B2 )
% 3.16/1.65 => ? [C2: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert565337510ecrets @ B2 @ C2 ) )
% 3.16/1.65 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert565337510ecrets @ A2 @ C2 ) )
% 3.16/1.65 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_117_insert__absorb,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ A2 @ A )
% 3.16/1.65 => ( ( insert_Secrecy_KS @ A2 @ A )
% 3.16/1.65 = A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_118_insert__absorb,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ A2 @ A )
% 3.16/1.65 => ( ( insert751661162chanID @ A2 @ A )
% 3.16/1.65 = A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_119_insert__absorb,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ A2 @ A )
% 3.16/1.65 => ( ( insert1671894227specID @ A2 @ A )
% 3.16/1.65 = A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_120_insert__absorb,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ A2 @ A )
% 3.16/1.65 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 3.16/1.65 = A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_121_insert__absorb,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ A2 @ A )
% 3.16/1.65 => ( ( insert565337510ecrets @ A2 @ A )
% 3.16/1.65 = A ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_122_insert__ident,axiom,
% 3.16/1.65 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ~ ( member_Secrecy_KS @ X @ A )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ X @ B )
% 3.16/1.65 => ( ( ( insert_Secrecy_KS @ X @ A )
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ B ) )
% 3.16/1.65 = ( A = B ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_123_insert__ident,axiom,
% 3.16/1.65 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ~ ( member1967978193chanID @ X @ A )
% 3.16/1.65 => ( ~ ( member1967978193chanID @ X @ B )
% 3.16/1.65 => ( ( ( insert751661162chanID @ X @ A )
% 3.16/1.65 = ( insert751661162chanID @ X @ B ) )
% 3.16/1.65 = ( A = B ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_124_insert__ident,axiom,
% 3.16/1.65 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ~ ( member740727610specID @ X @ A )
% 3.16/1.65 => ( ~ ( member740727610specID @ X @ B )
% 3.16/1.65 => ( ( ( insert1671894227specID @ X @ A )
% 3.16/1.65 = ( insert1671894227specID @ X @ B ) )
% 3.16/1.65 = ( A = B ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_125_insert__ident,axiom,
% 3.16/1.65 ! [X: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.16/1.65 ( ~ ( member_Secrecy_Keys @ X @ A )
% 3.16/1.65 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 3.16/1.65 => ( ( ( insert_Secrecy_Keys @ X @ A )
% 3.16/1.65 = ( insert_Secrecy_Keys @ X @ B ) )
% 3.16/1.65 = ( A = B ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_126_insert__ident,axiom,
% 3.16/1.65 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.16/1.65 ( ~ ( member2138796287ecrets @ X @ A )
% 3.16/1.65 => ( ~ ( member2138796287ecrets @ X @ B )
% 3.16/1.65 => ( ( ( insert565337510ecrets @ X @ A )
% 3.16/1.65 = ( insert565337510ecrets @ X @ B ) )
% 3.16/1.65 = ( A = B ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_127_Set_Oset__insert,axiom,
% 3.16/1.65 ! [X: secrecy_KS,A: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X @ A )
% 3.16/1.65 => ~ ! [B3: set_Secrecy_KS] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ B3 ) )
% 3.16/1.65 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_128_Set_Oset__insert,axiom,
% 3.16/1.65 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X @ A )
% 3.16/1.65 => ~ ! [B3: set_Secrecy_chanID] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert751661162chanID @ X @ B3 ) )
% 3.16/1.65 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_129_Set_Oset__insert,axiom,
% 3.16/1.65 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ X @ A )
% 3.16/1.65 => ~ ! [B3: set_Secrecy_specID] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert1671894227specID @ X @ B3 ) )
% 3.16/1.65 => ( member740727610specID @ X @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_130_Set_Oset__insert,axiom,
% 3.16/1.65 ! [X: secrecy_Keys,A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ X @ A )
% 3.16/1.65 => ~ ! [B3: set_Secrecy_Keys] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 3.16/1.65 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_131_Set_Oset__insert,axiom,
% 3.16/1.65 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ X @ A )
% 3.16/1.65 => ~ ! [B3: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( A
% 3.16/1.65 = ( insert565337510ecrets @ X @ B3 ) )
% 3.16/1.65 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_132_insertI2,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ A2 @ B )
% 3.16/1.65 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_133_insertI2,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ A2 @ B )
% 3.16/1.65 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_134_insertI2,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ A2 @ B )
% 3.16/1.65 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_135_insertI2,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ A2 @ B )
% 3.16/1.65 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_136_insertI2,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ A2 @ B )
% 3.16/1.65 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_137_insertI1,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_138_insertI1,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_139_insertI1,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_140_insertI1,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_141_insertI1,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_142_insertE,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 3.16/1.65 => ( ( A2 != B2 )
% 3.16/1.65 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_143_insertE,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 3.16/1.65 => ( ( A2 != B2 )
% 3.16/1.65 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_144_insertE,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 3.16/1.65 => ( ( A2 != B2 )
% 3.16/1.65 => ( member740727610specID @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_145_insertE,axiom,
% 3.16/1.65 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 3.16/1.65 => ( ( A2 != B2 )
% 3.16/1.65 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_146_insertE,axiom,
% 3.16/1.65 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 3.16/1.65 => ( ( A2 != B2 )
% 3.16/1.65 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_147_correctCompositionIn__L1,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.65 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_148_singleton__inject,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 3.16/1.65 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 3.16/1.65 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 3.16/1.65 => ( A2 = B2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_149_singleton__inject,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 3.16/1.65 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 3.16/1.65 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 3.16/1.65 => ( A2 = B2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_150_insert__not__empty,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( insert1671894227specID @ A2 @ A )
% 3.16/1.65 != bot_bo1785112429specID ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_151_insert__not__empty,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( insert751661162chanID @ A2 @ A )
% 3.16/1.65 != bot_bo443197316chanID ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_152_doubleton__eq__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 3.16/1.65 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 3.16/1.65 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 3.16/1.65 = ( ( ( A2 = C )
% 3.16/1.65 & ( B2 = D ) )
% 3.16/1.65 | ( ( A2 = D )
% 3.16/1.65 & ( B2 = C ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_153_doubleton__eq__iff,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 3.16/1.65 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 3.16/1.65 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 3.16/1.65 = ( ( ( A2 = C )
% 3.16/1.65 & ( B2 = D ) )
% 3.16/1.65 | ( ( A2 = D )
% 3.16/1.65 & ( B2 = C ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_154_singleton__iff,axiom,
% 3.16/1.65 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 3.16/1.65 = ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_155_singleton__iff,axiom,
% 3.16/1.65 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 3.16/1.65 = ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_156_singleton__iff,axiom,
% 3.16/1.65 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 3.16/1.65 = ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_157_singleton__iff,axiom,
% 3.16/1.65 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 3.16/1.65 = ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_158_singleton__iff,axiom,
% 3.16/1.65 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 3.16/1.65 = ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_159_singletonD,axiom,
% 3.16/1.65 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 3.16/1.65 => ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_160_singletonD,axiom,
% 3.16/1.65 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 3.16/1.65 => ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_161_singletonD,axiom,
% 3.16/1.65 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 3.16/1.65 => ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_162_singletonD,axiom,
% 3.16/1.65 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 3.16/1.65 => ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_163_singletonD,axiom,
% 3.16/1.65 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 3.16/1.65 => ( B2 = A2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_164_correctCompositionInLoc__exprChannel,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ M )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ( ins @ PQ ) )
% 3.16/1.65 => ~ ( exprChannel @ X5 @ M ) )
% 3.16/1.65 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_165_subcomponents__loc,axiom,
% 3.16/1.65 ! [X: secrecy_specID] :
% 3.16/1.65 ( ( correc965049635ionLoc @ X )
% 3.16/1.65 => ( ( ( subcomponents @ X )
% 3.16/1.65 = bot_bo1785112429specID )
% 3.16/1.65 => ( ( loc @ X )
% 3.16/1.65 = bot_bo443197316chanID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_166_TBtheorem4b__notP1,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ineM @ P @ M2 @ E )
% 3.16/1.65 => ( ~ ( ineM @ Q @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ M2 )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_167_TBtheorem4a__notP1,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ine @ P @ E )
% 3.16/1.65 => ( ~ ( ine @ Q @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_168_TBtheorem4b__notPQ,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.16/1.65 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetP )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_169_TBtheorem4b__notP2,axiom,
% 3.16/1.65 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.16/1.65 ( ~ ( ineM @ Q @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSet )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_170_TBtheorem4a__notPQ,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.16/1.65 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetP )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_171_TBtheorem4a__notP2,axiom,
% 3.16/1.65 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.16/1.65 ( ~ ( ine @ Q @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSet )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_172_ine__exprChannelSet__Single,axiom,
% 3.16/1.65 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.65 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 3.16/1.65 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_173_ine__exprChannelSingle__Set,axiom,
% 3.16/1.65 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.65 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 3.16/1.65 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_174_ine__nonempty__exprChannelSet,axiom,
% 3.16/1.65 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.65 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.16/1.65 => ( ( ChSet != bot_bo443197316chanID )
% 3.16/1.65 => ( ine @ P @ E ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_175_ine__empty__exprChannelSet,axiom,
% 3.16/1.65 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.65 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.16/1.65 => ( ( ChSet = bot_bo443197316chanID )
% 3.16/1.65 => ~ ( ine @ P @ E ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_176_ine__exprChannelSet__def,axiom,
% 3.16/1.65 ( ine_exprChannelSet
% 3.16/1.65 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.16/1.65 ( ! [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ ChSet2 )
% 3.16/1.65 => ( ( member1967978193chanID @ X6 @ ( ins @ SP ) )
% 3.16/1.65 & ( exprChannel @ X6 @ E2 ) ) )
% 3.16/1.65 & ! [X6: secrecy_chanID] :
% 3.16/1.65 ( ( ~ ( member1967978193chanID @ X6 @ ChSet2 )
% 3.16/1.65 & ( member1967978193chanID @ X6 @ ( ins @ SP ) ) )
% 3.16/1.65 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_177_ine__exprChannelSingle__def,axiom,
% 3.16/1.65 ( ine_ex1303305700Single
% 3.16/1.65 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch2 @ ( ins @ SP ) )
% 3.16/1.65 & ( exprChannel @ Ch2 @ E2 )
% 3.16/1.65 & ! [X6: secrecy_chanID,T: nat] :
% 3.16/1.65 ( ( ( member1967978193chanID @ X6 @ ( ins @ SP ) )
% 3.16/1.65 & ( X6 != Ch2 ) )
% 3.16/1.65 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_178_LocalSecretsComposition__neg1,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ! [M4: secrecy_Keys] :
% 3.16/1.65 ( ( Ks
% 3.16/1.65 = ( secrecy_kKS @ M4 ) )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.16/1.65 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.16/1.65 => ( ! [M4: secrecy_Secrets] :
% 3.16/1.65 ( ( Ks
% 3.16/1.65 = ( secrecy_sKS @ M4 ) )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.16/1.65 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_179_locStream__def,axiom,
% 3.16/1.65 ( locStream
% 3.16/1.65 = ( ^ [X6: secrecy_specID] :
% 3.16/1.65 ( ^ [Y6: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y6 = Z )
% 3.16/1.65 @ ( loc @ X6 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_180_inStream__def,axiom,
% 3.16/1.65 ( inStream
% 3.16/1.65 = ( ^ [X6: secrecy_specID] :
% 3.16/1.65 ( ^ [Y6: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y6 = Z )
% 3.16/1.65 @ ( ins @ X6 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_181_the__elem__eq,axiom,
% 3.16/1.65 ! [X: secrecy_specID] :
% 3.16/1.65 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_182_the__elem__eq,axiom,
% 3.16/1.65 ! [X: secrecy_chanID] :
% 3.16/1.65 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_183_LocalSecretsComposition__ine1__s,axiom,
% 3.16/1.65 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.16/1.65 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_184_KS_Oinject_I2_J,axiom,
% 3.16/1.65 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 3.16/1.65 ( ( ( secrecy_sKS @ X2 )
% 3.16/1.65 = ( secrecy_sKS @ Y2 ) )
% 3.16/1.65 = ( X2 = Y2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_185_bot__set__def,axiom,
% 3.16/1.65 ( bot_bo1785112429specID
% 3.16/1.65 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_186_bot__set__def,axiom,
% 3.16/1.65 ( bot_bo443197316chanID
% 3.16/1.65 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_187_KS_Oexhaust,axiom,
% 3.16/1.65 ! [Y: secrecy_KS] :
% 3.16/1.65 ( ! [X12: secrecy_Keys] :
% 3.16/1.65 ( Y
% 3.16/1.65 != ( secrecy_kKS @ X12 ) )
% 3.16/1.65 => ~ ! [X22: secrecy_Secrets] :
% 3.16/1.65 ( Y
% 3.16/1.65 != ( secrecy_sKS @ X22 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_188_KS_Oinduct,axiom,
% 3.16/1.65 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 3.16/1.65 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kKS @ X5 ) )
% 3.16/1.65 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X5 ) )
% 3.16/1.65 => ( P @ KS ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_189_KS_Odistinct_I1_J,axiom,
% 3.16/1.65 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 3.16/1.65 ( ( secrecy_kKS @ X1 )
% 3.16/1.65 != ( secrecy_sKS @ X2 ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_190_KS2Expression_Osimps_I2_J,axiom,
% 3.16/1.65 ! [M: secrecy_Secrets] :
% 3.16/1.65 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 3.16/1.65 = ( secrecy_sE @ M ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_191_not__know__s__not__ine,axiom,
% 3.16/1.65 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 3.16/1.65 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 3.16/1.65 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_192_know_Osimps_I2_J,axiom,
% 3.16/1.65 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 3.16/1.65 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 3.16/1.65 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 3.16/1.65 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_193_LocalSecretsComposition__neg1__s,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.16/1.65 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_194_LocalSecretsComposition__ine2__s,axiom,
% 3.16/1.65 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.16/1.65 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_195_is__singleton__the__elem,axiom,
% 3.16/1.65 ( is_sin1501507247specID
% 3.16/1.65 = ( ^ [A3: set_Secrecy_specID] :
% 3.16/1.65 ( A3
% 3.16/1.65 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_196_is__singleton__the__elem,axiom,
% 3.16/1.65 ( is_sin581274182chanID
% 3.16/1.65 = ( ^ [A3: set_Secrecy_chanID] :
% 3.16/1.65 ( A3
% 3.16/1.65 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_197_is__singletonI,axiom,
% 3.16/1.65 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_198_is__singletonI,axiom,
% 3.16/1.65 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_199_LocalSecretsComposition__neg__loc__s,axiom,
% 3.16/1.65 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.16/1.65 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_200_LocalSecretsComposition__neg__loc__k,axiom,
% 3.16/1.65 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.16/1.65 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_201_correctCompositionKS__exprChannel__s__Qex,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ? [Ch4: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_202_correctCompositionKS__PQ,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.16/1.65 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_203_correctCompositionKS__neg1,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_204_correctCompositionKS__negP,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_205_correctCompositionKS__negQ,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_206_is__singletonI_H,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS] :
% 3.16/1.65 ( ( A != bot_bo1943466239ecy_KS )
% 3.16/1.65 => ( ! [X5: secrecy_KS,Y5: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X5 @ A )
% 3.16/1.65 => ( ( member_Secrecy_KS @ Y5 @ A )
% 3.16/1.65 => ( X5 = Y5 ) ) )
% 3.16/1.65 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_207_is__singletonI_H,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( A != bot_bo701486667y_Keys )
% 3.16/1.65 => ( ! [X5: secrecy_Keys,Y5: secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ X5 @ A )
% 3.16/1.65 => ( ( member_Secrecy_Keys @ Y5 @ A )
% 3.16/1.65 => ( X5 = Y5 ) ) )
% 3.16/1.65 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_208_is__singletonI_H,axiom,
% 3.16/1.65 ! [A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( A != bot_bo1124690338ecrets )
% 3.16/1.65 => ( ! [X5: secrecy_Secrets,Y5: secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ X5 @ A )
% 3.16/1.65 => ( ( member2138796287ecrets @ Y5 @ A )
% 3.16/1.65 => ( X5 = Y5 ) ) )
% 3.16/1.65 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_209_is__singletonI_H,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID] :
% 3.16/1.65 ( ( A != bot_bo1785112429specID )
% 3.16/1.65 => ( ! [X5: secrecy_specID,Y5: secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ X5 @ A )
% 3.16/1.65 => ( ( member740727610specID @ Y5 @ A )
% 3.16/1.65 => ( X5 = Y5 ) ) )
% 3.16/1.65 => ( is_sin1501507247specID @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_210_is__singletonI_H,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( A != bot_bo443197316chanID )
% 3.16/1.65 => ( ! [X5: secrecy_chanID,Y5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ A )
% 3.16/1.65 => ( ( member1967978193chanID @ Y5 @ A )
% 3.16/1.65 => ( X5 = Y5 ) ) )
% 3.16/1.65 => ( is_sin581274182chanID @ A ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_211_know__composition,axiom,
% 3.16/1.65 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.16/1.65 => ( ( ( knowle945212990e_know @ P @ M )
% 3.16/1.65 | ( knowle945212990e_know @ Q @ M ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_212_know__composition1,axiom,
% 3.16/1.65 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.16/1.65 => ( ( knowle945212990e_know @ P @ M )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_213_know__composition2,axiom,
% 3.16/1.65 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.16/1.65 => ( ( knowle945212990e_know @ Q @ M )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_214_is__singletonE,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID] :
% 3.16/1.65 ( ( is_sin1501507247specID @ A )
% 3.16/1.65 => ~ ! [X5: secrecy_specID] :
% 3.16/1.65 ( A
% 3.16/1.65 != ( insert1671894227specID @ X5 @ bot_bo1785112429specID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_215_is__singletonE,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( is_sin581274182chanID @ A )
% 3.16/1.65 => ~ ! [X5: secrecy_chanID] :
% 3.16/1.65 ( A
% 3.16/1.65 != ( insert751661162chanID @ X5 @ bot_bo443197316chanID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_216_is__singleton__def,axiom,
% 3.16/1.65 ( is_sin1501507247specID
% 3.16/1.65 = ( ^ [A3: set_Secrecy_specID] :
% 3.16/1.65 ? [X6: secrecy_specID] :
% 3.16/1.65 ( A3
% 3.16/1.65 = ( insert1671894227specID @ X6 @ bot_bo1785112429specID ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_217_is__singleton__def,axiom,
% 3.16/1.65 ( is_sin581274182chanID
% 3.16/1.65 = ( ^ [A3: set_Secrecy_chanID] :
% 3.16/1.65 ? [X6: secrecy_chanID] :
% 3.16/1.65 ( A3
% 3.16/1.65 = ( insert751661162chanID @ X6 @ bot_bo443197316chanID ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_218_correctCompositionKS__exprChannel__k__P,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_219_correctCompositionKS__exprChannel__k__Q,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_220_correctCompositionKS__exprChannel__k__Pex,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ? [Ch4: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_221_correctCompositionKS__exprChannel__k__Qex,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ? [Ch4: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_222_correctCompositionKS__exprChannel__s__P,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_223_correctCompositionKS__exprChannel__s__Q,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_224_correctCompositionKS__exprChannel__s__Pex,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 3.16/1.65 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.16/1.65 => ( ( correctCompositionIn @ PQ )
% 3.16/1.65 => ? [Ch4: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 3.16/1.65 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_225_LocalSecretsComposition__neg,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.16/1.65 => ( ! [M4: secrecy_Keys] :
% 3.16/1.65 ( ( Ks
% 3.16/1.65 = ( secrecy_kKS @ M4 ) )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.16/1.65 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.16/1.65 => ( ! [M4: secrecy_Secrets] :
% 3.16/1.65 ( ( Ks
% 3.16/1.65 = ( secrecy_sKS @ M4 ) )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.16/1.65 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_226_LocalSecretsComposition__neg__s,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 3.16/1.65 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_227_LocalSecretsComposition__neg__k,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc965049635ionLoc @ PQ )
% 3.16/1.65 => ( ( correctCompositionKS @ PQ )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 3.16/1.65 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 3.16/1.65 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_228_bot__empty__eq,axiom,
% 3.16/1.65 ( bot_bot_Secrecy_KS_o
% 3.16/1.65 = ( ^ [X6: secrecy_KS] : ( member_Secrecy_KS @ X6 @ bot_bo1943466239ecy_KS ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_229_bot__empty__eq,axiom,
% 3.16/1.65 ( bot_bo2072920570Keys_o
% 3.16/1.65 = ( ^ [X6: secrecy_Keys] : ( member_Secrecy_Keys @ X6 @ bot_bo701486667y_Keys ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_230_bot__empty__eq,axiom,
% 3.16/1.65 ( bot_bo1909946299rets_o
% 3.16/1.65 = ( ^ [X6: secrecy_Secrets] : ( member2138796287ecrets @ X6 @ bot_bo1124690338ecrets ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_231_bot__empty__eq,axiom,
% 3.16/1.65 ( bot_bo1767780696ecID_o
% 3.16/1.65 = ( ^ [X6: secrecy_specID] : ( member740727610specID @ X6 @ bot_bo1785112429specID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_232_bot__empty__eq,axiom,
% 3.16/1.65 ( bot_bo1012329985anID_o
% 3.16/1.65 = ( ^ [X6: secrecy_chanID] : ( member1967978193chanID @ X6 @ bot_bo443197316chanID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_233_UnCI,axiom,
% 3.16/1.65 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( ~ ( member740727610specID @ C @ B )
% 3.16/1.65 => ( member740727610specID @ C @ A ) )
% 3.16/1.65 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_234_UnCI,axiom,
% 3.16/1.65 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 3.16/1.65 => ( member_Secrecy_Keys @ C @ A ) )
% 3.16/1.65 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_235_UnCI,axiom,
% 3.16/1.65 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( ~ ( member2138796287ecrets @ C @ B )
% 3.16/1.65 => ( member2138796287ecrets @ C @ A ) )
% 3.16/1.65 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_236_UnCI,axiom,
% 3.16/1.65 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 3.16/1.65 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 3.16/1.65 => ( member_Secrecy_KS @ C @ A ) )
% 3.16/1.65 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_237_UnCI,axiom,
% 3.16/1.65 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ~ ( member1967978193chanID @ C @ B )
% 3.16/1.65 => ( member1967978193chanID @ C @ A ) )
% 3.16/1.65 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_238_Un__iff,axiom,
% 3.16/1.65 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 3.16/1.65 = ( ( member740727610specID @ C @ A )
% 3.16/1.65 | ( member740727610specID @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_239_Un__iff,axiom,
% 3.16/1.65 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 3.16/1.65 = ( ( member_Secrecy_Keys @ C @ A )
% 3.16/1.65 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_240_Un__iff,axiom,
% 3.16/1.65 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 3.16/1.65 = ( ( member2138796287ecrets @ C @ A )
% 3.16/1.65 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_241_Un__iff,axiom,
% 3.16/1.65 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 3.16/1.65 = ( ( member_Secrecy_KS @ C @ A )
% 3.16/1.65 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_242_Un__iff,axiom,
% 3.16/1.65 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 3.16/1.65 = ( ( member1967978193chanID @ C @ A )
% 3.16/1.65 | ( member1967978193chanID @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_243_Un__empty,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 3.16/1.65 = bot_bo1943466239ecy_KS )
% 3.16/1.65 = ( ( A = bot_bo1943466239ecy_KS )
% 3.16/1.65 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_244_Un__empty,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ( ( sup_su1712599557specID @ A @ B )
% 3.16/1.65 = bot_bo1785112429specID )
% 3.16/1.65 = ( ( A = bot_bo1785112429specID )
% 3.16/1.65 & ( B = bot_bo1785112429specID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_245_Un__empty,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ( sup_su370684444chanID @ A @ B )
% 3.16/1.65 = bot_bo443197316chanID )
% 3.16/1.65 = ( ( A = bot_bo443197316chanID )
% 3.16/1.65 & ( B = bot_bo443197316chanID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_246_Un__insert__right,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 3.16/1.65 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_247_Un__insert__right,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 3.16/1.65 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_248_Un__insert__right,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 3.16/1.65 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_249_Un__insert__left,axiom,
% 3.16/1.65 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 3.16/1.65 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_250_Un__insert__left,axiom,
% 3.16/1.65 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 3.16/1.65 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_251_Un__insert__left,axiom,
% 3.16/1.65 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 3.16/1.65 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_252_Un__empty__right,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_253_Un__empty__right,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_254_Un__empty__right,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_255_Un__empty__left,axiom,
% 3.16/1.65 ! [B: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 3.16/1.65 = B ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_256_Un__empty__left,axiom,
% 3.16/1.65 ! [B: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 3.16/1.65 = B ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_257_Un__empty__left,axiom,
% 3.16/1.65 ! [B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 3.16/1.65 = B ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_258_UnE,axiom,
% 3.16/1.65 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 3.16/1.65 => ( ~ ( member740727610specID @ C @ A )
% 3.16/1.65 => ( member740727610specID @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_259_UnE,axiom,
% 3.16/1.65 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 3.16/1.65 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_260_UnE,axiom,
% 3.16/1.65 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 3.16/1.65 => ( ~ ( member2138796287ecrets @ C @ A )
% 3.16/1.65 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_261_UnE,axiom,
% 3.16/1.65 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 3.16/1.65 => ( ~ ( member_Secrecy_KS @ C @ A )
% 3.16/1.65 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_262_UnE,axiom,
% 3.16/1.65 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 3.16/1.65 => ( ~ ( member1967978193chanID @ C @ A )
% 3.16/1.65 => ( member1967978193chanID @ C @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_263_UnI1,axiom,
% 3.16/1.65 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ C @ A )
% 3.16/1.65 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_264_UnI1,axiom,
% 3.16/1.65 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ C @ A )
% 3.16/1.65 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_265_UnI1,axiom,
% 3.16/1.65 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ C @ A )
% 3.16/1.65 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_266_UnI1,axiom,
% 3.16/1.65 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ C @ A )
% 3.16/1.65 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_267_UnI1,axiom,
% 3.16/1.65 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ C @ A )
% 3.16/1.65 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_268_UnI2,axiom,
% 3.16/1.65 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ C @ B )
% 3.16/1.65 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_269_UnI2,axiom,
% 3.16/1.65 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 3.16/1.65 ( ( member_Secrecy_Keys @ C @ B )
% 3.16/1.65 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_270_UnI2,axiom,
% 3.16/1.65 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 3.16/1.65 ( ( member2138796287ecrets @ C @ B )
% 3.16/1.65 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_271_UnI2,axiom,
% 3.16/1.65 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ C @ B )
% 3.16/1.65 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_272_UnI2,axiom,
% 3.16/1.65 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ C @ B )
% 3.16/1.65 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_273_bex__Un,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 3.16/1.65 ( ( ? [X6: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X6 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 3.16/1.65 & ( P @ X6 ) ) )
% 3.16/1.65 = ( ? [X6: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X6 @ A )
% 3.16/1.65 & ( P @ X6 ) )
% 3.16/1.65 | ? [X6: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X6 @ B )
% 3.16/1.65 & ( P @ X6 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_274_bex__Un,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 3.16/1.65 ( ( ? [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ ( sup_su370684444chanID @ A @ B ) )
% 3.16/1.65 & ( P @ X6 ) ) )
% 3.16/1.65 = ( ? [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ A )
% 3.16/1.65 & ( P @ X6 ) )
% 3.16/1.65 | ? [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ B )
% 3.16/1.65 & ( P @ X6 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_275_ball__Un,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 3.16/1.65 ( ( ! [X6: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X6 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 3.16/1.65 => ( P @ X6 ) ) )
% 3.16/1.65 = ( ! [X6: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X6 @ A )
% 3.16/1.65 => ( P @ X6 ) )
% 3.16/1.65 & ! [X6: secrecy_KS] :
% 3.16/1.65 ( ( member_Secrecy_KS @ X6 @ B )
% 3.16/1.65 => ( P @ X6 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_276_ball__Un,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 3.16/1.65 ( ( ! [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ ( sup_su370684444chanID @ A @ B ) )
% 3.16/1.65 => ( P @ X6 ) ) )
% 3.16/1.65 = ( ! [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ A )
% 3.16/1.65 => ( P @ X6 ) )
% 3.16/1.65 & ! [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ B )
% 3.16/1.65 => ( P @ X6 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_277_Un__assoc,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 3.16/1.65 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_278_Un__assoc,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 3.16/1.65 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_279_Un__absorb,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ A @ A )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_280_Un__absorb,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ A @ A )
% 3.16/1.65 = A ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_281_Un__commute,axiom,
% 3.16/1.65 ( sup_su1301156759ecy_KS
% 3.16/1.65 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_282_Un__commute,axiom,
% 3.16/1.65 ( sup_su370684444chanID
% 3.16/1.65 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_283_Un__left__absorb,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 3.16/1.65 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_284_Un__left__absorb,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 3.16/1.65 = ( sup_su370684444chanID @ A @ B ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_285_Un__left__commute,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 3.16/1.65 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_286_Un__left__commute,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 3.16/1.65 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_287_singleton__Un__iff,axiom,
% 3.16/1.65 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 3.16/1.65 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 3.16/1.65 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 3.16/1.65 = ( ( ( A = bot_bo1943466239ecy_KS )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.16/1.65 & ( B = bot_bo1943466239ecy_KS ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_288_singleton__Un__iff,axiom,
% 3.16/1.65 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 3.16/1.65 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 3.16/1.65 = ( sup_su1712599557specID @ A @ B ) )
% 3.16/1.65 = ( ( ( A = bot_bo1785112429specID )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.16/1.65 & ( B = bot_bo1785112429specID ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_289_singleton__Un__iff,axiom,
% 3.16/1.65 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 3.16/1.65 = ( sup_su370684444chanID @ A @ B ) )
% 3.16/1.65 = ( ( ( A = bot_bo443197316chanID )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.16/1.65 & ( B = bot_bo443197316chanID ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_290_Un__singleton__iff,axiom,
% 3.16/1.65 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 3.16/1.65 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.16/1.65 = ( ( ( A = bot_bo1943466239ecy_KS )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.16/1.65 & ( B = bot_bo1943466239ecy_KS ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_291_Un__singleton__iff,axiom,
% 3.16/1.65 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 3.16/1.65 ( ( ( sup_su1712599557specID @ A @ B )
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.16/1.65 = ( ( ( A = bot_bo1785112429specID )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.16/1.65 & ( B = bot_bo1785112429specID ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_292_Un__singleton__iff,axiom,
% 3.16/1.65 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 3.16/1.65 ( ( ( sup_su370684444chanID @ A @ B )
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.16/1.65 = ( ( ( A = bot_bo443197316chanID )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.16/1.65 & ( B = bot_bo443197316chanID ) )
% 3.16/1.65 | ( ( A
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 3.16/1.65 & ( B
% 3.16/1.65 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_293_insert__is__Un,axiom,
% 3.16/1.65 ( insert_Secrecy_KS
% 3.16/1.65 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_294_insert__is__Un,axiom,
% 3.16/1.65 ( insert1671894227specID
% 3.16/1.65 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_295_insert__is__Un,axiom,
% 3.16/1.65 ( insert751661162chanID
% 3.16/1.65 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_296_sup__bot_Oright__neutral,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 3.16/1.65 = A2 ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_297_sup__bot_Oright__neutral,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 3.16/1.65 = A2 ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_298_sup__bot_Oright__neutral,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 3.16/1.65 = A2 ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_299_sup__bot_Oneutr__eq__iff,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 3.16/1.65 ( ( bot_bo1943466239ecy_KS
% 3.16/1.65 = ( sup_su1301156759ecy_KS @ A2 @ B2 ) )
% 3.16/1.65 = ( ( A2 = bot_bo1943466239ecy_KS )
% 3.16/1.65 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_300_sup__bot_Oneutr__eq__iff,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 3.16/1.65 ( ( bot_bo1785112429specID
% 3.16/1.65 = ( sup_su1712599557specID @ A2 @ B2 ) )
% 3.16/1.65 = ( ( A2 = bot_bo1785112429specID )
% 3.16/1.65 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_301_sup__bot_Oneutr__eq__iff,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 3.16/1.65 ( ( bot_bo443197316chanID
% 3.16/1.65 = ( sup_su370684444chanID @ A2 @ B2 ) )
% 3.16/1.65 = ( ( A2 = bot_bo443197316chanID )
% 3.16/1.65 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_302_sup__bot_Oleft__neutral,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A2 )
% 3.16/1.65 = A2 ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_303_sup__bot_Oleft__neutral,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A2 )
% 3.16/1.65 = A2 ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_304_sup__bot_Oleft__neutral,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A2 )
% 3.16/1.65 = A2 ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_305_sup__bot_Oeq__neutr__iff,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 3.16/1.65 ( ( ( sup_su1301156759ecy_KS @ A2 @ B2 )
% 3.16/1.65 = bot_bo1943466239ecy_KS )
% 3.16/1.65 = ( ( A2 = bot_bo1943466239ecy_KS )
% 3.16/1.65 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_306_sup__bot_Oeq__neutr__iff,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 3.16/1.65 ( ( ( sup_su1712599557specID @ A2 @ B2 )
% 3.16/1.65 = bot_bo1785112429specID )
% 3.16/1.65 = ( ( A2 = bot_bo1785112429specID )
% 3.16/1.65 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_307_sup__bot_Oeq__neutr__iff,axiom,
% 3.16/1.65 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ( sup_su370684444chanID @ A2 @ B2 )
% 3.16/1.65 = bot_bo443197316chanID )
% 3.16/1.65 = ( ( A2 = bot_bo443197316chanID )
% 3.16/1.65 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_308_sup__bot__left,axiom,
% 3.16/1.65 ! [X: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_309_sup__bot__left,axiom,
% 3.16/1.65 ! [X: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_310_sup__bot__left,axiom,
% 3.16/1.65 ! [X: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_311_sup__bot__right,axiom,
% 3.16/1.65 ! [X: set_Secrecy_KS] :
% 3.16/1.65 ( ( sup_su1301156759ecy_KS @ X @ bot_bo1943466239ecy_KS )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_312_sup__bot__right,axiom,
% 3.16/1.65 ! [X: set_Secrecy_specID] :
% 3.16/1.65 ( ( sup_su1712599557specID @ X @ bot_bo1785112429specID )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_313_sup__bot__right,axiom,
% 3.16/1.65 ! [X: set_Secrecy_chanID] :
% 3.16/1.65 ( ( sup_su370684444chanID @ X @ bot_bo443197316chanID )
% 3.16/1.65 = X ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_314_bot__eq__sup__iff,axiom,
% 3.16/1.65 ! [X: set_Secrecy_KS,Y: set_Secrecy_KS] :
% 3.16/1.65 ( ( bot_bo1943466239ecy_KS
% 3.16/1.65 = ( sup_su1301156759ecy_KS @ X @ Y ) )
% 3.16/1.65 = ( ( X = bot_bo1943466239ecy_KS )
% 3.16/1.65 & ( Y = bot_bo1943466239ecy_KS ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_315_bot__eq__sup__iff,axiom,
% 3.16/1.65 ! [X: set_Secrecy_specID,Y: set_Secrecy_specID] :
% 3.16/1.65 ( ( bot_bo1785112429specID
% 3.16/1.65 = ( sup_su1712599557specID @ X @ Y ) )
% 3.16/1.65 = ( ( X = bot_bo1785112429specID )
% 3.16/1.65 & ( Y = bot_bo1785112429specID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_316_bot__eq__sup__iff,axiom,
% 3.16/1.65 ! [X: set_Secrecy_chanID,Y: set_Secrecy_chanID] :
% 3.16/1.65 ( ( bot_bo443197316chanID
% 3.16/1.65 = ( sup_su370684444chanID @ X @ Y ) )
% 3.16/1.65 = ( ( X = bot_bo443197316chanID )
% 3.16/1.65 & ( Y = bot_bo443197316chanID ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_317_ineM__Un1,axiom,
% 3.16/1.65 ! [P: secrecy_specID,A: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ineM @ P @ A @ E )
% 3.16/1.65 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_318_notSpecKeysSecretsExpr__def,axiom,
% 3.16/1.65 ( notSpe1586871396tsExpr
% 3.16/1.65 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 3.16/1.65 ( ! [X6: secrecy_Keys] :
% 3.16/1.65 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X6 ) @ E3 )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X6 ) @ ( specKeysSecrets @ P2 ) ) )
% 3.16/1.65 & ! [Y7: secrecy_Secrets] :
% 3.16/1.65 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y7 ) @ E3 )
% 3.16/1.65 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y7 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_319_TBtheorem5a__empty,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ( eout @ P @ E )
% 3.16/1.65 | ( eout @ Q @ E ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( ( loc @ PQ )
% 3.16/1.65 = bot_bo443197316chanID )
% 3.16/1.65 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_320_correctCompositionKS__subcomp1,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.16/1.65 ( ( correctCompositionKS @ C3 )
% 3.16/1.65 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.16/1.65 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 3.16/1.65 => ? [X5: secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ X5 @ ( subcomponents @ C3 ) )
% 3.16/1.65 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X5 ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_321_correctCompositionKS__subcomp2,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.16/1.65 ( ( correctCompositionKS @ C3 )
% 3.16/1.65 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.16/1.65 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 3.16/1.65 => ? [X5: secrecy_specID] :
% 3.16/1.65 ( ( member740727610specID @ X5 @ ( subcomponents @ C3 ) )
% 3.16/1.65 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X5 ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_322_TBtheorem2a,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( eout @ PQ @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( eout @ P @ E )
% 3.16/1.65 | ( eout @ Q @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_323_correctCompositionKS__subcomp4,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.16/1.65 ( ( correctCompositionKS @ C3 )
% 3.16/1.65 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.16/1.65 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 3.16/1.65 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_324_correctCompositionKS__subcomp3,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.16/1.65 ( ( correctCompositionKS @ C3 )
% 3.16/1.65 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 3.16/1.65 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 3.16/1.65 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_325_TBtheorem5a__notP1,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( eout @ P @ E )
% 3.16/1.65 => ( ~ ( eout @ Q @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_326_TBtheorem5a__notP2,axiom,
% 3.16/1.65 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.16/1.65 ( ~ ( eout @ Q @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSet )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_327_TBtheorem5a__notPQ,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.16/1.65 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetP )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_328_out__exprChannelSingle__Set,axiom,
% 3.16/1.65 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.65 ( ( out_ex985543062Single @ P @ Ch @ E )
% 3.16/1.65 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_329_out__exprChannelSet__Single,axiom,
% 3.16/1.65 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.65 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 3.16/1.65 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_330_TBtheorem5b__notPQ,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.16/1.65 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.16/1.65 => ( ( M2
% 3.16/1.65 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetP )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSetQ )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_331_eout__know__s,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 3.16/1.65 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 3.16/1.65 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 3.16/1.65 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 3.16/1.65 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_332_not__know__s__not__eout,axiom,
% 3.16/1.65 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 3.16/1.65 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 3.16/1.65 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 3.16/1.65 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 3.16/1.65 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_333_eoutM__eout,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression] :
% 3.16/1.65 ( ( eoutM @ P @ M2 @ E )
% 3.16/1.65 => ( eout @ P @ E ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_334_not__eout__eoutM,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,M2: set_Secrecy_chanID] :
% 3.16/1.65 ( ~ ( eout @ P @ E )
% 3.16/1.65 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_335_TBtheorem2b,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( eoutM @ PQ @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( eoutM @ P @ M2 @ E )
% 3.16/1.65 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_336_TBtheorem5b__notP2,axiom,
% 3.16/1.65 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 3.16/1.65 ( ~ ( eoutM @ Q @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.16/1.65 => ( ! [X5: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X5 @ ChSet )
% 3.16/1.65 => ( member1967978193chanID @ X5 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_337_TBtheorem5b__notP1,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( eoutM @ P @ M2 @ E )
% 3.16/1.65 => ( ~ ( eoutM @ Q @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ M2 )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_338_eout__know__nonKS__k,axiom,
% 3.16/1.65 ! [M: secrecy_Keys,A: secrecy_specID] :
% 3.16/1.65 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 3.16/1.65 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 3.16/1.65 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 3.16/1.65 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_339_eoutKnowCorrect__L1k,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 3.16/1.65 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 3.16/1.65 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 3.16/1.65 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 3.16/1.65 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_340_not__know__k__not__eout,axiom,
% 3.16/1.65 ! [M: secrecy_Keys,A: secrecy_specID] :
% 3.16/1.65 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 3.16/1.65 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 3.16/1.65 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 3.16/1.65 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_341_eout__know__k,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 3.16/1.65 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 3.16/1.65 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 3.16/1.65 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 3.16/1.65 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_342_eout__know__nonKS__s,axiom,
% 3.16/1.65 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 3.16/1.65 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 3.16/1.65 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 3.16/1.65 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 3.16/1.65 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_343_eoutKnowCorrect__L1s,axiom,
% 3.16/1.65 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 3.16/1.65 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 3.16/1.65 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 3.16/1.65 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 3.16/1.65 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_344_TBtheore54b__P,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( eoutM @ P @ M2 @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch3 @ ( out @ Q ) )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ M2 ) )
% 3.16/1.65 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_345_TBtheorem5b__PQ,axiom,
% 3.16/1.65 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ( eoutM @ P @ M2 @ E )
% 3.16/1.65 | ( eoutM @ Q @ M2 @ E ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 3.16/1.65 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 3.16/1.65 & ( member1967978193chanID @ Ch3 @ M2 )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_346_TBtheorem45a__P,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.16/1.65 ( ( eout @ P @ E )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_347_eout__def,axiom,
% 3.16/1.65 ( eout
% 3.16/1.65 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.16/1.65 ? [Ch2: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 3.16/1.65 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_348_eoutM__def,axiom,
% 3.16/1.65 ( eoutM
% 3.16/1.65 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.16/1.65 ? [Ch2: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 3.16/1.65 & ( member1967978193chanID @ Ch2 @ M3 )
% 3.16/1.65 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_349_out__exprChannelSet__def,axiom,
% 3.16/1.65 ( out_exprChannelSet
% 3.16/1.65 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 3.16/1.65 ( ! [X6: secrecy_chanID] :
% 3.16/1.65 ( ( member1967978193chanID @ X6 @ ChSet2 )
% 3.16/1.65 => ( ( member1967978193chanID @ X6 @ ( out @ SP ) )
% 3.16/1.65 & ( exprChannel @ X6 @ E2 ) ) )
% 3.16/1.65 & ! [X6: secrecy_chanID] :
% 3.16/1.65 ( ( ~ ( member1967978193chanID @ X6 @ ChSet2 )
% 3.16/1.65 & ( member1967978193chanID @ X6 @ ( out @ SP ) ) )
% 3.16/1.65 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_350_out__exprChannelSingle__def,axiom,
% 3.16/1.65 ( out_ex985543062Single
% 3.16/1.65 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 3.16/1.65 ( ( member1967978193chanID @ Ch2 @ ( out @ SP ) )
% 3.16/1.65 & ( exprChannel @ Ch2 @ E2 )
% 3.16/1.65 & ! [X6: secrecy_chanID,T: nat] :
% 3.16/1.65 ( ( ( member1967978193chanID @ X6 @ ( out @ SP ) )
% 3.16/1.65 & ( X6 != Ch2 ) )
% 3.16/1.65 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_351_correctCompositionOut__prop1,axiom,
% 3.16/1.65 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.16/1.65 ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 3.16/1.65 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 3.16/1.65 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_352_TBtheorem5a__PQ,axiom,
% 3.16/1.65 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.16/1.65 ( ( ( eout @ P @ E )
% 3.16/1.65 | ( eout @ Q @ E ) )
% 3.16/1.65 => ( ( ( subcomponents @ PQ )
% 3.16/1.65 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 3.16/1.65 => ( ( correc990227761ionOut @ PQ )
% 3.16/1.65 => ( ? [Ch3: secrecy_chanID] :
% 3.16/1.65 ( ( ( member1967978193chanID @ Ch3 @ ( out @ P ) )
% 3.16/1.65 | ( member1967978193chanID @ Ch3 @ ( out @ Q ) ) )
% 3.16/1.65 & ( exprChannel @ Ch3 @ E )
% 3.16/1.65 & ~ ( member1967978193chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.16/1.65 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_353_outStream__def,axiom,
% 3.16/1.65 ( outStream
% 3.16/1.65 = ( ^ [X6: secrecy_specID] :
% 3.16/1.65 ( ^ [Y6: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y6 = Z )
% 3.16/1.65 @ ( out @ X6 ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(fact_354_adv__not__know2,axiom,
% 3.16/1.65 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 3.16/1.65 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 3.16/1.65 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 3.16/1.65 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 3.16/1.65
% 3.16/1.65 thf(conj_0,conjecture,
% 3.16/1.65 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 3.16/1.65 ------------------------
% 3.16/1.69 % (6540)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_6360 for (2999ds/275Mi)
% 3.16/1.69 % (6537)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_6360 for (2999ds/27Mi)
% 3.16/1.69 % (6541)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/18Mi)
% 3.16/1.69 % (6536)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_6360 for (2999ds/4Mi)
% 3.16/1.69 % (6539)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_6360 for (2999ds/2Mi)
% 3.16/1.69 % (6535)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/183Mi)
% 3.16/1.69 % (6539)Instruction limit reached!
% 3.16/1.69 % (6539)------------------------------
% 3.16/1.69 % (6539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (6539)Termination reason: Unknown
% 3.16/1.69 % (6539)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (6539)Memory used [KB]: 1407
% 3.16/1.69 % (6539)Time elapsed: 0.002 s
% 3.16/1.69 % (6539)Instructions burned: 3 (million)
% 3.16/1.69 % (6539)------------------------------
% 3.16/1.69 % (6539)------------------------------
% 3.16/1.69 % (6536)Instruction limit reached!
% 3.16/1.69 % (6536)------------------------------
% 3.16/1.69 % (6536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.69 % (6536)Termination reason: Unknown
% 3.16/1.69 % (6536)Termination phase: shuffling
% 3.16/1.69
% 3.16/1.69 % (6536)Memory used [KB]: 1535
% 3.16/1.69 % (6536)Time elapsed: 0.004 s
% 3.16/1.69 % (6536)Instructions burned: 7 (million)
% 3.16/1.69 % (6536)------------------------------
% 3.16/1.69 % (6536)------------------------------
% 3.16/1.69 % (6538)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/2Mi)
% 3.16/1.70 % (6538)Instruction limit reached!
% 3.16/1.70 % (6538)------------------------------
% 3.16/1.70 % (6538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.70 % (6538)Termination reason: Unknown
% 3.16/1.70 % (6538)Termination phase: shuffling
% 3.16/1.70
% 3.16/1.70 % (6538)Memory used [KB]: 1407
% 3.16/1.70 % (6538)Time elapsed: 0.003 s
% 3.16/1.70 % (6538)Instructions burned: 2 (million)
% 3.16/1.70 % (6538)------------------------------
% 3.16/1.70 % (6538)------------------------------
% 3.22/1.70 % (6541)Instruction limit reached!
% 3.22/1.70 % (6541)------------------------------
% 3.22/1.70 % (6541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.70 % (6541)Termination reason: Unknown
% 3.22/1.70 % (6541)Termination phase: shuffling
% 3.22/1.70
% 3.22/1.70 % (6541)Memory used [KB]: 1791
% 3.22/1.70 % (6541)Time elapsed: 0.008 s
% 3.22/1.70 % (6541)Instructions burned: 20 (million)
% 3.22/1.70 % (6541)------------------------------
% 3.22/1.70 % (6541)------------------------------
% 3.22/1.70 % (6537)Instruction limit reached!
% 3.22/1.70 % (6537)------------------------------
% 3.22/1.70 % (6537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.70 % (6537)Termination reason: Unknown
% 3.22/1.70 % (6537)Termination phase: shuffling
% 3.22/1.70
% 3.22/1.70 % (6537)Memory used [KB]: 1918
% 3.22/1.70 % (6537)Time elapsed: 0.011 s
% 3.22/1.70 % (6537)Instructions burned: 29 (million)
% 3.22/1.70 % (6537)------------------------------
% 3.22/1.70 % (6537)------------------------------
% 3.22/1.70 % (6543)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_6360 for (2999ds/37Mi)
% 3.22/1.70 % (6542)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/3Mi)
% 3.22/1.70 % (6542)Instruction limit reached!
% 3.22/1.70 % (6542)------------------------------
% 3.22/1.70 % (6542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.70 % (6542)Termination reason: Unknown
% 3.22/1.70 % (6542)Termination phase: shuffling
% 3.22/1.70
% 3.22/1.70 % (6542)Memory used [KB]: 1535
% 3.22/1.70 % (6542)Time elapsed: 0.003 s
% 3.22/1.70 % (6542)Instructions burned: 3 (million)
% 3.22/1.70 % (6542)------------------------------
% 3.22/1.70 % (6542)------------------------------
% 3.22/1.71 % (6545)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_6360 for (2999ds/3Mi)
% 3.22/1.71 % (6545)Instruction limit reached!
% 3.22/1.71 % (6545)------------------------------
% 3.22/1.71 % (6545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.71 % (6545)Termination reason: Unknown
% 3.22/1.71 % (6545)Termination phase: shuffling
% 3.22/1.71
% 3.22/1.71 % (6545)Memory used [KB]: 1535
% 3.22/1.71 % (6545)Time elapsed: 0.002 s
% 3.22/1.71 % (6545)Instructions burned: 3 (million)
% 3.22/1.71 % (6545)------------------------------
% 3.22/1.71 % (6545)------------------------------
% 3.22/1.71 % (6546)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_6360 for (2999ds/1041Mi)
% 3.22/1.71 % (6544)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_6360 for (2999ds/15Mi)
% 3.22/1.71 % (6540)Refutation not found, incomplete strategy
% 3.22/1.71 % (6540)------------------------------
% 3.22/1.71 % (6540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.71 % (6540)Termination reason: Refutation not found, incomplete strategy
% 3.22/1.71
% 3.22/1.71
% 3.22/1.71 % (6540)Memory used [KB]: 6652
% 3.22/1.71 % (6540)Time elapsed: 0.020 s
% 3.22/1.71 % (6540)Instructions burned: 61 (million)
% 3.22/1.71 % (6540)------------------------------
% 3.22/1.71 % (6540)------------------------------
% 3.22/1.71 % (6543)Instruction limit reached!
% 3.22/1.71 % (6543)------------------------------
% 3.22/1.71 % (6543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.71 % (6543)Termination reason: Unknown
% 3.22/1.71 % (6543)Termination phase: shuffling
% 3.22/1.71
% 3.22/1.71 % (6543)Memory used [KB]: 2174
% 3.22/1.71 % (6543)Time elapsed: 0.011 s
% 3.22/1.71 % (6543)Instructions burned: 37 (million)
% 3.22/1.71 % (6543)------------------------------
% 3.22/1.71 % (6543)------------------------------
% 3.22/1.71 % (6547)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/7Mi)
% 3.22/1.72 % (6544)Instruction limit reached!
% 3.22/1.72 % (6544)------------------------------
% 3.22/1.72 % (6544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.72 % (6544)Termination reason: Unknown
% 3.22/1.72 % (6544)Termination phase: shuffling
% 3.22/1.72
% 3.22/1.72 % (6544)Memory used [KB]: 1663
% 3.22/1.72 % (6544)Time elapsed: 0.009 s
% 3.22/1.72 % (6544)Instructions burned: 17 (million)
% 3.22/1.72 % (6544)------------------------------
% 3.22/1.72 % (6544)------------------------------
% 3.22/1.72 % (6547)Instruction limit reached!
% 3.22/1.72 % (6547)------------------------------
% 3.22/1.72 % (6547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.72 % (6547)Termination reason: Unknown
% 3.22/1.72 % (6547)Termination phase: shuffling
% 3.22/1.72
% 3.22/1.72 % (6547)Memory used [KB]: 1535
% 3.22/1.72 % (6547)Time elapsed: 0.005 s
% 3.22/1.72 % (6547)Instructions burned: 9 (million)
% 3.22/1.72 % (6547)------------------------------
% 3.22/1.72 % (6547)------------------------------
% 3.22/1.72 % (6548)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/16Mi)
% 3.22/1.72 % (6549)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_6360 for (2999ds/3Mi)
% 3.22/1.72 % (6549)Instruction limit reached!
% 3.22/1.72 % (6549)------------------------------
% 3.22/1.72 % (6549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.72 % (6549)Termination reason: Unknown
% 3.22/1.72 % (6549)Termination phase: shuffling
% 3.22/1.72
% 3.22/1.72 % (6549)Memory used [KB]: 1407
% 3.22/1.72 % (6549)Time elapsed: 0.002 s
% 3.22/1.72 % (6549)Instructions burned: 3 (million)
% 3.22/1.72 % (6549)------------------------------
% 3.22/1.72 % (6549)------------------------------
% 3.22/1.72 % (6550)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_6360 for (2999ds/3Mi)
% 3.22/1.72 % (6548)Instruction limit reached!
% 3.22/1.72 % (6548)------------------------------
% 3.22/1.72 % (6548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.72 % (6548)Termination reason: Unknown
% 3.22/1.72 % (6548)Termination phase: shuffling
% 3.22/1.72
% 3.22/1.72 % (6548)Memory used [KB]: 1791
% 3.22/1.72 % (6548)Time elapsed: 0.006 s
% 3.22/1.72 % (6548)Instructions burned: 16 (million)
% 3.22/1.72 % (6548)------------------------------
% 3.22/1.72 % (6548)------------------------------
% 3.22/1.72 % (6550)Instruction limit reached!
% 3.22/1.72 % (6550)------------------------------
% 3.22/1.72 % (6550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.72 % (6550)Termination reason: Unknown
% 3.22/1.72 % (6550)Termination phase: shuffling
% 3.22/1.72
% 3.22/1.72 % (6550)Memory used [KB]: 1407
% 3.22/1.72 % (6550)Time elapsed: 0.002 s
% 3.22/1.72 % (6550)Instructions burned: 3 (million)
% 3.22/1.72 % (6550)------------------------------
% 3.22/1.72 % (6550)------------------------------
% 3.22/1.73 % (6552)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/3Mi)
% 3.22/1.73 % (6552)Instruction limit reached!
% 3.22/1.73 % (6552)------------------------------
% 3.22/1.73 % (6552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.73 % (6552)Termination reason: Unknown
% 3.22/1.73 % (6552)Termination phase: shuffling
% 3.22/1.73
% 3.22/1.73 % (6552)Memory used [KB]: 1535
% 3.22/1.73 % (6552)Time elapsed: 0.003 s
% 3.22/1.73 % (6552)Instructions burned: 5 (million)
% 3.22/1.73 % (6552)------------------------------
% 3.22/1.73 % (6552)------------------------------
% 3.22/1.73 % (6551)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/7Mi)
% 3.22/1.73 % (6553)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/4Mi)
% 3.22/1.73 % (6554)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/18Mi)
% 3.22/1.73 % (6553)Instruction limit reached!
% 3.22/1.73 % (6553)------------------------------
% 3.22/1.73 % (6553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.73 % (6553)Termination reason: Unknown
% 3.22/1.73 % (6553)Termination phase: shuffling
% 3.22/1.73
% 3.22/1.73 % (6553)Memory used [KB]: 1535
% 3.22/1.73 % (6553)Time elapsed: 0.003 s
% 3.22/1.73 % (6553)Instructions burned: 6 (million)
% 3.22/1.73 % (6553)------------------------------
% 3.22/1.73 % (6553)------------------------------
% 3.22/1.73 % (6551)Instruction limit reached!
% 3.22/1.73 % (6551)------------------------------
% 3.22/1.73 % (6551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.73 % (6551)Termination reason: Unknown
% 3.22/1.73 % (6551)Termination phase: shuffling
% 3.22/1.73
% 3.22/1.73 % (6551)Memory used [KB]: 1535
% 3.22/1.73 % (6551)Time elapsed: 0.006 s
% 3.22/1.73 % (6551)Instructions burned: 8 (million)
% 3.22/1.73 % (6551)------------------------------
% 3.22/1.73 % (6551)------------------------------
% 3.22/1.73 % (6555)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/710Mi)
% 3.22/1.74 % (6554)Instruction limit reached!
% 3.22/1.74 % (6554)------------------------------
% 3.22/1.74 % (6554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.74 % (6554)Termination reason: Unknown
% 3.22/1.74 % (6554)Termination phase: shuffling
% 3.22/1.74
% 3.22/1.74 % (6554)Memory used [KB]: 1918
% 3.22/1.74 % (6554)Time elapsed: 0.007 s
% 3.22/1.74 % (6554)Instructions burned: 19 (million)
% 3.22/1.74 % (6554)------------------------------
% 3.22/1.74 % (6554)------------------------------
% 3.22/1.74 % (6556)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/6Mi)
% 3.22/1.74 % (6556)Instruction limit reached!
% 3.22/1.74 % (6556)------------------------------
% 3.22/1.74 % (6556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.74 % (6556)Termination reason: Unknown
% 3.22/1.74 % (6556)Termination phase: shuffling
% 3.22/1.74
% 3.22/1.74 % (6556)Memory used [KB]: 1535
% 3.22/1.74 % (6556)Time elapsed: 0.003 s
% 3.22/1.74 % (6556)Instructions burned: 6 (million)
% 3.22/1.74 % (6556)------------------------------
% 3.22/1.74 % (6556)------------------------------
% 3.22/1.74 % (6557)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_6360 for (2999ds/902Mi)
% 3.22/1.75 % (6535)Instruction limit reached!
% 3.22/1.75 % (6535)------------------------------
% 3.22/1.75 % (6535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.75 % (6535)Termination reason: Unknown
% 3.22/1.75 % (6535)Termination phase: Saturation
% 3.22/1.75
% 3.22/1.75 % (6535)Memory used [KB]: 7419
% 3.22/1.75 % (6535)Time elapsed: 0.057 s
% 3.22/1.75 % (6535)Instructions burned: 186 (million)
% 3.22/1.75 % (6535)------------------------------
% 3.22/1.75 % (6535)------------------------------
% 3.22/1.75 % (6560)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_6360 for (2999ds/6Mi)
% 3.22/1.75 % (6560)Instruction limit reached!
% 3.22/1.75 % (6560)------------------------------
% 3.22/1.75 % (6560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.75 % (6560)Termination reason: Unknown
% 3.22/1.75 % (6560)Termination phase: shuffling
% 3.22/1.75
% 3.22/1.75 % (6560)Memory used [KB]: 1535
% 3.22/1.75 % (6560)Time elapsed: 0.003 s
% 3.22/1.75 % (6560)Instructions burned: 7 (million)
% 3.22/1.75 % (6560)------------------------------
% 3.22/1.75 % (6560)------------------------------
% 3.22/1.75 % (6558)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_6360 for (2999ds/21Mi)
% 3.22/1.75 % (6559)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/5Mi)
% 3.22/1.76 % (6559)Instruction limit reached!
% 3.22/1.76 % (6559)------------------------------
% 3.22/1.76 % (6559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.76 % (6559)Termination reason: Unknown
% 3.22/1.76 % (6559)Termination phase: shuffling
% 3.22/1.76
% 3.22/1.76 % (6559)Memory used [KB]: 1535
% 3.22/1.76 % (6559)Time elapsed: 0.003 s
% 3.22/1.76 % (6559)Instructions burned: 6 (million)
% 3.22/1.76 % (6559)------------------------------
% 3.22/1.76 % (6559)------------------------------
% 3.22/1.76 % (6561)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6360 for (2999ds/377Mi)
% 3.22/1.76 % (6562)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_6360 for (2998ds/779Mi)
% 3.22/1.77 % (6558)Instruction limit reached!
% 3.22/1.77 % (6558)------------------------------
% 3.22/1.77 % (6558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.77 % (6558)Termination reason: Unknown
% 3.22/1.77 % (6558)Termination phase: shuffling
% 3.22/1.77
% 3.22/1.77 % (6558)Memory used [KB]: 1918
% 3.22/1.77 % (6558)Time elapsed: 0.015 s
% 3.22/1.77 % (6558)Instructions burned: 21 (million)
% 3.22/1.77 % (6558)------------------------------
% 3.22/1.77 % (6558)------------------------------
% 3.22/1.77 % (6563)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_6360 for (2998ds/19Mi)
% 3.22/1.77 % (6555)Refutation not found, incomplete strategy
% 3.22/1.77 % (6555)------------------------------
% 3.22/1.77 % (6555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.77 % (6555)Termination reason: Refutation not found, incomplete strategy
% 3.22/1.77
% 3.22/1.77
% 3.22/1.77 % (6555)Memory used [KB]: 6652
% 3.22/1.77 % (6555)Time elapsed: 0.036 s
% 3.22/1.77 % (6555)Instructions burned: 59 (million)
% 3.22/1.77 % (6555)------------------------------
% 3.22/1.77 % (6555)------------------------------
% 3.22/1.78 % (6564)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/879Mi)
% 3.22/1.78 % (6563)Instruction limit reached!
% 3.22/1.78 % (6563)------------------------------
% 3.22/1.78 % (6563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.78 % (6563)Termination reason: Unknown
% 3.22/1.78 % (6563)Termination phase: shuffling
% 3.22/1.78
% 3.22/1.78 % (6563)Memory used [KB]: 1791
% 3.22/1.78 % (6563)Time elapsed: 0.012 s
% 3.22/1.78 % (6563)Instructions burned: 20 (million)
% 3.22/1.78 % (6563)------------------------------
% 3.22/1.78 % (6563)------------------------------
% 3.22/1.79 % (6565)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/17Mi)
% 3.22/1.79 % (6566)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/3Mi)
% 3.22/1.79 % (6566)Instruction limit reached!
% 3.22/1.79 % (6566)------------------------------
% 3.22/1.79 % (6566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.79 % (6566)Termination reason: Unknown
% 3.22/1.79 % (6566)Termination phase: shuffling
% 3.22/1.79
% 3.22/1.79 % (6566)Memory used [KB]: 1407
% 3.22/1.79 % (6566)Time elapsed: 0.002 s
% 3.22/1.79 % (6566)Instructions burned: 3 (million)
% 3.22/1.79 % (6566)------------------------------
% 3.22/1.79 % (6566)------------------------------
% 3.22/1.79 % (6557)Refutation not found, incomplete strategy
% 3.22/1.79 % (6557)------------------------------
% 3.22/1.79 % (6557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.79 % (6557)Termination reason: Refutation not found, incomplete strategy
% 3.22/1.79
% 3.22/1.79
% 3.22/1.79 % (6557)Memory used [KB]: 7803
% 3.22/1.79 % (6557)Time elapsed: 0.051 s
% 3.22/1.79 % (6557)Instructions burned: 175 (million)
% 3.22/1.79 % (6557)------------------------------
% 3.22/1.79 % (6557)------------------------------
% 3.22/1.79 % (6565)Instruction limit reached!
% 3.22/1.79 % (6565)------------------------------
% 3.22/1.79 % (6565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.79 % (6565)Termination reason: Unknown
% 3.22/1.79 % (6565)Termination phase: shuffling
% 3.22/1.79
% 3.22/1.79 % (6565)Memory used [KB]: 1791
% 3.22/1.79 % (6565)Time elapsed: 0.008 s
% 3.22/1.79 % (6565)Instructions burned: 17 (million)
% 3.22/1.79 % (6565)------------------------------
% 3.22/1.79 % (6565)------------------------------
% 3.22/1.80 % (6568)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/30Mi)
% 3.22/1.80 % (6571)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/127Mi)
% 3.22/1.80 % (6572)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/100Mi)
% 3.22/1.81 % (6568)Instruction limit reached!
% 3.22/1.81 % (6568)------------------------------
% 3.22/1.81 % (6568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.81 % (6568)Termination reason: Unknown
% 3.22/1.81 % (6568)Termination phase: shuffling
% 3.22/1.81
% 3.22/1.81 % (6568)Memory used [KB]: 2046
% 3.22/1.81 % (6568)Time elapsed: 0.011 s
% 3.22/1.81 % (6568)Instructions burned: 32 (million)
% 3.22/1.81 % (6568)------------------------------
% 3.22/1.81 % (6568)------------------------------
% 3.22/1.82 % (6580)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/3Mi)
% 3.22/1.82 % (6580)Instruction limit reached!
% 3.22/1.82 % (6580)------------------------------
% 3.22/1.82 % (6580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.82 % (6580)Termination reason: Unknown
% 3.22/1.82 % (6580)Termination phase: shuffling
% 3.22/1.82
% 3.22/1.82 % (6580)Memory used [KB]: 1535
% 3.22/1.82 % (6580)Time elapsed: 0.003 s
% 3.22/1.82 % (6580)Instructions burned: 5 (million)
% 3.22/1.82 % (6580)------------------------------
% 3.22/1.82 % (6580)------------------------------
% 3.22/1.83 % (6587)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/20Mi)
% 3.22/1.83 % (6572)Instruction limit reached!
% 3.22/1.83 % (6572)------------------------------
% 3.22/1.83 % (6572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.83 % (6572)Termination reason: Unknown
% 3.22/1.83 % (6572)Termination phase: Preprocessing 3
% 3.22/1.83
% 3.22/1.83 % (6572)Memory used [KB]: 2814
% 3.22/1.83 % (6572)Time elapsed: 0.031 s
% 3.22/1.83 % (6572)Instructions burned: 103 (million)
% 3.22/1.83 % (6572)------------------------------
% 3.22/1.83 % (6572)------------------------------
% 3.22/1.84 % (6587)Instruction limit reached!
% 3.22/1.84 % (6587)------------------------------
% 3.22/1.84 % (6587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.84 % (6587)Termination reason: Unknown
% 3.22/1.84 % (6587)Termination phase: shuffling
% 3.22/1.84
% 3.22/1.84 % (6587)Memory used [KB]: 1791
% 3.22/1.84 % (6587)Time elapsed: 0.008 s
% 3.22/1.84 % (6587)Instructions burned: 21 (million)
% 3.22/1.84 % (6587)------------------------------
% 3.22/1.84 % (6587)------------------------------
% 3.22/1.84 % (6571)Instruction limit reached!
% 3.22/1.84 % (6571)------------------------------
% 3.22/1.84 % (6571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.84 % (6571)Termination reason: Unknown
% 3.22/1.84 % (6571)Termination phase: Property scanning
% 3.22/1.84
% 3.22/1.84 % (6571)Memory used [KB]: 2558
% 3.22/1.84 % (6571)Time elapsed: 0.037 s
% 3.22/1.84 % (6571)Instructions burned: 129 (million)
% 3.22/1.84 % (6571)------------------------------
% 3.22/1.84 % (6571)------------------------------
% 3.22/1.84 % (6594)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/86Mi)
% 3.22/1.85 % (6596)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/107Mi)
% 3.22/1.85 % (6599)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_6360 for (2998ds/39Mi)
% 3.22/1.86 % (6599)Instruction limit reached!
% 3.22/1.86 % (6599)------------------------------
% 3.22/1.86 % (6599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.86 % (6599)Termination reason: Unknown
% 3.22/1.86 % (6599)Termination phase: shuffling
% 3.22/1.86
% 3.22/1.86 % (6599)Memory used [KB]: 2302
% 3.22/1.86 % (6599)Time elapsed: 0.013 s
% 3.22/1.86 % (6599)Instructions burned: 42 (million)
% 3.22/1.86 % (6599)------------------------------
% 3.22/1.86 % (6599)------------------------------
% 3.22/1.87 % (6561)Instruction limit reached!
% 3.22/1.87 % (6561)------------------------------
% 3.22/1.87 % (6561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.87 % (6561)Termination reason: Unknown
% 3.22/1.87 % (6561)Termination phase: Saturation
% 3.22/1.87
% 3.22/1.87 % (6561)Memory used [KB]: 8443
% 3.22/1.87 % (6561)Time elapsed: 0.110 s
% 3.22/1.87 % (6561)Instructions burned: 380 (million)
% 3.22/1.87 % (6561)------------------------------
% 3.22/1.87 % (6561)------------------------------
% 3.22/1.87 % (6594)Instruction limit reached!
% 3.22/1.87 % (6594)------------------------------
% 3.22/1.87 % (6594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.87 % (6594)Termination reason: Unknown
% 3.22/1.87 % (6594)Termination phase: Property scanning
% 3.22/1.87
% 3.22/1.87 % (6594)Memory used [KB]: 2430
% 3.22/1.87 % (6594)Time elapsed: 0.026 s
% 3.22/1.87 % (6594)Instructions burned: 86 (million)
% 3.22/1.87 % (6594)------------------------------
% 3.22/1.87 % (6594)------------------------------
% 3.22/1.87 % (6612)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/448Mi)
% 3.22/1.88 % (6616)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/46Mi)
% 3.22/1.88 % (6596)Instruction limit reached!
% 3.22/1.88 % (6596)------------------------------
% 3.22/1.88 % (6596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.88 % (6596)Termination reason: Unknown
% 3.22/1.88 % (6596)Termination phase: Property scanning
% 3.22/1.88
% 3.22/1.88 % (6596)Memory used [KB]: 2558
% 3.22/1.88 % (6596)Time elapsed: 0.032 s
% 3.22/1.88 % (6596)Instructions burned: 108 (million)
% 3.22/1.88 % (6596)------------------------------
% 3.22/1.88 % (6596)------------------------------
% 3.22/1.88 % (6617)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/98Mi)
% 3.22/1.89 % (6620)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/507Mi)
% 3.22/1.89 % (6616)Instruction limit reached!
% 3.22/1.89 % (6616)------------------------------
% 3.22/1.89 % (6616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.89 % (6616)Termination reason: Unknown
% 3.22/1.89 % (6616)Termination phase: Property scanning
% 3.22/1.89
% 3.22/1.89 % (6616)Memory used [KB]: 2046
% 3.22/1.89 % (6616)Time elapsed: 0.015 s
% 3.22/1.89 % (6616)Instructions burned: 46 (million)
% 3.22/1.89 % (6616)------------------------------
% 3.22/1.89 % (6616)------------------------------
% 3.22/1.90 % (6628)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/149Mi)
% 3.22/1.90 % (6617)Instruction limit reached!
% 3.22/1.90 % (6617)------------------------------
% 3.22/1.90 % (6617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.90 % (6617)Termination reason: Unknown
% 3.22/1.90 % (6617)Termination phase: Property scanning
% 3.22/1.90
% 3.22/1.90 % (6617)Memory used [KB]: 2814
% 3.22/1.90 % (6617)Time elapsed: 0.028 s
% 3.22/1.90 % (6617)Instructions burned: 101 (million)
% 3.22/1.90 % (6617)------------------------------
% 3.22/1.90 % (6617)------------------------------
% 3.22/1.91 % (6635)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/39Mi)
% 3.22/1.93 % (6635)Instruction limit reached!
% 3.22/1.93 % (6635)------------------------------
% 3.22/1.93 % (6635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.93 % (6635)Termination reason: Unknown
% 3.22/1.93 % (6635)Termination phase: Property scanning
% 3.22/1.93
% 3.22/1.93 % (6635)Memory used [KB]: 2046
% 3.22/1.93 % (6635)Time elapsed: 0.013 s
% 3.22/1.93 % (6635)Instructions burned: 39 (million)
% 3.22/1.93 % (6635)------------------------------
% 3.22/1.93 % (6635)------------------------------
% 3.22/1.94 % (6641)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/6Mi)
% 3.22/1.94 % (6641)Instruction limit reached!
% 3.22/1.94 % (6641)------------------------------
% 3.22/1.94 % (6641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.94 % (6641)Termination reason: Unknown
% 3.22/1.94 % (6641)Termination phase: shuffling
% 3.22/1.94
% 3.22/1.94 % (6641)Memory used [KB]: 1535
% 3.22/1.94 % (6641)Time elapsed: 0.003 s
% 3.22/1.94 % (6641)Instructions burned: 7 (million)
% 3.22/1.94 % (6641)------------------------------
% 3.22/1.94 % (6641)------------------------------
% 3.22/1.94 % (6628)Instruction limit reached!
% 3.22/1.94 % (6628)------------------------------
% 3.22/1.94 % (6628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.94 % (6628)Termination reason: Unknown
% 3.22/1.94 % (6628)Termination phase: Saturation
% 3.22/1.94
% 3.22/1.94 % (6628)Memory used [KB]: 7164
% 3.22/1.94 % (6628)Time elapsed: 0.042 s
% 3.22/1.94 % (6628)Instructions burned: 151 (million)
% 3.22/1.94 % (6628)------------------------------
% 3.22/1.94 % (6628)------------------------------
% 3.22/1.95 % (6648)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/1087Mi)
% 3.22/1.95 % (6649)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_6360 for (2997ds/47Mi)
% 3.22/1.96 % (6649)Instruction limit reached!
% 3.22/1.96 % (6649)------------------------------
% 3.22/1.96 % (6649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.96 % (6649)Termination reason: Unknown
% 3.22/1.96 % (6649)Termination phase: Property scanning
% 3.22/1.96
% 3.22/1.96 % (6649)Memory used [KB]: 2046
% 3.22/1.96 % (6649)Time elapsed: 0.015 s
% 3.22/1.96 % (6649)Instructions burned: 48 (million)
% 3.22/1.96 % (6649)------------------------------
% 3.22/1.96 % (6649)------------------------------
% 3.22/1.97 % (6662)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/44Mi)
% 3.22/1.99 % (6662)Instruction limit reached!
% 3.22/1.99 % (6662)------------------------------
% 3.22/1.99 % (6662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.99 % (6662)Termination reason: Unknown
% 3.22/1.99 % (6662)Termination phase: shuffling
% 3.22/1.99
% 3.22/1.99 % (6662)Memory used [KB]: 2302
% 3.22/1.99 % (6662)Time elapsed: 0.013 s
% 3.22/1.99 % (6662)Instructions burned: 44 (million)
% 3.22/1.99 % (6662)------------------------------
% 3.22/1.99 % (6662)------------------------------
% 3.22/1.99 % (6562)Instruction limit reached!
% 3.22/1.99 % (6562)------------------------------
% 3.22/1.99 % (6562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.99 % (6562)Termination reason: Unknown
% 3.22/1.99 % (6562)Termination phase: Saturation
% 3.22/1.99
% 3.22/1.99 % (6562)Memory used [KB]: 9594
% 3.22/1.99 % (6562)Time elapsed: 0.228 s
% 3.22/1.99 % (6562)Instructions burned: 781 (million)
% 3.22/1.99 % (6562)------------------------------
% 3.22/1.99 % (6562)------------------------------
% 3.22/1.99 % (6612)Instruction limit reached!
% 3.22/1.99 % (6612)------------------------------
% 3.22/1.99 % (6612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.99 % (6612)Termination reason: Unknown
% 3.22/1.99 % (6612)Termination phase: Saturation
% 3.22/1.99
% 3.22/1.99 % (6612)Memory used [KB]: 8827
% 3.22/1.99 % (6612)Time elapsed: 0.123 s
% 3.22/1.99 % (6612)Instructions burned: 448 (million)
% 3.22/1.99 % (6612)------------------------------
% 3.22/1.99 % (6612)------------------------------
% 3.22/2.00 % (6620)Refutation not found, incomplete strategy
% 3.22/2.00 % (6620)------------------------------
% 3.22/2.00 % (6620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/2.00 % (6620)Termination reason: Refutation not found, incomplete strategy
% 3.22/2.00
% 3.22/2.00
% 3.22/2.00 % (6620)Memory used [KB]: 8315
% 3.22/2.00 % (6620)Time elapsed: 0.110 s
% 3.22/2.00 % (6620)Instructions burned: 367 (million)
% 3.22/2.00 % (6620)------------------------------
% 3.22/2.00 % (6620)------------------------------
% 3.22/2.00 % (6671)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/432Mi)
% 3.22/2.00 % (6672)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/62Mi)
% 3.22/2.00 % (6674)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/31Mi)
% 3.22/2.01 % (6679)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/96Mi)
% 3.22/2.01 % (6674)Instruction limit reached!
% 3.22/2.01 % (6674)------------------------------
% 3.22/2.01 % (6674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/2.01 % (6674)Termination reason: Unknown
% 3.22/2.01 % (6674)Termination phase: shuffling
% 3.22/2.01
% 3.22/2.01 % (6674)Memory used [KB]: 2046
% 3.22/2.01 % (6674)Time elapsed: 0.011 s
% 3.22/2.01 % (6674)Instructions burned: 32 (million)
% 3.22/2.01 % (6674)------------------------------
% 3.22/2.01 % (6674)------------------------------
% 3.22/2.01 % (6672)Instruction limit reached!
% 3.22/2.01 % (6672)------------------------------
% 3.22/2.01 % (6672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/2.01 % (6672)Termination reason: Unknown
% 3.22/2.01 % (6672)Termination phase: shuffling
% 3.22/2.01
% 3.22/2.01 % (6672)Memory used [KB]: 2814
% 3.22/2.01 % (6672)Time elapsed: 0.018 s
% 3.22/2.01 % (6672)Instructions burned: 62 (million)
% 3.22/2.01 % (6672)------------------------------
% 3.22/2.01 % (6672)------------------------------
% 3.22/2.02 % (6691)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/453Mi)
% 5.54/2.02 % (6695)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/71Mi)
% 5.54/2.03 % (6546)Instruction limit reached!
% 5.54/2.03 % (6546)------------------------------
% 5.54/2.03 % (6546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.03 % (6546)Termination reason: Unknown
% 5.54/2.03 % (6546)Termination phase: Saturation
% 5.54/2.03
% 5.54/2.03 % (6546)Memory used [KB]: 10618
% 5.54/2.03 % (6546)Time elapsed: 0.320 s
% 5.54/2.03 % (6546)Instructions burned: 1042 (million)
% 5.54/2.03 % (6546)------------------------------
% 5.54/2.03 % (6546)------------------------------
% 5.54/2.03 % (6679)Instruction limit reached!
% 5.54/2.03 % (6679)------------------------------
% 5.54/2.03 % (6679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.03 % (6679)Termination reason: Unknown
% 5.54/2.03 % (6679)Termination phase: Function definition elimination
% 5.54/2.03
% 5.54/2.03 % (6679)Memory used [KB]: 2430
% 5.54/2.03 % (6679)Time elapsed: 0.028 s
% 5.54/2.03 % (6679)Instructions burned: 96 (million)
% 5.54/2.03 % (6679)------------------------------
% 5.54/2.03 % (6679)------------------------------
% 5.54/2.04 % (6701)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/83Mi)
% 5.54/2.04 % (6702)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/11Mi)
% 5.54/2.04 % (6702)Instruction limit reached!
% 5.54/2.04 % (6702)------------------------------
% 5.54/2.04 % (6702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.04 % (6702)Termination reason: Unknown
% 5.54/2.04 % (6702)Termination phase: shuffling
% 5.54/2.04
% 5.54/2.04 % (6702)Memory used [KB]: 1663
% 5.54/2.04 % (6702)Time elapsed: 0.004 s
% 5.54/2.04 % (6702)Instructions burned: 11 (million)
% 5.54/2.04 % (6702)------------------------------
% 5.54/2.04 % (6702)------------------------------
% 5.54/2.05 % (6695)Instruction limit reached!
% 5.54/2.05 % (6695)------------------------------
% 5.54/2.05 % (6695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.05 % (6695)Termination reason: Unknown
% 5.54/2.05 % (6695)Termination phase: Preprocessing 3
% 5.54/2.05
% 5.54/2.05 % (6695)Memory used [KB]: 2430
% 5.54/2.05 % (6695)Time elapsed: 0.022 s
% 5.54/2.05 % (6695)Instructions burned: 71 (million)
% 5.54/2.05 % (6695)------------------------------
% 5.54/2.05 % (6695)------------------------------
% 5.54/2.05 % (6564)Instruction limit reached!
% 5.54/2.05 % (6564)------------------------------
% 5.54/2.05 % (6564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.05 % (6564)Termination reason: Unknown
% 5.54/2.05 % (6564)Termination phase: Saturation
% 5.54/2.05
% 5.54/2.05 % (6564)Memory used [KB]: 7803
% 5.54/2.05 % (6564)Time elapsed: 0.270 s
% 5.54/2.05 % (6564)Instructions burned: 881 (million)
% 5.54/2.05 % (6564)------------------------------
% 5.54/2.05 % (6564)------------------------------
% 5.54/2.05 % (6714)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/41Mi)
% 5.54/2.05 % (6715)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/6Mi)
% 5.54/2.06 % (6716)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/150Mi)
% 5.54/2.06 % (6715)Instruction limit reached!
% 5.54/2.06 % (6715)------------------------------
% 5.54/2.06 % (6715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.06 % (6715)Termination reason: Unknown
% 5.54/2.06 % (6715)Termination phase: shuffling
% 5.54/2.06
% 5.54/2.06 % (6715)Memory used [KB]: 1535
% 5.54/2.06 % (6715)Time elapsed: 0.003 s
% 5.54/2.06 % (6715)Instructions burned: 6 (million)
% 5.54/2.06 % (6715)------------------------------
% 5.54/2.06 % (6715)------------------------------
% 5.54/2.06 % (6701)Instruction limit reached!
% 5.54/2.06 % (6701)------------------------------
% 5.54/2.06 % (6701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.06 % (6701)Termination reason: Unknown
% 5.54/2.06 % (6701)Termination phase: Saturation
% 5.54/2.06
% 5.54/2.06 % (6701)Memory used [KB]: 6652
% 5.54/2.06 % (6701)Time elapsed: 0.027 s
% 5.54/2.06 % (6701)Instructions burned: 85 (million)
% 5.54/2.06 % (6701)------------------------------
% 5.54/2.06 % (6701)------------------------------
% 5.54/2.07 % (6714)Instruction limit reached!
% 5.54/2.07 % (6714)------------------------------
% 5.54/2.07 % (6714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.07 % (6714)Termination reason: Unknown
% 5.54/2.07 % (6714)Termination phase: shuffling
% 5.54/2.07
% 5.54/2.07 % (6714)Memory used [KB]: 2302
% 5.54/2.07 % (6714)Time elapsed: 0.013 s
% 5.54/2.07 % (6714)Instructions burned: 44 (million)
% 5.54/2.07 % (6714)------------------------------
% 5.54/2.07 % (6714)------------------------------
% 5.54/2.07 % (6722)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_6360 for (2996ds/343Mi)
% 5.54/2.07 % (6725)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/109Mi)
% 5.54/2.08 % (6726)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/253Mi)
% 5.54/2.10 % (6716)Instruction limit reached!
% 5.54/2.10 % (6716)------------------------------
% 5.54/2.10 % (6716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.10 % (6716)Termination reason: Unknown
% 5.54/2.10 % (6716)Termination phase: Property scanning
% 5.54/2.10
% 5.54/2.10 % (6716)Memory used [KB]: 2814
% 5.54/2.10 % (6716)Time elapsed: 0.047 s
% 5.54/2.10 % (6716)Instructions burned: 152 (million)
% 5.54/2.10 % (6716)------------------------------
% 5.54/2.10 % (6716)------------------------------
% 5.54/2.11 % (6725)Instruction limit reached!
% 5.54/2.11 % (6725)------------------------------
% 5.54/2.11 % (6725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.11 % (6725)Termination reason: Unknown
% 5.54/2.11 % (6725)Termination phase: Function definition elimination
% 5.54/2.11
% 5.54/2.11 % (6725)Memory used [KB]: 2558
% 5.54/2.11 % (6725)Time elapsed: 0.032 s
% 5.54/2.11 % (6725)Instructions burned: 110 (million)
% 5.54/2.11 % (6725)------------------------------
% 5.54/2.11 % (6725)------------------------------
% 5.54/2.11 % (6743)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/140Mi)
% 5.54/2.11 % (6746)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/614Mi)
% 5.54/2.12 % (6671)Instruction limit reached!
% 5.54/2.12 % (6671)------------------------------
% 5.54/2.12 % (6671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.54/2.12 % (6671)Termination reason: Unknown
% 5.54/2.12 % (6671)Termination phase: Saturation
% 5.54/2.12
% 5.54/2.12 % (6671)Memory used [KB]: 3965
% 5.54/2.12 % (6671)Time elapsed: 0.124 s
% 5.54/2.12 % (6671)Instructions burned: 433 (million)
% 5.54/2.12 % (6671)------------------------------
% 5.54/2.12 % (6671)------------------------------
% 6.05/2.13 % (6751)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/202Mi)
% 6.05/2.13 % (6743)Refutation not found, incomplete strategy
% 6.05/2.13 % (6743)------------------------------
% 6.05/2.13 % (6743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.13 % (6743)Termination reason: Refutation not found, incomplete strategy
% 6.05/2.13
% 6.05/2.13
% 6.05/2.13 % (6743)Memory used [KB]: 6652
% 6.05/2.13 % (6743)Time elapsed: 0.023 s
% 6.05/2.13 % (6743)Instructions burned: 67 (million)
% 6.05/2.13 % (6743)------------------------------
% 6.05/2.13 % (6743)------------------------------
% 6.05/2.14 % (6691)Instruction limit reached!
% 6.05/2.14 % (6691)------------------------------
% 6.05/2.14 % (6691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.14 % (6691)Termination reason: Unknown
% 6.05/2.14 % (6691)Termination phase: Saturation
% 6.05/2.14
% 6.05/2.14 % (6691)Memory used [KB]: 8187
% 6.05/2.14 % (6691)Time elapsed: 0.121 s
% 6.05/2.14 % (6691)Instructions burned: 454 (million)
% 6.05/2.14 % (6691)------------------------------
% 6.05/2.14 % (6691)------------------------------
% 6.05/2.14 % (6757)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/339Mi)
% 6.05/2.15 % (6751)Refutation not found, incomplete strategy
% 6.05/2.15 % (6751)------------------------------
% 6.05/2.15 % (6751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.15 % (6751)Termination reason: Refutation not found, incomplete strategy
% 6.05/2.15
% 6.05/2.15
% 6.05/2.15 % (6751)Memory used [KB]: 6652
% 6.05/2.15 % (6751)Time elapsed: 0.022 s
% 6.05/2.15 % (6751)Instructions burned: 71 (million)
% 6.05/2.15 % (6751)------------------------------
% 6.05/2.15 % (6751)------------------------------
% 6.05/2.15 % (6760)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/283Mi)
% 6.05/2.15 % (6726)Instruction limit reached!
% 6.05/2.15 % (6726)------------------------------
% 6.05/2.15 % (6726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.15 % (6726)Termination reason: Unknown
% 6.05/2.15 % (6726)Termination phase: Saturation
% 6.05/2.15
% 6.05/2.15 % (6726)Memory used [KB]: 6908
% 6.05/2.15 % (6726)Time elapsed: 0.079 s
% 6.05/2.15 % (6726)Instructions burned: 255 (million)
% 6.05/2.15 % (6726)------------------------------
% 6.05/2.15 % (6726)------------------------------
% 6.05/2.16 % (6765)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/134Mi)
% 6.05/2.16 % (6769)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_6360 for (2995ds/298Mi)
% 6.05/2.17 % (6722)Instruction limit reached!
% 6.05/2.17 % (6722)------------------------------
% 6.05/2.17 % (6722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.17 % (6722)Termination reason: Unknown
% 6.05/2.17 % (6722)Termination phase: Saturation
% 6.05/2.17
% 6.05/2.17 % (6722)Memory used [KB]: 7803
% 6.05/2.17 % (6722)Time elapsed: 0.106 s
% 6.05/2.17 % (6722)Instructions burned: 345 (million)
% 6.05/2.17 % (6722)------------------------------
% 6.05/2.17 % (6722)------------------------------
% 6.05/2.18 % (6776)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_6360 for (2994ds/192Mi)
% 6.52/2.20 % (6765)Instruction limit reached!
% 6.52/2.20 % (6765)------------------------------
% 6.52/2.20 % (6765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.20 % (6765)Termination reason: Unknown
% 6.52/2.20 % (6765)Termination phase: Property scanning
% 6.52/2.20
% 6.52/2.20 % (6765)Memory used [KB]: 2558
% 6.52/2.20 % (6765)Time elapsed: 0.038 s
% 6.52/2.20 % (6765)Instructions burned: 137 (million)
% 6.52/2.20 % (6765)------------------------------
% 6.52/2.20 % (6765)------------------------------
% 6.52/2.21 % (6784)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_6360 for (2994ds/258Mi)
% 6.52/2.23 % (6760)Instruction limit reached!
% 6.52/2.23 % (6760)------------------------------
% 6.52/2.23 % (6760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.23 % (6760)Termination reason: Unknown
% 6.52/2.23 % (6760)Termination phase: Saturation
% 6.52/2.23
% 6.52/2.23 % (6760)Memory used [KB]: 7803
% 6.52/2.23 % (6760)Time elapsed: 0.097 s
% 6.52/2.23 % (6760)Instructions burned: 284 (million)
% 6.52/2.23 % (6760)------------------------------
% 6.52/2.23 % (6760)------------------------------
% 6.52/2.23 % (6798)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_6360 for (2994ds/90Mi)
% 6.52/2.24 % (6776)Instruction limit reached!
% 6.52/2.24 % (6776)------------------------------
% 6.52/2.24 % (6776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.24 % (6776)Termination reason: Unknown
% 6.52/2.24 % (6776)Termination phase: Saturation
% 6.52/2.24
% 6.52/2.24 % (6776)Memory used [KB]: 3326
% 6.52/2.24 % (6776)Time elapsed: 0.056 s
% 6.52/2.24 % (6776)Instructions burned: 193 (million)
% 6.52/2.24 % (6776)------------------------------
% 6.52/2.24 % (6776)------------------------------
% 6.52/2.24 % (6769)Instruction limit reached!
% 6.52/2.24 % (6769)------------------------------
% 6.52/2.24 % (6769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.24 % (6769)Termination reason: Unknown
% 6.52/2.24 % (6769)Termination phase: Saturation
% 6.52/2.24
% 6.52/2.24 % (6769)Memory used [KB]: 7803
% 6.52/2.24 % (6769)Time elapsed: 0.079 s
% 6.52/2.24 % (6769)Instructions burned: 300 (million)
% 6.52/2.24 % (6769)------------------------------
% 6.52/2.24 % (6769)------------------------------
% 6.52/2.24 % (6757)Instruction limit reached!
% 6.52/2.24 % (6757)------------------------------
% 6.52/2.24 % (6757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.24 % (6757)Termination reason: Unknown
% 6.52/2.24 % (6757)Termination phase: Saturation
% 6.52/2.24
% 6.52/2.24 % (6757)Memory used [KB]: 7419
% 6.52/2.24 % (6757)Time elapsed: 0.098 s
% 6.52/2.24 % (6757)Instructions burned: 339 (million)
% 6.52/2.24 % (6757)------------------------------
% 6.52/2.24 % (6757)------------------------------
% 6.52/2.25 % (6802)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_6360 for (2994ds/231Mi)
% 6.52/2.25 % (6805)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_6360 for (2994ds/458Mi)
% 6.52/2.25 % (6806)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6360 for (2994ds/31Mi)
% 6.52/2.26 % (6648)First to succeed.
% 6.52/2.26 % (6806)Instruction limit reached!
% 6.52/2.26 % (6806)------------------------------
% 6.52/2.26 % (6806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.26 % (6806)Termination reason: Unknown
% 6.52/2.26 % (6806)Termination phase: shuffling
% 6.52/2.26
% 6.52/2.26 % (6798)Instruction limit reached!
% 6.52/2.26 % (6798)------------------------------
% 6.52/2.26 % (6798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.26 % (6806)Memory used [KB]: 2046
% 6.52/2.26 % (6798)Termination reason: Unknown
% 6.52/2.26 % (6806)Time elapsed: 0.011 s
% 6.52/2.26 % (6806)Instructions burned: 31 (million)
% 6.52/2.26 % (6806)------------------------------
% 6.52/2.26 % (6806)------------------------------
% 6.52/2.26 % (6798)Termination phase: Property scanning
% 6.52/2.26
% 6.52/2.26 % (6798)Memory used [KB]: 2430
% 6.52/2.26 % (6798)Time elapsed: 0.027 s
% 6.52/2.26 % (6798)Instructions burned: 92 (million)
% 6.52/2.26 % (6798)------------------------------
% 6.52/2.26 % (6798)------------------------------
% 6.52/2.26 % (6648)Refutation found. Thanks to Tanya!
% 6.52/2.26 % SZS status Theorem for DTF2THF_6360
% 6.52/2.26 % SZS output start Proof for DTF2THF_6360
% 6.52/2.26 thf(type_def_5, type, secrecy_specID: $tType).
% 6.52/2.26 thf(type_def_6, type, set_Secrecy_KS: $tType).
% 6.52/2.26 thf(type_def_8, type, secrecy_KS: $tType).
% 6.52/2.26 thf(type_def_9, type, set_Secrecy_Keys: $tType).
% 6.52/2.26 thf(type_def_10, type, set_Secrecy_Secrets: $tType).
% 6.52/2.26 thf(type_def_11, type, set_Secrecy_chanID: $tType).
% 6.52/2.26 thf(type_def_12, type, set_Secrecy_specID: $tType).
% 6.52/2.26 thf(type_def_13, type, secrecy_Expression: $tType).
% 6.52/2.26 thf(type_def_14, type, list_S529945141ession: $tType).
% 6.52/2.26 thf(type_def_15, type, secrecy_Keys: $tType).
% 6.52/2.26 thf(type_def_16, type, secrecy_Secrets: $tType).
% 6.52/2.26 thf(type_def_17, type, secrecy_chanID: $tType).
% 6.52/2.26 thf(type_def_18, type, nat: $tType).
% 6.52/2.26 thf(func_def_0, type, list_S529945141ession: $tType).
% 6.52/2.26 thf(func_def_1, type, set_Secrecy_Secrets: $tType).
% 6.52/2.26 thf(func_def_2, type, set_Secrecy_specID: $tType).
% 6.52/2.26 thf(func_def_3, type, set_Secrecy_chanID: $tType).
% 6.52/2.26 thf(func_def_4, type, set_Secrecy_Keys: $tType).
% 6.52/2.26 thf(func_def_5, type, set_Secrecy_KS: $tType).
% 6.52/2.26 thf(func_def_6, type, secrecy_Expression: $tType).
% 6.52/2.26 thf(func_def_7, type, secrecy_Secrets: $tType).
% 6.52/2.26 thf(func_def_8, type, secrecy_specID: $tType).
% 6.52/2.26 thf(func_def_9, type, secrecy_chanID: $tType).
% 6.52/2.26 thf(func_def_10, type, secrecy_Keys: $tType).
% 6.52/2.26 thf(func_def_11, type, secrecy_KS: $tType).
% 6.52/2.26 thf(func_def_12, type, nat: $tType).
% 6.52/2.26 thf(func_def_13, type, localSecrets: secrecy_specID > set_Secrecy_KS).
% 6.52/2.26 thf(func_def_14, type, knowle233900195orrect: secrecy_specID > secrecy_KS > $o).
% 6.52/2.26 thf(func_def_15, type, knowle945212990e_know: secrecy_specID > secrecy_KS > $o).
% 6.52/2.26 thf(func_def_16, type, sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 6.52/2.26 thf(func_def_17, type, sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 6.52/2.26 thf(func_def_18, type, sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 6.52/2.26 thf(func_def_19, type, sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 6.52/2.26 thf(func_def_20, type, sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 6.52/2.26 thf(func_def_21, type, mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o).
% 6.52/2.26 thf(func_def_22, type, bot_bot_Secrecy_KS_o: secrecy_KS > $o).
% 6.52/2.26 thf(func_def_23, type, bot_bo2072920570Keys_o: secrecy_Keys > $o).
% 6.52/2.26 thf(func_def_24, type, bot_bo1909946299rets_o: secrecy_Secrets > $o).
% 6.52/2.26 thf(func_def_25, type, bot_bo1012329985anID_o: secrecy_chanID > $o).
% 6.52/2.26 thf(func_def_26, type, bot_bo1767780696ecID_o: secrecy_specID > $o).
% 6.52/2.26 thf(func_def_27, type, bot_bo1943466239ecy_KS: set_Secrecy_KS).
% 6.52/2.26 thf(func_def_28, type, bot_bo701486667y_Keys: set_Secrecy_Keys).
% 6.52/2.26 thf(func_def_29, type, bot_bo1124690338ecrets: set_Secrecy_Secrets).
% 6.52/2.26 thf(func_def_30, type, bot_bo443197316chanID: set_Secrecy_chanID).
% 6.52/2.26 thf(func_def_31, type, bot_bo1785112429specID: set_Secrecy_specID).
% 6.52/2.26 thf(func_def_32, type, ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o).
% 6.52/2.26 thf(func_def_33, type, correctCompositionKS: secrecy_specID > $o).
% 6.52/2.26 thf(func_def_34, type, eout: secrecy_specID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_35, type, eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_36, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_37, type, ine: secrecy_specID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_38, type, ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_39, type, ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_40, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_41, type, notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o).
% 6.52/2.26 thf(func_def_42, type, out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_43, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_44, type, specKeys: secrecy_specID > set_Secrecy_Keys).
% 6.52/2.26 thf(func_def_45, type, specKeysSecrets: secrecy_specID > set_Secrecy_KS).
% 6.52/2.26 thf(func_def_46, type, specSecrets: secrecy_specID > set_Secrecy_Secrets).
% 6.52/2.26 thf(func_def_47, type, secrecy_dE: nat > secrecy_Expression).
% 6.52/2.26 thf(func_def_48, type, secrecy_idE: secrecy_specID > secrecy_Expression).
% 6.52/2.26 thf(func_def_49, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 6.52/2.26 thf(func_def_50, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 6.52/2.26 thf(func_def_51, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 6.52/2.26 thf(func_def_52, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 6.52/2.26 thf(func_def_53, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 6.52/2.26 thf(func_def_54, type, collect_Secrecy_KS: (secrecy_KS > $o) > set_Secrecy_KS).
% 6.52/2.26 thf(func_def_55, type, collect_Secrecy_Keys: (secrecy_Keys > $o) > set_Secrecy_Keys).
% 6.52/2.26 thf(func_def_56, type, collec836099393ecrets: (secrecy_Secrets > $o) > set_Secrecy_Secrets).
% 6.52/2.26 thf(func_def_57, type, collec625564175chanID: (secrecy_chanID > $o) > set_Secrecy_chanID).
% 6.52/2.26 thf(func_def_58, type, collec1545797240specID: (secrecy_specID > $o) > set_Secrecy_specID).
% 6.52/2.26 thf(func_def_59, type, insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 6.52/2.26 thf(func_def_60, type, insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 6.52/2.26 thf(func_def_61, type, insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 6.52/2.26 thf(func_def_62, type, insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 6.52/2.26 thf(func_def_63, type, insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 6.52/2.26 thf(func_def_64, type, is_sin1442426433ecy_KS: set_Secrecy_KS > $o).
% 6.52/2.26 thf(func_def_65, type, is_sin1096471309y_Keys: set_Secrecy_Keys > $o).
% 6.52/2.26 thf(func_def_66, type, is_sin1002224330ecrets: set_Secrecy_Secrets > $o).
% 6.52/2.26 thf(func_def_67, type, is_sin581274182chanID: set_Secrecy_chanID > $o).
% 6.52/2.26 thf(func_def_68, type, is_sin1501507247specID: set_Secrecy_specID > $o).
% 6.52/2.26 thf(func_def_69, type, the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID).
% 6.52/2.26 thf(func_def_70, type, the_el827131246specID: set_Secrecy_specID > secrecy_specID).
% 6.52/2.26 thf(func_def_71, type, correctCompositionIn: secrecy_specID > $o).
% 6.52/2.26 thf(func_def_72, type, correc965049635ionLoc: secrecy_specID > $o).
% 6.52/2.26 thf(func_def_73, type, correc990227761ionOut: secrecy_specID > $o).
% 6.52/2.26 thf(func_def_74, type, inStream: secrecy_specID > set_Secrecy_chanID > $o).
% 6.52/2.26 thf(func_def_75, type, ins: secrecy_specID > set_Secrecy_chanID).
% 6.52/2.26 thf(func_def_76, type, loc: secrecy_specID > set_Secrecy_chanID).
% 6.52/2.26 thf(func_def_77, type, locStream: secrecy_specID > set_Secrecy_chanID > $o).
% 6.52/2.26 thf(func_def_78, type, out: secrecy_specID > set_Secrecy_chanID).
% 6.52/2.26 thf(func_def_79, type, outStream: secrecy_specID > set_Secrecy_chanID > $o).
% 6.52/2.26 thf(func_def_80, type, subcomponents: secrecy_specID > set_Secrecy_specID).
% 6.52/2.26 thf(func_def_81, type, member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o).
% 6.52/2.26 thf(func_def_82, type, member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o).
% 6.52/2.26 thf(func_def_83, type, member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o).
% 6.52/2.26 thf(func_def_84, type, member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o).
% 6.52/2.26 thf(func_def_85, type, member740727610specID: secrecy_specID > set_Secrecy_specID > $o).
% 6.52/2.26 thf(func_def_86, type, p: secrecy_specID).
% 6.52/2.26 thf(func_def_87, type, pq: secrecy_specID).
% 6.52/2.26 thf(func_def_88, type, q: secrecy_specID).
% 6.52/2.26 thf(func_def_89, type, key: secrecy_Keys).
% 6.52/2.26 thf(func_def_104, type, sP0: secrecy_specID > secrecy_specID > secrecy_specID > secrecy_Expression > $o).
% 6.52/2.26 thf(func_def_105, type, sP1: secrecy_KS > secrecy_specID > secrecy_specID > $o).
% 6.52/2.26 thf(func_def_106, type, sP2: secrecy_specID > secrecy_specID > secrecy_specID > secrecy_specID > $o).
% 6.52/2.26 thf(func_def_107, type, sP3: secrecy_specID > secrecy_specID > secrecy_specID > secrecy_specID > $o).
% 6.52/2.26 thf(func_def_108, type, sP4: secrecy_specID > secrecy_specID > secrecy_KS > $o).
% 6.52/2.26 thf(func_def_109, type, sK5: secrecy_specID > secrecy_Keys > secrecy_chanID).
% 6.52/2.26 thf(func_def_110, type, sK6: secrecy_KS > secrecy_Keys).
% 6.52/2.26 thf(func_def_111, type, sK7: secrecy_KS > secrecy_Secrets).
% 6.52/2.26 thf(func_def_112, type, sK8: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets).
% 6.52/2.26 thf(func_def_113, type, sK9: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys).
% 6.52/2.26 thf(func_def_114, type, sK10: (secrecy_KS > $o) > secrecy_Keys).
% 6.52/2.26 thf(func_def_115, type, sK11: (secrecy_KS > $o) > secrecy_Secrets).
% 6.52/2.26 thf(func_def_116, type, sK12: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 6.52/2.26 thf(func_def_117, type, sK13: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys).
% 6.52/2.26 thf(func_def_118, type, sK14: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets).
% 6.52/2.26 thf(func_def_120, type, ph16: !>[X0: $tType]:(X0)).
% 6.52/2.26 thf(f2049,plain,(
% 6.52/2.26 $false),
% 6.52/2.26 inference(subsumption_resolution,[status(thm)],[f2045,f1147])).
% 6.52/2.26 thf(f1147,plain,(
% 6.52/2.26 ((correctCompositionIn @ pq) = $true)),
% 6.52/2.26 inference(cnf_transformation,[status(thm)],[f879])).
% 6.52/2.26 thf(f879,plain,(
% 6.52/2.26 ((correctCompositionIn @ pq) = $true)),
% 6.52/2.26 inference(fool_elimination,[status(thm)],[f878])).
% 6.52/2.26 thf(f878,plain,(
% 6.52/2.26 (correctCompositionIn @ pq)),
% 6.52/2.26 inference(rectify,[status(thm)],[f1])).
% 6.52/2.26 thf(f1,axiom,(
% 6.52/2.26 (correctCompositionIn @ pq)),
% 6.52/2.26 file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_0_assms_I4_J)).
% 6.52/2.26 thf(f2045,plain,(
% 6.52/2.26 ((correctCompositionIn @ pq) != $true)),
% 6.52/2.26 inference(trivial_inequality_removal,[status(thm)],[f2039])).
% 6.52/2.26 thf(f2039,plain,(
% 6.52/2.26 ((correctCompositionIn @ pq) != $true) | ($true != $true) | ((subcomponents @ pq) != (subcomponents @ pq))),
% 6.52/2.26 inference(superposition,[status(thm)],[f2038,f1120])).
% 6.52/2.26 thf(f1120,plain,(
% 6.52/2.26 ((ine @ pq @ (secrecy_kE @ key)) = $true)),
% 6.52/2.26 inference(cnf_transformation,[status(thm)],[f947])).
% 6.52/2.26 thf(f947,plain,(
% 6.52/2.26 ((ine @ pq @ (secrecy_kE @ key)) = $true)),
% 6.52/2.26 inference(flattening,[status(thm)],[f699])).
% 6.52/2.26 thf(f699,plain,(
% 6.52/2.26 ~~((ine @ pq @ (secrecy_kE @ key)) = $true)),
% 6.52/2.26 inference(fool_elimination,[status(thm)],[f698])).
% 6.52/2.26 thf(f698,plain,(
% 6.52/2.26 ~~(ine @ pq @ (secrecy_kE @ key))),
% 6.52/2.26 inference(rectify,[status(thm)],[f357])).
% 6.52/2.26 thf(f357,negated_conjecture,(
% 6.52/2.26 ~~(ine @ pq @ (secrecy_kE @ key))),
% 6.52/2.26 inference(negated_conjecture,[status(cth)],[f356])).
% 6.52/2.26 thf(f356,conjecture,(
% 6.52/2.26 ~(ine @ pq @ (secrecy_kE @ key))),
% 6.52/2.26 file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',conj_0)).
% 6.52/2.26 thf(f2038,plain,(
% 6.52/2.26 ( ! [X0 : secrecy_specID] : (($true != (ine @ X0 @ (secrecy_kE @ key))) | ($true != (correctCompositionIn @ X0)) | ((subcomponents @ pq) != (subcomponents @ X0))) )),
% 6.52/2.26 inference(subsumption_resolution,[status(thm)],[f2037,f1183])).
% 6.52/2.26 thf(f1183,plain,(
% 6.52/2.26 ($true != (ine @ p @ (secrecy_kE @ key)))),
% 6.52/2.26 inference(trivial_inequality_removal,[status(thm)],[f1181])).
% 6.52/2.26 thf(f1181,plain,(
% 6.52/2.26 ($true != (ine @ p @ (secrecy_kE @ key))) | ($true != $true)),
% 6.52/2.26 inference(superposition,[status(thm)],[f1082,f1089])).
% 6.52/2.26 thf(f1089,plain,(
% 6.52/2.26 ( ! [X0 : secrecy_Keys,X1 : secrecy_specID] : (((knowle945212990e_know @ X1 @ (secrecy_kKS @ X0)) = $true) | ($true != (ine @ X1 @ (secrecy_kE @ X0)))) )),
% 6.52/2.26 inference(cnf_transformation,[status(thm)],[f991])).
% 6.52/2.26 thf(f991,plain,(
% 6.52/2.26 ! [X0 : secrecy_Keys,X1 : secrecy_specID] : (($true != (ine @ X1 @ (secrecy_kE @ X0))) | ((knowle945212990e_know @ X1 @ (secrecy_kKS @ X0)) = $true))),
% 6.52/2.26 inference(ennf_transformation,[status(thm)],[f969])).
% 6.52/2.26 thf(f969,plain,(
% 6.52/2.26 ! [X0 : secrecy_Keys,X1 : secrecy_specID] : (((knowle945212990e_know @ X1 @ (secrecy_kKS @ X0)) != $true) => ($true != (ine @ X1 @ (secrecy_kE @ X0))))),
% 6.52/2.26 inference(flattening,[status(thm)],[f585])).
% 6.52/2.26 thf(f585,plain,(
% 6.52/2.26 ! [X0 : secrecy_Keys,X1 : secrecy_specID] : (~((knowle945212990e_know @ X1 @ (secrecy_kKS @ X0)) = $true) => ~($true = (ine @ X1 @ (secrecy_kE @ X0))))),
% 6.52/2.26 inference(fool_elimination,[status(thm)],[f584])).
% 6.52/2.26 thf(f584,plain,(
% 6.52/2.26 ! [X0 : secrecy_Keys,X1 : secrecy_specID] : (~(knowle945212990e_know @ X1 @ (secrecy_kKS @ X0)) => ~(ine @ X1 @ (secrecy_kE @ X0)))),
% 6.52/2.26 inference(rectify,[status(thm)],[f6])).
% 6.52/2.26 thf(f6,axiom,(
% 6.52/2.26 ! [X3 : secrecy_Keys,X2 : secrecy_specID] : (~(knowle945212990e_know @ X2 @ (secrecy_kKS @ X3)) => ~(ine @ X2 @ (secrecy_kE @ X3)))),
% 6.52/2.26 file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_5_not__know__k__not__ine)).
% 6.52/2.26 thf(f1082,plain,(
% 6.52/2.26 ((knowle945212990e_know @ p @ (secrecy_kKS @ key)) != $true)),
% 6.52/2.26 inference(cnf_transformation,[status(thm)],[f979])).
% 6.52/2.26 thf(f979,plain,(
% 6.52/2.26 ((knowle945212990e_know @ p @ (secrecy_kKS @ key)) != $true)),
% 6.52/2.26 inference(flattening,[status(thm)],[f803])).
% 6.52/2.26 thf(f803,plain,(
% 6.52/2.26 ~((knowle945212990e_know @ p @ (secrecy_kKS @ key)) = $true)),
% 6.52/2.26 inference(fool_elimination,[status(thm)],[f802])).
% 6.52/2.26 thf(f802,plain,(
% 6.52/2.26 ~(knowle945212990e_know @ p @ (secrecy_kKS @ key))),
% 6.52/2.26 inference(rectify,[status(thm)],[f3])).
% 6.52/2.26 thf(f3,axiom,(
% 6.52/2.26 ~(knowle945212990e_know @ p @ (secrecy_kKS @ key))),
% 6.52/2.26 file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_2_assms_I1_J)).
% 6.52/2.26 thf(f2037,plain,(
% 6.52/2.26 ( ! [X0 : secrecy_specID] : (($true = (ine @ p @ (secrecy_kE @ key))) | ($true != (ine @ X0 @ (secrecy_kE @ key))) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true != (correctCompositionIn @ X0))) )),
% 6.52/2.26 inference(trivial_inequality_removal,[status(thm)],[f2034])).
% 6.52/2.26 thf(f2034,plain,(
% 6.52/2.26 ( ! [X0 : secrecy_specID] : (($true != $true) | ($true != (ine @ X0 @ (secrecy_kE @ key))) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true != (correctCompositionIn @ X0)) | ($true = (ine @ p @ (secrecy_kE @ key)))) )),
% 6.52/2.26 inference(superposition,[status(thm)],[f1184,f1366])).
% 6.52/2.26 thf(f1366,plain,(
% 6.52/2.26 ( ! [X0 : secrecy_specID,X1 : secrecy_Expression] : (((ine @ q @ X1) = $true) | ((ine @ p @ X1) = $true) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true != (correctCompositionIn @ X0)) | ($true != (ine @ X0 @ X1))) )),
% 6.52/2.26 inference(superposition,[status(thm)],[f1127,f1134])).
% 6.52/2.26 thf(f1134,plain,(
% 6.52/2.26 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 6.52/2.26 inference(cnf_transformation,[status(thm)],[f4])).
% 6.52/2.26 thf(f4,axiom,(
% 6.52/2.26 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 6.52/2.26 file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_3_assms_I3_J)).
% 6.52/2.26 thf(f1127,plain,(
% 6.52/2.26 ( ! [X2 : secrecy_Expression,X3 : secrecy_specID,X0 : secrecy_specID,X1 : secrecy_specID] : (((insert1671894227specID @ X3 @ (insert1671894227specID @ X1 @ bot_bo1785112429specID)) != (subcomponents @ X0)) | ($true = (ine @ X1 @ X2)) | ((ine @ X3 @ X2) = $true) | ($true != (ine @ X0 @ X2)) | ($true != (correctCompositionIn @ X0))) )),
% 6.52/2.26 inference(cnf_transformation,[status(thm)],[f1034])).
% 6.52/2.26 thf(f1034,plain,(
% 6.52/2.26 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_Expression,X3 : secrecy_specID] : (((ine @ X3 @ X2) = $true) | ($true != (ine @ X0 @ X2)) | ($true != (correctCompositionIn @ X0)) | ($true = (ine @ X1 @ X2)) | ((insert1671894227specID @ X3 @ (insert1671894227specID @ X1 @ bot_bo1785112429specID)) != (subcomponents @ X0)))),
% 6.52/2.26 inference(flattening,[status(thm)],[f1033])).
% 6.52/2.26 thf(f1033,plain,(
% 6.52/2.26 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_Expression,X3 : secrecy_specID] : ((((($true = (ine @ X1 @ X2)) | ((ine @ X3 @ X2) = $true)) | ($true != (correctCompositionIn @ X0))) | ((insert1671894227specID @ X3 @ (insert1671894227specID @ X1 @ bot_bo1785112429specID)) != (subcomponents @ X0))) | ($true != (ine @ X0 @ X2)))),
% 6.52/2.26 inference(ennf_transformation,[status(thm)],[f785])).
% 6.52/2.26 thf(f785,plain,(
% 6.52/2.26 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_Expression,X3 : secrecy_specID] : (($true = (ine @ X0 @ X2)) => (((insert1671894227specID @ X3 @ (insert1671894227specID @ X1 @ bot_bo1785112429specID)) = (subcomponents @ X0)) => (($true = (correctCompositionIn @ X0)) => (($true = (ine @ X1 @ X2)) | ((ine @ X3 @ X2) = $true)))))),
% 6.52/2.26 inference(fool_elimination,[status(thm)],[f784])).
% 6.52/2.26 thf(f784,plain,(
% 6.52/2.26 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_Expression,X3 : secrecy_specID] : ((ine @ X0 @ X2) => (((insert1671894227specID @ X3 @ (insert1671894227specID @ X1 @ bot_bo1785112429specID)) = (subcomponents @ X0)) => ((correctCompositionIn @ X0) => ((ine @ X3 @ X2) | (ine @ X1 @ X2)))))),
% 6.52/2.26 inference(rectify,[status(thm)],[f36])).
% 6.52/2.26 thf(f36,axiom,(
% 6.52/2.26 ! [X21 : secrecy_specID,X11 : secrecy_specID,X8 : secrecy_Expression,X6 : secrecy_specID] : ((ine @ X21 @ X8) => (((subcomponents @ X21) = (insert1671894227specID @ X6 @ (insert1671894227specID @ X11 @ bot_bo1785112429specID))) => ((correctCompositionIn @ X21) => ((ine @ X6 @ X8) | (ine @ X11 @ X8)))))),
% 6.52/2.26 file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_35_TBtheorem1a)).
% 6.52/2.26 thf(f1184,plain,(
% 6.52/2.26 ($true != (ine @ q @ (secrecy_kE @ key)))),
% 6.52/2.26 inference(trivial_inequality_removal,[status(thm)],[f1182])).
% 6.52/2.26 thf(f1182,plain,(
% 6.52/2.26 ($true != $true) | ($true != (ine @ q @ (secrecy_kE @ key)))),
% 6.52/2.26 inference(superposition,[status(thm)],[f1128,f1089])).
% 6.52/2.26 thf(f1128,plain,(
% 6.52/2.26 ((knowle945212990e_know @ q @ (secrecy_kKS @ key)) != $true)),
% 6.52/2.26 inference(cnf_transformation,[status(thm)],[f980])).
% 6.52/2.26 thf(f980,plain,(
% 6.52/2.26 ((knowle945212990e_know @ q @ (secrecy_kKS @ key)) != $true)),
% 6.52/2.26 inference(flattening,[status(thm)],[f362])).
% 6.52/2.26 thf(f362,plain,(
% 6.52/2.26 ~((knowle945212990e_know @ q @ (secrecy_kKS @ key)) = $true)),
% 6.52/2.26 inference(fool_elimination,[status(thm)],[f361])).
% 6.52/2.26 thf(f361,plain,(
% 6.52/2.26 ~(knowle945212990e_know @ q @ (secrecy_kKS @ key))),
% 6.52/2.26 inference(rectify,[status(thm)],[f2])).
% 6.52/2.26 thf(f2,axiom,(
% 6.52/2.26 ~(knowle945212990e_know @ q @ (secrecy_kKS @ key))),
% 6.52/2.26 file('/export/starexec/sandbox2/tmp/tmp.5RcVmp6YCL/DTF2THF_6360.p',fact_1_assms_I2_J)).
% 6.52/2.26 % SZS output end Proof for DTF2THF_6360
% 6.52/2.26 % (6648)------------------------------
% 6.52/2.26 % (6648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.26 % (6648)Termination reason: Refutation
% 6.52/2.26
% 6.52/2.26 % (6648)Memory used [KB]: 7675
% 6.52/2.26 % (6648)Time elapsed: 0.316 s
% 6.52/2.26 % (6648)Instructions burned: 989 (million)
% 6.52/2.26 % (6648)------------------------------
% 6.52/2.26 % (6648)------------------------------
% 6.52/2.26 % (6525)Success in time 0.621 s
%------------------------------------------------------------------------------