%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP090^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:28 AM UTC 2026
% Result : Theorem 2.74s 1.66s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 31 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 159 ( 21 ~; 11 |; 4 &; 122 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 84 usr; 12 con; 0-3 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% 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,
list_S529945141ession: $tType ).
thf(type_def_10,type,
set_Secrecy_Keys: $tType ).
thf(type_def_11,type,
set_Secrecy_Secrets: $tType ).
thf(type_def_12,type,
set_Secrecy_chanID: $tType ).
thf(type_def_13,type,
set_Secrecy_specID: $tType ).
thf(type_def_14,type,
secrecy_Expression: $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,
knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_17,type,
sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_18,type,
sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_19,type,
sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_20,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_21,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_22,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_23,type,
bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
thf(func_def_24,type,
bot_bo2072920570Keys_o: secrecy_Keys > $o ).
thf(func_def_25,type,
bot_bo1909946299rets_o: secrecy_Secrets > $o ).
thf(func_def_26,type,
bot_bo1012329985anID_o: secrecy_chanID > $o ).
thf(func_def_27,type,
bot_bo1767780696ecID_o: secrecy_specID > $o ).
thf(func_def_28,type,
bot_bo1943466239ecy_KS: set_Secrecy_KS ).
thf(func_def_29,type,
bot_bo701486667y_Keys: set_Secrecy_Keys ).
thf(func_def_30,type,
bot_bo1124690338ecrets: set_Secrecy_Secrets ).
thf(func_def_31,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(func_def_32,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(func_def_33,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_34,type,
decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_35,type,
enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_36,type,
encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
thf(func_def_37,type,
ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_38,type,
sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(func_def_39,type,
correctCompositionKS: secrecy_specID > $o ).
thf(func_def_40,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_41,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_42,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_43,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_44,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_45,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_46,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_47,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_48,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_49,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_50,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_51,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_52,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_53,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_54,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_55,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_56,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_57,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_58,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_59,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_60,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_61,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(func_def_62,type,
collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
thf(func_def_63,type,
insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_64,type,
insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_65,type,
insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_66,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_67,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_68,type,
is_emp928984296chanID: set_Secrecy_chanID > $o ).
thf(func_def_69,type,
is_emp1849217361specID: set_Secrecy_specID > $o ).
thf(func_def_70,type,
is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
thf(func_def_71,type,
is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
thf(func_def_72,type,
is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
thf(func_def_73,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(func_def_74,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(func_def_75,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_76,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(func_def_77,type,
correctCompositionIn: secrecy_specID > $o ).
thf(func_def_78,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(func_def_79,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(func_def_80,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_81,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_82,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_83,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_84,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_85,type,
outStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_86,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(func_def_87,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(func_def_88,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(func_def_89,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(func_def_90,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_91,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(func_def_92,type,
p: secrecy_specID ).
thf(func_def_93,type,
pq: secrecy_specID ).
thf(func_def_94,type,
q: secrecy_specID ).
thf(func_def_95,type,
key: secrecy_Keys ).
thf(func_def_96,type,
m: secrecy_KS ).
thf(f1000,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f999,f993]) ).
thf(f993,plain,
( ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f982,f983]) ).
thf(f983,plain,
( m
= ( secrecy_kKS @ key ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
( m
= ( secrecy_kKS @ key ) ),
file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',fact_1_a1) ).
thf(f982,plain,
( ( knowle945212990e_know @ q @ m )
!= $true ),
inference(cnf_transformation,[status(thm)],[f972]) ).
thf(f972,plain,
( ( knowle945212990e_know @ q @ m )
!= $true ),
inference(flattening,[status(thm)],[f836]) ).
thf(f836,plain,
( ( knowle945212990e_know @ q @ m )
!= $true ),
inference(fool_elimination,[status(thm)],[f835]) ).
thf(f835,plain,
~ ( knowle945212990e_know @ q @ m ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ( knowle945212990e_know @ q @ m ),
file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',fact_0_not__knowQm) ).
thf(f999,plain,
( ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f996]) ).
thf(f996,plain,
( ( $true != $true )
| ( ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) )
= $true ) ),
inference(superposition,[status(thm)],[f991,f981]) ).
thf(f981,plain,
( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f971]) ).
thf(f971,plain,
( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) )
= $true ),
inference(flattening,[status(thm)],[f726]) ).
thf(f726,plain,
~ ( ( ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f725]) ).
thf(f725,plain,
~ ~ ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ~ ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
~ ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ),
file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',conj_0) ).
thf(f991,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ X0 ) )
!= $true )
| ( $true
= ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f979]) ).
thf(f979,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( ( $true
= ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) ) )
| ( ( ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ X0 ) )
!= $true )
& ( ( ine @ X0 @ ( secrecy_kE @ X1 ) )
!= $true ) ) )
& ( ( ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ X0 ) )
= $true )
| ( ( ine @ X0 @ ( secrecy_kE @ X1 ) )
= $true )
| ( $true
!= ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f978]) ).
thf(f978,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( ( $true
= ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) ) )
| ( ( ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ X0 ) )
!= $true )
& ( ( ine @ X0 @ ( secrecy_kE @ X1 ) )
!= $true ) ) )
& ( ( ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ X0 ) )
= $true )
| ( ( ine @ X0 @ ( secrecy_kE @ X1 ) )
= $true )
| ( $true
!= ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f886]) ).
thf(f886,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( $true
= ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) ) )
<=> ( ( ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ X0 ) )
= $true )
| ( ( ine @ X0 @ ( secrecy_kE @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f885]) ).
thf(f885,plain,
! [X0: secrecy_specID,X1: secrecy_Keys] :
( ( ( knowle945212990e_know @ X0 @ ( secrecy_kKS @ X1 ) )
= ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ X0 ) ) )
| ( ine @ X0 @ ( secrecy_kE @ X1 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: secrecy_specID,X3: secrecy_Keys] :
( ( ( knowle945212990e_know @ X2 @ ( secrecy_kKS @ X3 ) )
= ( member_Secrecy_KS @ ( secrecy_kKS @ X3 ) @ ( localSecrets @ X2 ) ) )
| ( ine @ X2 @ ( secrecy_kE @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',fact_8_know_Osimps_I1_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP090^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 08:26:22 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ITP090^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.45 % Domain : Interactive Theorem Proving
% 0.30/0.45 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_426__3295732_1
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Des21]
% 0.30/0.45 % Names : KnowledgeKeysSecrets/prob_426__3295732_1 [Des21]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.30/0.45 % Syntax : Number of formulae : 453 ( 169 unt; 97 typ; 0 def)
% 0.30/0.45 % Number of atoms : 1285 ( 448 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 13 ( 3 avg)
% 0.30/0.45 % Number of connectives : 3944 ( 293 ~; 51 |; 130 &;2903 @)
% 0.30/0.45 % ( 0 <=>; 567 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 19 ( 7 avg)
% 0.30/0.45 % Number of types : 14 ( 13 usr)
% 0.30/0.45 % Number of type conns : 143 ( 143 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 85 ( 84 usr; 10 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 1016 ( 56 ^; 915 !; 45 ?;1016 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:35:43.041
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % Could-be-implicit typings (13)
% 0.30/0.45 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.30/0.45 list_S529945141ession: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.30/0.45 set_Secrecy_Secrets: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.30/0.45 set_Secrecy_specID: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.30/0.45 set_Secrecy_chanID: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.30/0.45 set_Secrecy_Keys: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.30/0.45 set_Secrecy_KS: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.30/0.45 secrecy_Expression: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.30/0.45 secrecy_Secrets: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.30/0.45 secrecy_specID: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Secrecy____types__OchanID,type,
% 0.30/0.45 secrecy_chanID: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.30/0.45 secrecy_Keys: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.30/0.45 secrecy_KS: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_n_t__Nat__Onat,type,
% 0.30/0.45 nat: $tType ).
% 0.30/0.45
% 0.30/0.45 % Explicit typings (84)
% 0.30/0.45 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.30/0.45 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.30/0.45 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.30/0.45 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknows,type,
% 0.30/0.45 knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.30/0.46 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.30/0.46 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.30/0.46 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.30/0.46 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.30/0.46 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.30/0.46 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 0.30/0.46 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 0.30/0.46 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 0.30/0.46 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 0.30/0.46 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 0.30/0.46 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.30/0.46 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.30/0.46 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.30/0.46 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.30/0.46 bot_bo443197316chanID: set_Secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.30/0.46 bot_bo1785112429specID: set_Secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.30/0.46 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_ODecr,type,
% 0.30/0.46 decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OEnc,type,
% 0.30/0.46 enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 0.30/0.46 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OExt,type,
% 0.30/0.46 ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OSign,type,
% 0.30/0.46 sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.30/0.46 correctCompositionKS: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oeout,type,
% 0.30/0.46 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OeoutM,type,
% 0.30/0.46 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OexprChannel,type,
% 0.30/0.46 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.30/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OineM,type,
% 0.30/0.46 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.30/0.46 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.30/0.46 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.30/0.46 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.30/0.46 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.30/0.46 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.30/0.46 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.30/0.46 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.30/0.46 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.30/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.30/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.30/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.30/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.30/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.30/0.46 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.30/0.46 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.30/0.46 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 0.30/0.46 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 0.30/0.46 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 0.30/0.46 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 0.30/0.46 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 0.30/0.46 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 0.30/0.46 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 0.30/0.46 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 0.30/0.46 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 0.30/0.46 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 0.30/0.46 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 0.30/0.46 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 0.30/0.46 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 0.30/0.46 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 0.30/0.46 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 0.30/0.46 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 0.30/0.46 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.30/0.46 correctCompositionIn: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.30/0.46 correc965049635ionLoc: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.30/0.46 correc990227761ionOut: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OinStream,type,
% 0.30/0.46 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Oins,type,
% 0.30/0.46 ins: secrecy_specID > set_Secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Oloc,type,
% 0.30/0.46 loc: secrecy_specID > set_Secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OlocStream,type,
% 0.30/0.46 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Oout,type,
% 0.30/0.46 out: secrecy_specID > set_Secrecy_chanID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OoutStream,type,
% 0.30/0.46 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Osubcomponents,type,
% 0.30/0.46 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.30/0.46 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.30/0.46 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.30/0.46 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 0.30/0.46 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 0.30/0.46 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_P,type,
% 0.30/0.46 p: secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_PQ,type,
% 0.30/0.46 pq: secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_Q,type,
% 0.30/0.46 q: secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_key____,type,
% 0.30/0.46 key: secrecy_Keys ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_m,type,
% 0.30/0.46 m: secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (355)
% 0.30/0.46 thf(fact_0_not__knowQm,axiom,
% 0.30/0.46 ~ ( knowle945212990e_know @ q @ m ) ).
% 0.30/0.46
% 0.30/0.46 % not_knowQm
% 0.30/0.46 thf(fact_1_a1,axiom,
% 0.30/0.46 ( m
% 0.30/0.46 = ( secrecy_kKS @ key ) ) ).
% 0.30/0.46
% 0.30/0.46 % a1
% 0.30/0.46 thf(fact_2_knowPQ,axiom,
% 0.30/0.46 knowle945212990e_know @ pq @ m ).
% 0.30/0.46
% 0.30/0.46 % knowPQ
% 0.30/0.46 thf(fact_3_sg2,axiom,
% 0.30/0.46 member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ pq ) ).
% 0.30/0.46
% 0.30/0.46 % sg2
% 0.30/0.46 thf(fact_4_KS_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.30/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.30/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.inject(1)
% 0.30/0.46 thf(fact_5_sg3a,axiom,
% 0.30/0.46 ~ ( ine @ q @ ( secrecy_kE @ key ) ) ).
% 0.30/0.46
% 0.30/0.46 % sg3a
% 0.30/0.46 thf(fact_6_cCompLoc,axiom,
% 0.30/0.46 correc965049635ionLoc @ pq ).
% 0.30/0.46
% 0.30/0.46 % cCompLoc
% 0.30/0.46 thf(fact_7_a12,axiom,
% 0.30/0.46 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 0.30/0.46
% 0.30/0.46 % a12
% 0.30/0.46 thf(fact_8_know_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.30/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.30/0.46 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.30/0.46 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know.simps(1)
% 0.30/0.46 thf(fact_9_subPQ,axiom,
% 0.30/0.46 ( ( subcomponents @ pq )
% 0.30/0.46 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subPQ
% 0.30/0.46 thf(fact_10_knows4,axiom,
% 0.30/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.30/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.30/0.46 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K2 ) )
% 0.30/0.46 & ( knowle731562421_knows @ A @ ( enc @ K1 @ E ) ) )
% 0.30/0.46 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % knows4
% 0.30/0.46 thf(fact_11_knows5,axiom,
% 0.30/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.30/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.30/0.46 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K1 ) )
% 0.30/0.46 & ( knowle731562421_knows @ A @ ( sign @ K2 @ E ) ) )
% 0.30/0.46 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % knows5
% 0.30/0.46 thf(fact_12_knows6,axiom,
% 0.30/0.46 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.30/0.46 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.30/0.46 & ( knowle731562421_knows @ A @ E1 ) )
% 0.30/0.46 => ( knowle731562421_knows @ A @ ( enc @ K @ E1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % knows6
% 0.30/0.46 thf(fact_13_Expression_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.30/0.46 ( ( ( secrecy_kE @ X1 )
% 0.30/0.46 = ( secrecy_kE @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Expression.inject(1)
% 0.30/0.46 thf(fact_14_cCompI,axiom,
% 0.30/0.46 correctCompositionIn @ pq ).
% 0.30/0.46
% 0.30/0.46 % cCompI
% 0.30/0.46 thf(fact_15_not__know__k__not__ine,axiom,
% 0.30/0.46 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.30/0.46 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.30/0.46 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_k_not_ine
% 0.30/0.46 thf(fact_16_knows7,axiom,
% 0.30/0.46 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.30/0.46 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.30/0.46 & ( knowle731562421_knows @ A @ E1 ) )
% 0.30/0.46 => ( knowle731562421_knows @ A @ ( sign @ K @ E1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % knows7
% 0.30/0.46 thf(fact_17_LocalSecretsComposition__ine1__k,axiom,
% 0.30/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine1_k
% 0.30/0.46 thf(fact_18_LocalSecretsComposition__ine2__k,axiom,
% 0.30/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine2_k
% 0.30/0.46 thf(fact_19_LocalSecretsComposition__neg1__k,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg1_k
% 0.30/0.46 thf(fact_20_singletonI,axiom,
% 0.30/0.46 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_21_singletonI,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_22_singletonI,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_23_singletonI,axiom,
% 0.30/0.46 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_24_singletonI,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_25_LocalSecretsComposition1,axiom,
% 0.30/0.46 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition1
% 0.30/0.46 thf(fact_26_know__composition__neg__ine__k,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( knowle945212990e_know @ P @ ( secrecy_kKS @ Key ) )
% 0.30/0.46 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_kKS @ Key ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know_composition_neg_ine_k
% 0.30/0.46 thf(fact_27_insertCI,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.30/0.46 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 0.30/0.46 => ( A2 = B2 ) )
% 0.30/0.46 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_28_insertCI,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.30/0.46 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 0.30/0.46 => ( A2 = B2 ) )
% 0.30/0.46 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_29_insertCI,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.30/0.46 ( ( ~ ( member740727610specID @ A2 @ B )
% 0.30/0.46 => ( A2 = B2 ) )
% 0.30/0.46 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_30_insertCI,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.30/0.46 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 0.30/0.46 => ( A2 = B2 ) )
% 0.30/0.46 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_31_insertCI,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.30/0.46 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 0.30/0.46 => ( A2 = B2 ) )
% 0.30/0.46 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_32_insert__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_33_insert__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_34_insert__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 | ( member740727610specID @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_35_insert__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_36_insert__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_37_insert__absorb2,axiom,
% 0.30/0.46 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A ) )
% 0.30/0.46 = ( insert1671894227specID @ X @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb2
% 0.30/0.46 thf(fact_38_insert__absorb2,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A ) )
% 0.30/0.46 = ( insert751661162chanID @ X @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb2
% 0.30/0.46 thf(fact_39_empty__iff,axiom,
% 0.30/0.46 ! [C: secrecy_KS] :
% 0.30/0.46 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_40_empty__iff,axiom,
% 0.30/0.46 ! [C: secrecy_Keys] :
% 0.30/0.46 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_41_empty__iff,axiom,
% 0.30/0.46 ! [C: secrecy_Secrets] :
% 0.30/0.46 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_42_empty__iff,axiom,
% 0.30/0.46 ! [C: secrecy_specID] :
% 0.30/0.46 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_43_empty__iff,axiom,
% 0.30/0.46 ! [C: secrecy_chanID] :
% 0.30/0.46 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_44_empty__Collect__eq,axiom,
% 0.30/0.46 ! [P: secrecy_specID > $o] :
% 0.30/0.46 ( ( bot_bo1785112429specID
% 0.30/0.46 = ( collec1545797240specID @ P ) )
% 0.30/0.46 = ( ! [X2: secrecy_specID] :
% 0.30/0.46 ~ ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_45_empty__Collect__eq,axiom,
% 0.30/0.46 ! [P: secrecy_chanID > $o] :
% 0.30/0.46 ( ( bot_bo443197316chanID
% 0.30/0.46 = ( collec625564175chanID @ P ) )
% 0.30/0.46 = ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ~ ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__empty__eq,axiom,
% 0.30/0.46 ! [P: secrecy_specID > $o] :
% 0.30/0.46 ( ( ( collec1545797240specID @ P )
% 0.30/0.46 = bot_bo1785112429specID )
% 0.30/0.46 = ( ! [X2: secrecy_specID] :
% 0.30/0.46 ~ ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_47_Collect__empty__eq,axiom,
% 0.30/0.46 ! [P: secrecy_chanID > $o] :
% 0.30/0.46 ( ( ( collec625564175chanID @ P )
% 0.30/0.46 = bot_bo443197316chanID )
% 0.30/0.46 = ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ~ ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_48_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS] :
% 0.30/0.46 ( ( ! [X2: secrecy_KS] :
% 0.30/0.46 ~ ( member_Secrecy_KS @ X2 @ A ) )
% 0.30/0.46 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_49_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( ! [X2: secrecy_Keys] :
% 0.30/0.46 ~ ( member_Secrecy_Keys @ X2 @ A ) )
% 0.30/0.46 = ( A = bot_bo701486667y_Keys ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_50_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( ! [X2: secrecy_Secrets] :
% 0.30/0.46 ~ ( member2138796287ecrets @ X2 @ A ) )
% 0.30/0.46 = ( A = bot_bo1124690338ecrets ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_51_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID] :
% 0.30/0.46 ( ( ! [X2: secrecy_specID] :
% 0.30/0.46 ~ ( member740727610specID @ X2 @ A ) )
% 0.30/0.46 = ( A = bot_bo1785112429specID ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_52_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ~ ( member1967978193chanID @ X2 @ A ) )
% 0.30/0.46 = ( A = bot_bo443197316chanID ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_53_ex__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS] :
% 0.30/0.46 ( ( ? [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A ) )
% 0.30/0.46 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_54_ex__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( ? [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A ) )
% 0.30/0.46 = ( A != bot_bo701486667y_Keys ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_55_ex__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( ? [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A ) )
% 0.30/0.46 = ( A != bot_bo1124690338ecrets ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_56_ex__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID] :
% 0.30/0.46 ( ( ? [X2: secrecy_specID] : ( member740727610specID @ X2 @ A ) )
% 0.30/0.46 = ( A != bot_bo1785112429specID ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_57_ex__in__conv,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ? [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A ) )
% 0.30/0.46 = ( A != bot_bo443197316chanID ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_58_equals0I,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS] :
% 0.30/0.46 ( ! [Y: secrecy_KS] :
% 0.30/0.46 ~ ( member_Secrecy_KS @ Y @ A )
% 0.30/0.46 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_59_equals0I,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Keys] :
% 0.30/0.46 ( ! [Y: secrecy_Keys] :
% 0.30/0.46 ~ ( member_Secrecy_Keys @ Y @ A )
% 0.30/0.46 => ( A = bot_bo701486667y_Keys ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_60_equals0I,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ! [Y: secrecy_Secrets] :
% 0.30/0.46 ~ ( member2138796287ecrets @ Y @ A )
% 0.30/0.46 => ( A = bot_bo1124690338ecrets ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_61_equals0I,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID] :
% 0.30/0.46 ( ! [Y: secrecy_specID] :
% 0.30/0.46 ~ ( member740727610specID @ Y @ A )
% 0.30/0.46 => ( A = bot_bo1785112429specID ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_62_equals0I,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ! [Y: secrecy_chanID] :
% 0.30/0.46 ~ ( member1967978193chanID @ Y @ A )
% 0.30/0.46 => ( A = bot_bo443197316chanID ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_63_equals0D,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 0.30/0.46 ( ( A = bot_bo1943466239ecy_KS )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_64_equals0D,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 0.30/0.46 ( ( A = bot_bo701486667y_Keys )
% 0.30/0.46 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_65_equals0D,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 0.30/0.46 ( ( A = bot_bo1124690338ecrets )
% 0.30/0.46 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_66_equals0D,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 0.30/0.46 ( ( A = bot_bo1785112429specID )
% 0.30/0.46 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_67_equals0D,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 0.30/0.46 ( ( A = bot_bo443197316chanID )
% 0.30/0.46 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_68_emptyE,axiom,
% 0.30/0.46 ! [A2: secrecy_KS] :
% 0.30/0.46 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_69_emptyE,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys] :
% 0.30/0.46 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_70_emptyE,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets] :
% 0.30/0.46 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_71_emptyE,axiom,
% 0.30/0.46 ! [A2: secrecy_specID] :
% 0.30/0.46 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_72_emptyE,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID] :
% 0.30/0.46 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_73_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ A2 @ A )
% 0.30/0.46 => ? [B3: set_Secrecy_KS] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 0.30/0.46 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_74_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ A2 @ A )
% 0.30/0.46 => ? [B3: set_Secrecy_chanID] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert751661162chanID @ A2 @ B3 ) )
% 0.30/0.46 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_75_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ A2 @ A )
% 0.30/0.46 => ? [B3: set_Secrecy_specID] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert1671894227specID @ A2 @ B3 ) )
% 0.30/0.46 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_76_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.30/0.46 => ? [B3: set_Secrecy_Keys] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 0.30/0.46 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_77_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ A2 @ A )
% 0.30/0.46 => ? [B3: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert565337510ecrets @ A2 @ B3 ) )
% 0.30/0.46 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_78_insert__commute,axiom,
% 0.30/0.46 ! [X: secrecy_specID,Y2: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y2 @ A ) )
% 0.30/0.46 = ( insert1671894227specID @ Y2 @ ( insert1671894227specID @ X @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_commute
% 0.30/0.46 thf(fact_79_insert__commute,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,Y2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y2 @ A ) )
% 0.30/0.46 = ( insert751661162chanID @ Y2 @ ( insert751661162chanID @ X @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_commute
% 0.30/0.46 thf(fact_80_insert__eq__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 0.30/0.46 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 0.30/0.46 = ( insert_Secrecy_KS @ B2 @ B ) )
% 0.30/0.46 = ( ( ( A2 = B2 )
% 0.30/0.46 => ( A = B ) )
% 0.30/0.46 & ( ( A2 != B2 )
% 0.30/0.46 => ? [C2: set_Secrecy_KS] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 0.30/0.46 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 0.30/0.46 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_81_insert__eq__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( member1967978193chanID @ A2 @ A )
% 0.30/0.46 => ( ~ ( member1967978193chanID @ B2 @ B )
% 0.30/0.46 => ( ( ( insert751661162chanID @ A2 @ A )
% 0.30/0.46 = ( insert751661162chanID @ B2 @ B ) )
% 0.30/0.46 = ( ( ( A2 = B2 )
% 0.30/0.46 => ( A = B ) )
% 0.30/0.46 & ( ( A2 != B2 )
% 0.30/0.46 => ? [C2: set_Secrecy_chanID] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert751661162chanID @ B2 @ C2 ) )
% 0.30/0.46 & ~ ( member1967978193chanID @ B2 @ C2 )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert751661162chanID @ A2 @ C2 ) )
% 0.30/0.46 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_82_insert__eq__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ~ ( member740727610specID @ A2 @ A )
% 0.30/0.46 => ( ~ ( member740727610specID @ B2 @ B )
% 0.30/0.46 => ( ( ( insert1671894227specID @ A2 @ A )
% 0.30/0.46 = ( insert1671894227specID @ B2 @ B ) )
% 0.30/0.46 = ( ( ( A2 = B2 )
% 0.30/0.46 => ( A = B ) )
% 0.30/0.46 & ( ( A2 != B2 )
% 0.30/0.46 => ? [C2: set_Secrecy_specID] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert1671894227specID @ B2 @ C2 ) )
% 0.30/0.46 & ~ ( member740727610specID @ B2 @ C2 )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert1671894227specID @ A2 @ C2 ) )
% 0.30/0.46 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_83_insert__eq__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 0.30/0.46 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 0.30/0.46 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 0.30/0.46 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.30/0.46 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 0.30/0.46 = ( ( ( A2 = B2 )
% 0.30/0.46 => ( A = B ) )
% 0.30/0.46 & ( ( A2 != B2 )
% 0.30/0.46 => ? [C2: set_Secrecy_Keys] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 0.30/0.46 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 0.30/0.46 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_84_insert__eq__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.30/0.46 ( ~ ( member2138796287ecrets @ A2 @ A )
% 0.30/0.46 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 0.30/0.46 => ( ( ( insert565337510ecrets @ A2 @ A )
% 0.30/0.46 = ( insert565337510ecrets @ B2 @ B ) )
% 0.30/0.46 = ( ( ( A2 = B2 )
% 0.30/0.46 => ( A = B ) )
% 0.30/0.46 & ( ( A2 != B2 )
% 0.30/0.46 => ? [C2: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert565337510ecrets @ B2 @ C2 ) )
% 0.30/0.46 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert565337510ecrets @ A2 @ C2 ) )
% 0.30/0.46 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_85_insert__absorb,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ A2 @ A )
% 0.30/0.46 => ( ( insert_Secrecy_KS @ A2 @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_86_insert__absorb,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ A2 @ A )
% 0.30/0.46 => ( ( insert751661162chanID @ A2 @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_87_insert__absorb,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ A2 @ A )
% 0.30/0.46 => ( ( insert1671894227specID @ A2 @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_88_insert__absorb,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.30/0.46 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_89_insert__absorb,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ A2 @ A )
% 0.30/0.46 => ( ( insert565337510ecrets @ A2 @ A )
% 0.30/0.46 = A ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_90_insert__ident,axiom,
% 0.30/0.46 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ~ ( member_Secrecy_KS @ X @ A )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ X @ B )
% 0.30/0.46 => ( ( ( insert_Secrecy_KS @ X @ A )
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ B ) )
% 0.30/0.46 = ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_91_insert__ident,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( member1967978193chanID @ X @ A )
% 0.30/0.46 => ( ~ ( member1967978193chanID @ X @ B )
% 0.30/0.46 => ( ( ( insert751661162chanID @ X @ A )
% 0.30/0.46 = ( insert751661162chanID @ X @ B ) )
% 0.30/0.46 = ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_92_insert__ident,axiom,
% 0.30/0.46 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ~ ( member740727610specID @ X @ A )
% 0.30/0.46 => ( ~ ( member740727610specID @ X @ B )
% 0.30/0.46 => ( ( ( insert1671894227specID @ X @ A )
% 0.30/0.46 = ( insert1671894227specID @ X @ B ) )
% 0.30/0.46 = ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_93_insert__ident,axiom,
% 0.30/0.46 ! [X: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.30/0.46 ( ~ ( member_Secrecy_Keys @ X @ A )
% 0.30/0.46 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 0.30/0.46 => ( ( ( insert_Secrecy_Keys @ X @ A )
% 0.30/0.46 = ( insert_Secrecy_Keys @ X @ B ) )
% 0.30/0.46 = ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_94_insert__ident,axiom,
% 0.30/0.46 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.30/0.46 ( ~ ( member2138796287ecrets @ X @ A )
% 0.30/0.46 => ( ~ ( member2138796287ecrets @ X @ B )
% 0.30/0.46 => ( ( ( insert565337510ecrets @ X @ A )
% 0.30/0.46 = ( insert565337510ecrets @ X @ B ) )
% 0.30/0.46 = ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_95_Set_Oset__insert,axiom,
% 0.30/0.46 ! [X: secrecy_KS,A: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X @ A )
% 0.30/0.46 => ~ ! [B3: set_Secrecy_KS] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ B3 ) )
% 0.30/0.46 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_96_Set_Oset__insert,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X @ A )
% 0.30/0.46 => ~ ! [B3: set_Secrecy_chanID] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert751661162chanID @ X @ B3 ) )
% 0.30/0.46 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_97_Set_Oset__insert,axiom,
% 0.30/0.46 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ X @ A )
% 0.30/0.46 => ~ ! [B3: set_Secrecy_specID] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert1671894227specID @ X @ B3 ) )
% 0.30/0.46 => ( member740727610specID @ X @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_98_Set_Oset__insert,axiom,
% 0.30/0.46 ! [X: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ X @ A )
% 0.30/0.46 => ~ ! [B3: set_Secrecy_Keys] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 0.30/0.46 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_99_Set_Oset__insert,axiom,
% 0.30/0.46 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ X @ A )
% 0.30/0.46 => ~ ! [B3: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( A
% 0.30/0.46 = ( insert565337510ecrets @ X @ B3 ) )
% 0.30/0.46 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_100_insertI2,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ A2 @ B )
% 0.30/0.46 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_101_insertI2,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ A2 @ B )
% 0.30/0.46 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_102_insertI2,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ A2 @ B )
% 0.30/0.46 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_103_insertI2,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ A2 @ B )
% 0.30/0.46 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_104_insertI2,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ A2 @ B )
% 0.30/0.46 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_105_insertI1,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_106_insertI1,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_107_insertI1,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_108_insertI1,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_109_insertI1,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_110_insertE,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_111_insertE,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_112_insertE,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( member740727610specID @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_113_insertE,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_114_insertE,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_115_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 0.30/0.46 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_116_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 0.30/0.46 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_117_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 0.30/0.46 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_118_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_119_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.30/0.46 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_120_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS] :
% 0.30/0.46 ( ( collect_Secrecy_KS
% 0.30/0.46 @ ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_121_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( collec625564175chanID
% 0.30/0.46 @ ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_122_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID] :
% 0.30/0.46 ( ( collec1545797240specID
% 0.30/0.46 @ ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_123_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( collect_Secrecy_Keys
% 0.30/0.46 @ ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_124_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( collec836099393ecrets
% 0.30/0.46 @ ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A ) )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_125_know__composition__neg1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: secrecy_KS,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( knowle945212990e_know @ P @ M )
% 0.30/0.46 => ( ~ ( knowle945212990e_know @ Q @ M )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ~ ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know_composition_neg1
% 0.30/0.46 thf(fact_126_singleton__inject,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 0.30/0.46 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 0.30/0.46 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.30/0.46 => ( A2 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_inject
% 0.30/0.46 thf(fact_127_singleton__inject,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 0.30/0.46 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 0.30/0.46 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.30/0.46 => ( A2 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_inject
% 0.30/0.46 thf(fact_128_insert__not__empty,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( insert1671894227specID @ A2 @ A )
% 0.30/0.46 != bot_bo1785112429specID ) ).
% 0.30/0.46
% 0.30/0.46 % insert_not_empty
% 0.30/0.46 thf(fact_129_insert__not__empty,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( insert751661162chanID @ A2 @ A )
% 0.30/0.46 != bot_bo443197316chanID ) ).
% 0.30/0.46
% 0.30/0.46 % insert_not_empty
% 0.30/0.46 thf(fact_130_doubleton__eq__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 0.30/0.46 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.30/0.46 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 0.30/0.46 = ( ( ( A2 = C )
% 0.30/0.46 & ( B2 = D ) )
% 0.30/0.46 | ( ( A2 = D )
% 0.30/0.46 & ( B2 = C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % doubleton_eq_iff
% 0.30/0.46 thf(fact_131_doubleton__eq__iff,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 0.30/0.46 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.30/0.46 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 0.30/0.46 = ( ( ( A2 = C )
% 0.30/0.46 & ( B2 = D ) )
% 0.30/0.46 | ( ( A2 = D )
% 0.30/0.46 & ( B2 = C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % doubleton_eq_iff
% 0.30/0.46 thf(fact_132_singleton__iff,axiom,
% 0.30/0.46 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.30/0.46 = ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_133_singleton__iff,axiom,
% 0.30/0.46 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.30/0.46 = ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_134_singleton__iff,axiom,
% 0.30/0.46 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.30/0.46 = ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_135_singleton__iff,axiom,
% 0.30/0.46 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.30/0.46 = ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_136_singleton__iff,axiom,
% 0.30/0.46 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.30/0.46 = ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_137_singletonD,axiom,
% 0.30/0.46 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.30/0.46 => ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_138_singletonD,axiom,
% 0.30/0.46 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.30/0.46 => ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_139_singletonD,axiom,
% 0.30/0.46 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.30/0.46 => ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_140_singletonD,axiom,
% 0.30/0.46 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.30/0.46 => ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_141_singletonD,axiom,
% 0.30/0.46 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.30/0.46 => ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_142_TBtheorem3a,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( ine @ P @ E2 )
% 0.30/0.46 => ( ~ ( ine @ Q @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem3a
% 0.30/0.46 thf(fact_143_TBtheorem1a,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ine @ PQ @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine @ P @ E2 )
% 0.30/0.46 | ( ine @ Q @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem1a
% 0.30/0.46 thf(fact_144_the__elem__eq,axiom,
% 0.30/0.46 ! [X: secrecy_specID] :
% 0.30/0.46 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % the_elem_eq
% 0.30/0.46 thf(fact_145_the__elem__eq,axiom,
% 0.30/0.46 ! [X: secrecy_chanID] :
% 0.30/0.46 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % the_elem_eq
% 0.30/0.46 thf(fact_146_is__singletonI,axiom,
% 0.30/0.46 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI
% 0.30/0.46 thf(fact_147_is__singletonI,axiom,
% 0.30/0.46 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI
% 0.30/0.46 thf(fact_148_KS2Expression_Osimps_I1_J,axiom,
% 0.30/0.46 ! [M: secrecy_Keys] :
% 0.30/0.46 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.30/0.46 = ( secrecy_kE @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS2Expression.simps(1)
% 0.30/0.46 thf(fact_149_Set_Ois__empty__def,axiom,
% 0.30/0.46 ( is_emp1849217361specID
% 0.30/0.46 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.is_empty_def
% 0.30/0.46 thf(fact_150_Set_Ois__empty__def,axiom,
% 0.30/0.46 ( is_emp928984296chanID
% 0.30/0.46 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.is_empty_def
% 0.30/0.46 thf(fact_151_is__singleton__def,axiom,
% 0.30/0.46 ( is_sin1501507247specID
% 0.30/0.46 = ( ^ [A3: set_Secrecy_specID] :
% 0.30/0.46 ? [X2: secrecy_specID] :
% 0.30/0.46 ( A3
% 0.30/0.46 = ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_def
% 0.30/0.46 thf(fact_152_is__singleton__def,axiom,
% 0.30/0.46 ( is_sin581274182chanID
% 0.30/0.46 = ( ^ [A3: set_Secrecy_chanID] :
% 0.30/0.46 ? [X2: secrecy_chanID] :
% 0.30/0.46 ( A3
% 0.30/0.46 = ( insert751661162chanID @ X2 @ bot_bo443197316chanID ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_def
% 0.30/0.46 thf(fact_153_is__singletonE,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID] :
% 0.30/0.46 ( ( is_sin1501507247specID @ A )
% 0.30/0.46 => ~ ! [X3: secrecy_specID] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonE
% 0.30/0.46 thf(fact_154_is__singletonE,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( is_sin581274182chanID @ A )
% 0.30/0.46 => ~ ! [X3: secrecy_chanID] :
% 0.30/0.46 ( A
% 0.30/0.46 != ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonE
% 0.30/0.46 thf(fact_155_bot__set__def,axiom,
% 0.30/0.46 ( bot_bo1785112429specID
% 0.30/0.46 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_set_def
% 0.30/0.46 thf(fact_156_bot__set__def,axiom,
% 0.30/0.46 ( bot_bo443197316chanID
% 0.30/0.46 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_set_def
% 0.30/0.46 thf(fact_157_is__singleton__the__elem,axiom,
% 0.30/0.46 ( is_sin1501507247specID
% 0.30/0.46 = ( ^ [A3: set_Secrecy_specID] :
% 0.30/0.46 ( A3
% 0.30/0.46 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_the_elem
% 0.30/0.46 thf(fact_158_is__singleton__the__elem,axiom,
% 0.30/0.46 ( is_sin581274182chanID
% 0.30/0.46 = ( ^ [A3: set_Secrecy_chanID] :
% 0.30/0.46 ( A3
% 0.30/0.46 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_the_elem
% 0.30/0.46 thf(fact_159_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS] :
% 0.30/0.46 ( ( A != bot_bo1943466239ecy_KS )
% 0.30/0.46 => ( ! [X3: secrecy_KS,Y: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X3 @ A )
% 0.30/0.46 => ( ( member_Secrecy_KS @ Y @ A )
% 0.30/0.46 => ( X3 = Y ) ) )
% 0.30/0.46 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_160_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( A != bot_bo701486667y_Keys )
% 0.30/0.46 => ( ! [X3: secrecy_Keys,Y: secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ X3 @ A )
% 0.30/0.46 => ( ( member_Secrecy_Keys @ Y @ A )
% 0.30/0.46 => ( X3 = Y ) ) )
% 0.30/0.46 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_161_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( A != bot_bo1124690338ecrets )
% 0.30/0.46 => ( ! [X3: secrecy_Secrets,Y: secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ X3 @ A )
% 0.30/0.46 => ( ( member2138796287ecrets @ Y @ A )
% 0.30/0.46 => ( X3 = Y ) ) )
% 0.30/0.46 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_162_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID] :
% 0.30/0.46 ( ( A != bot_bo1785112429specID )
% 0.30/0.46 => ( ! [X3: secrecy_specID,Y: secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ X3 @ A )
% 0.30/0.46 => ( ( member740727610specID @ Y @ A )
% 0.30/0.46 => ( X3 = Y ) ) )
% 0.30/0.46 => ( is_sin1501507247specID @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_163_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( A != bot_bo443197316chanID )
% 0.30/0.46 => ( ! [X3: secrecy_chanID,Y: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ A )
% 0.30/0.46 => ( ( member1967978193chanID @ Y @ A )
% 0.30/0.46 => ( X3 = Y ) ) )
% 0.30/0.46 => ( is_sin581274182chanID @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_164_TBtheorem4a__empty,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( ine @ P @ E2 )
% 0.30/0.46 | ( ine @ Q @ E2 ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ( loc @ PQ )
% 0.30/0.46 = bot_bo443197316chanID )
% 0.30/0.46 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_empty
% 0.30/0.46 thf(fact_165_TBtheorem1b,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ineM @ PQ @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ineM @ P @ M2 @ E2 )
% 0.30/0.46 | ( ineM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem1b
% 0.30/0.46 thf(fact_166_TBtheorem3b,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( ineM @ P @ M2 @ E2 )
% 0.30/0.46 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem3b
% 0.30/0.46 thf(fact_167_DecrEnc,axiom,
% 0.30/0.46 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list_S529945141ession] :
% 0.30/0.46 ( ( encrDecrKeys @ K12 @ K22 )
% 0.30/0.46 => ( ( decr @ K22 @ ( enc @ K12 @ E2 ) )
% 0.30/0.46 = E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % DecrEnc
% 0.30/0.46 thf(fact_168_ExtSign,axiom,
% 0.30/0.46 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list_S529945141ession] :
% 0.30/0.46 ( ( encrDecrKeys @ K12 @ K22 )
% 0.30/0.46 => ( ( ext @ K12 @ ( sign @ K22 @ E2 ) )
% 0.30/0.46 = E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ExtSign
% 0.30/0.46 thf(fact_169_correctCompositionIn__L2,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionIn_L2
% 0.30/0.46 thf(fact_170_correctCompositionIn__prop1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.30/0.46 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionIn_prop1
% 0.30/0.46 thf(fact_171_not__ine__ineM,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( ine @ P @ E2 )
% 0.30/0.46 => ~ ( ineM @ P @ M2 @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_ine_ineM
% 0.30/0.46 thf(fact_172_ineM__ine,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( ineM @ P @ M2 @ E2 )
% 0.30/0.46 => ( ine @ P @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_ine
% 0.30/0.46 thf(fact_173_correctCompositionIn__L1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionIn_L1
% 0.30/0.46 thf(fact_174_subcomponents__loc,axiom,
% 0.30/0.46 ! [X: secrecy_specID] :
% 0.30/0.46 ( ( correc965049635ionLoc @ X )
% 0.30/0.46 => ( ( ( subcomponents @ X )
% 0.30/0.46 = bot_bo1785112429specID )
% 0.30/0.46 => ( ( loc @ X )
% 0.30/0.46 = bot_bo443197316chanID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subcomponents_loc
% 0.30/0.46 thf(fact_175_TBtheorem4b__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ineM @ P @ M2 @ E2 )
% 0.30/0.46 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_notP1
% 0.30/0.46 thf(fact_176_TBtheorem4a__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ine @ P @ E2 )
% 0.30/0.46 => ( ~ ( ine @ Q @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_notP1
% 0.30/0.46 thf(fact_177_TBtheorem4b__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 0.30/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_notPQ
% 0.30/0.46 thf(fact_178_TBtheorem4b__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_notP2
% 0.30/0.46 thf(fact_179_TBtheorem4a__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 0.30/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_notPQ
% 0.30/0.46 thf(fact_180_ine__exprChannelSingle__Set,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( ine_ex1303305700Single @ P @ Ch @ E2 )
% 0.30/0.46 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSingle_Set
% 0.30/0.46 thf(fact_181_ine__exprChannelSet__Single,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 )
% 0.30/0.46 => ( ine_ex1303305700Single @ P @ Ch @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSet_Single
% 0.30/0.46 thf(fact_182_ine__nonempty__exprChannelSet,axiom,
% 0.30/0.46 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.30/0.46 => ( ( ChSet != bot_bo443197316chanID )
% 0.30/0.46 => ( ine @ P @ E2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_nonempty_exprChannelSet
% 0.30/0.46 thf(fact_183_ine__empty__exprChannelSet,axiom,
% 0.30/0.46 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.30/0.46 => ( ( ChSet = bot_bo443197316chanID )
% 0.30/0.46 => ~ ( ine @ P @ E2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_empty_exprChannelSet
% 0.30/0.46 thf(fact_184_TBtheorem4a__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( ine @ Q @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_notP2
% 0.30/0.46 thf(fact_185_locStream__def,axiom,
% 0.30/0.46 ( locStream
% 0.30/0.46 = ( ^ [X2: secrecy_specID] :
% 0.30/0.46 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 0.30/0.46 @ ( loc @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % locStream_def
% 0.30/0.46 thf(fact_186_inStream__def,axiom,
% 0.30/0.46 ( inStream
% 0.30/0.46 = ( ^ [X2: secrecy_specID] :
% 0.30/0.46 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 0.30/0.46 @ ( ins @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inStream_def
% 0.30/0.46 thf(fact_187_TBtheorem4b__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ineM @ P @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 0.30/0.46 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_P
% 0.30/0.46 thf(fact_188_TBtheorem4b__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( ineM @ P @ M2 @ E2 )
% 0.30/0.46 | ( ineM @ Q @ M2 @ E2 ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.30/0.46 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_PQ
% 0.30/0.46 thf(fact_189_TBtheorem4a__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ine @ P @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_P
% 0.30/0.46 thf(fact_190_TBtheorem4a__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( ine @ P @ E2 )
% 0.30/0.46 | ( ine @ Q @ E2 ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.30/0.46 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_PQ
% 0.30/0.46 thf(fact_191_ine__ins__neg1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 0.30/0.46 ( ~ ( ine @ P @ M )
% 0.30/0.46 => ( ( exprChannel @ X @ M )
% 0.30/0.46 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_ins_neg1
% 0.30/0.46 thf(fact_192_ine__def,axiom,
% 0.30/0.46 ( ine
% 0.30/0.46 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 0.30/0.46 ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_def
% 0.30/0.46 thf(fact_193_ineM__L1,axiom,
% 0.30/0.46 ! [Ch: secrecy_chanID,M2: set_Secrecy_chanID,P: secrecy_specID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch @ M2 )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ E2 )
% 0.30/0.46 => ( ineM @ P @ M2 @ E2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_L1
% 0.30/0.46 thf(fact_194_ineM__def,axiom,
% 0.30/0.46 ( ineM
% 0.30/0.46 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E3: secrecy_Expression] :
% 0.30/0.46 ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.30/0.46 & ( member1967978193chanID @ Ch3 @ M3 )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_def
% 0.30/0.46 thf(fact_195_ine__exprChannelSet__def,axiom,
% 0.30/0.46 ( ine_exprChannelSet
% 0.30/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E3: secrecy_Expression] :
% 0.30/0.46 ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 0.30/0.46 => ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 0.30/0.46 & ( exprChannel @ X2 @ E3 ) ) )
% 0.30/0.46 & ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 0.30/0.46 & ( member1967978193chanID @ X2 @ ( ins @ SP ) ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSet_def
% 0.30/0.46 thf(fact_196_ine__exprChannelSingle__def,axiom,
% 0.30/0.46 ( ine_ex1303305700Single
% 0.30/0.46 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E3 )
% 0.30/0.46 & ! [X2: secrecy_chanID,T: nat] :
% 0.30/0.46 ( ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 0.30/0.46 & ( X2 != Ch3 ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSingle_def
% 0.30/0.46 thf(fact_197_LocalSecretsComposition__exprChannel__k,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.30/0.46 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_exprChannel_k
% 0.30/0.46 thf(fact_198_correctCompositionInLoc__exprChannel,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ M )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 0.30/0.46 => ~ ( exprChannel @ X3 @ M ) )
% 0.30/0.46 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionInLoc_exprChannel
% 0.30/0.46 thf(fact_199_TBlemma3b,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ~ ( ineM @ P @ M2 @ E2 )
% 0.30/0.46 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ M2 )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 => ~ ( exprChannel @ Ch @ E2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBlemma3b
% 0.30/0.46 thf(fact_200_bot__empty__eq,axiom,
% 0.30/0.46 ( bot_bot_Secrecy_KS_o
% 0.30/0.46 = ( ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ bot_bo1943466239ecy_KS ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_201_bot__empty__eq,axiom,
% 0.30/0.46 ( bot_bo2072920570Keys_o
% 0.30/0.46 = ( ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ bot_bo701486667y_Keys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_202_bot__empty__eq,axiom,
% 0.30/0.46 ( bot_bo1909946299rets_o
% 0.30/0.46 = ( ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ bot_bo1124690338ecrets ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_203_bot__empty__eq,axiom,
% 0.30/0.46 ( bot_bo1767780696ecID_o
% 0.30/0.46 = ( ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ bot_bo1785112429specID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_204_bot__empty__eq,axiom,
% 0.30/0.46 ( bot_bo1012329985anID_o
% 0.30/0.46 = ( ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ bot_bo443197316chanID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_205_Collect__empty__eq__bot,axiom,
% 0.30/0.46 ! [P: secrecy_specID > $o] :
% 0.30/0.46 ( ( ( collec1545797240specID @ P )
% 0.30/0.46 = bot_bo1785112429specID )
% 0.30/0.46 = ( P = bot_bo1767780696ecID_o ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq_bot
% 0.30/0.46 thf(fact_206_Collect__empty__eq__bot,axiom,
% 0.30/0.46 ! [P: secrecy_chanID > $o] :
% 0.30/0.46 ( ( ( collec625564175chanID @ P )
% 0.30/0.46 = bot_bo443197316chanID )
% 0.30/0.46 = ( P = bot_bo1012329985anID_o ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq_bot
% 0.30/0.46 thf(fact_207_LocalSecretsComposition__neg__loc__k,axiom,
% 0.30/0.46 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_loc_k
% 0.30/0.46 thf(fact_208_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_Qex
% 0.30/0.46 thf(fact_209_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_Pex
% 0.30/0.46 thf(fact_210_correctCompositionKS__PQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.30/0.46 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_PQ
% 0.30/0.46 thf(fact_211_correctCompositionKS__neg1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_neg1
% 0.30/0.46 thf(fact_212_correctCompositionKS__negP,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_negP
% 0.30/0.46 thf(fact_213_correctCompositionKS__negQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_negQ
% 0.30/0.46 thf(fact_214_know__composition,axiom,
% 0.30/0.46 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ( ( knowle945212990e_know @ P @ M )
% 0.30/0.46 | ( knowle945212990e_know @ Q @ M ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know_composition
% 0.30/0.46 thf(fact_215_know__composition1,axiom,
% 0.30/0.46 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ( knowle945212990e_know @ P @ M )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know_composition1
% 0.30/0.46 thf(fact_216_know__composition2,axiom,
% 0.30/0.46 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ( knowle945212990e_know @ Q @ M )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know_composition2
% 0.30/0.46 thf(fact_217_correctCompositionKS__exprChannel__k__P,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_P
% 0.30/0.46 thf(fact_218_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_Q
% 0.30/0.46 thf(fact_219_LocalSecretsComposition__neg__k,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_k
% 0.30/0.46 thf(fact_220_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_Qex
% 0.30/0.46 thf(fact_221_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_Pex
% 0.30/0.46 thf(fact_222_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_Q
% 0.30/0.46 thf(fact_223_correctCompositionKS__exprChannel__s__P,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_P
% 0.30/0.46 thf(fact_224_UnCI,axiom,
% 0.30/0.46 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( ~ ( member740727610specID @ C @ B )
% 0.30/0.46 => ( member740727610specID @ C @ A ) )
% 0.30/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_225_UnCI,axiom,
% 0.30/0.46 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 0.30/0.46 => ( member_Secrecy_Keys @ C @ A ) )
% 0.30/0.46 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_226_UnCI,axiom,
% 0.30/0.46 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( ~ ( member2138796287ecrets @ C @ B )
% 0.30/0.46 => ( member2138796287ecrets @ C @ A ) )
% 0.30/0.46 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_227_UnCI,axiom,
% 0.30/0.46 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.30/0.46 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 0.30/0.46 => ( member_Secrecy_KS @ C @ A ) )
% 0.30/0.46 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_228_UnCI,axiom,
% 0.30/0.46 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ~ ( member1967978193chanID @ C @ B )
% 0.30/0.46 => ( member1967978193chanID @ C @ A ) )
% 0.30/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_229_Un__iff,axiom,
% 0.30/0.46 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.30/0.46 = ( ( member740727610specID @ C @ A )
% 0.30/0.46 | ( member740727610specID @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_230_Un__iff,axiom,
% 0.30/0.46 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.30/0.46 = ( ( member_Secrecy_Keys @ C @ A )
% 0.30/0.46 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_231_Un__iff,axiom,
% 0.30/0.46 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.30/0.46 = ( ( member2138796287ecrets @ C @ A )
% 0.30/0.46 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_232_Un__iff,axiom,
% 0.30/0.46 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.30/0.46 = ( ( member_Secrecy_KS @ C @ A )
% 0.30/0.46 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_233_Un__iff,axiom,
% 0.30/0.46 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.30/0.46 = ( ( member1967978193chanID @ C @ A )
% 0.30/0.46 | ( member1967978193chanID @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_234_KS_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.30/0.46 ( ( ( secrecy_sKS @ X22 )
% 0.30/0.46 = ( secrecy_sKS @ Y22 ) )
% 0.30/0.46 = ( X22 = Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.inject(2)
% 0.30/0.46 thf(fact_235_Expression_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.30/0.46 ( ( ( secrecy_sE @ X22 )
% 0.30/0.46 = ( secrecy_sE @ Y22 ) )
% 0.30/0.46 = ( X22 = Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Expression.inject(2)
% 0.30/0.46 thf(fact_236_Un__empty,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.30/0.46 = bot_bo1943466239ecy_KS )
% 0.30/0.46 = ( ( A = bot_bo1943466239ecy_KS )
% 0.30/0.46 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty
% 0.30/0.46 thf(fact_237_Un__empty,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ( ( sup_su1712599557specID @ A @ B )
% 0.30/0.46 = bot_bo1785112429specID )
% 0.30/0.46 = ( ( A = bot_bo1785112429specID )
% 0.30/0.46 & ( B = bot_bo1785112429specID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty
% 0.30/0.46 thf(fact_238_Un__empty,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ( sup_su370684444chanID @ A @ B )
% 0.30/0.46 = bot_bo443197316chanID )
% 0.30/0.46 = ( ( A = bot_bo443197316chanID )
% 0.30/0.46 & ( B = bot_bo443197316chanID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty
% 0.30/0.46 thf(fact_239_Un__insert__right,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 0.30/0.46 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_right
% 0.30/0.46 thf(fact_240_Un__insert__right,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 0.30/0.46 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_right
% 0.30/0.46 thf(fact_241_Un__insert__right,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 0.30/0.46 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_right
% 0.30/0.46 thf(fact_242_Un__insert__left,axiom,
% 0.30/0.46 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 0.30/0.46 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 0.30/0.46 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_left
% 0.30/0.46 thf(fact_243_Un__insert__left,axiom,
% 0.30/0.46 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 0.30/0.46 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_left
% 0.30/0.46 thf(fact_244_Un__insert__left,axiom,
% 0.30/0.46 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 0.30/0.46 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_left
% 0.30/0.46 thf(fact_245_Un__empty__left,axiom,
% 0.30/0.46 ! [B: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 0.30/0.46 = B ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_left
% 0.30/0.46 thf(fact_246_Un__empty__left,axiom,
% 0.30/0.46 ! [B: set_Secrecy_specID] :
% 0.30/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 0.30/0.46 = B ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_left
% 0.30/0.46 thf(fact_247_Un__empty__left,axiom,
% 0.30/0.46 ! [B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 0.30/0.46 = B ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_left
% 0.30/0.46 thf(fact_248_Un__empty__right,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_right
% 0.30/0.46 thf(fact_249_Un__empty__right,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID] :
% 0.30/0.46 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_right
% 0.30/0.46 thf(fact_250_Un__empty__right,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_right
% 0.30/0.46 thf(fact_251_not__know__s__not__ine,axiom,
% 0.30/0.46 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.30/0.46 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.30/0.46 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_s_not_ine
% 0.30/0.46 thf(fact_252_UnE,axiom,
% 0.30/0.46 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.30/0.46 => ( ~ ( member740727610specID @ C @ A )
% 0.30/0.46 => ( member740727610specID @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_253_UnE,axiom,
% 0.30/0.46 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 0.30/0.46 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_254_UnE,axiom,
% 0.30/0.46 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.30/0.46 => ( ~ ( member2138796287ecrets @ C @ A )
% 0.30/0.46 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_255_UnE,axiom,
% 0.30/0.46 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ C @ A )
% 0.30/0.46 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_256_UnE,axiom,
% 0.30/0.46 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.30/0.46 => ( ~ ( member1967978193chanID @ C @ A )
% 0.30/0.46 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_257_UnI1,axiom,
% 0.30/0.46 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ C @ A )
% 0.30/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_258_UnI1,axiom,
% 0.30/0.46 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ C @ A )
% 0.30/0.46 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_259_UnI1,axiom,
% 0.30/0.46 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ C @ A )
% 0.30/0.46 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_260_UnI1,axiom,
% 0.30/0.46 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ C @ A )
% 0.30/0.46 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_261_UnI1,axiom,
% 0.30/0.46 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ C @ A )
% 0.30/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_262_UnI2,axiom,
% 0.30/0.46 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ C @ B )
% 0.30/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_263_UnI2,axiom,
% 0.30/0.46 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.30/0.46 ( ( member_Secrecy_Keys @ C @ B )
% 0.30/0.46 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_264_UnI2,axiom,
% 0.30/0.46 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.30/0.46 ( ( member2138796287ecrets @ C @ B )
% 0.30/0.46 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_265_UnI2,axiom,
% 0.30/0.46 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ C @ B )
% 0.30/0.46 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_266_UnI2,axiom,
% 0.30/0.46 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ C @ B )
% 0.30/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_267_bex__Un,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.30/0.46 ( ( ? [X2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.30/0.46 & ( P @ X2 ) ) )
% 0.30/0.46 = ( ? [X2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X2 @ A )
% 0.30/0.46 & ( P @ X2 ) )
% 0.30/0.46 | ? [X2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X2 @ B )
% 0.30/0.46 & ( P @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bex_Un
% 0.30/0.46 thf(fact_268_bex__Un,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.30/0.46 ( ( ? [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A @ B ) )
% 0.30/0.46 & ( P @ X2 ) ) )
% 0.30/0.46 = ( ? [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ A )
% 0.30/0.46 & ( P @ X2 ) )
% 0.30/0.46 | ? [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ B )
% 0.30/0.46 & ( P @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bex_Un
% 0.30/0.46 thf(fact_269_ball__Un,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.30/0.46 ( ( ! [X2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.30/0.46 => ( P @ X2 ) ) )
% 0.30/0.46 = ( ! [X2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X2 @ A )
% 0.30/0.46 => ( P @ X2 ) )
% 0.30/0.46 & ! [X2: secrecy_KS] :
% 0.30/0.46 ( ( member_Secrecy_KS @ X2 @ B )
% 0.30/0.46 => ( P @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ball_Un
% 0.30/0.46 thf(fact_270_ball__Un,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.30/0.46 ( ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A @ B ) )
% 0.30/0.46 => ( P @ X2 ) ) )
% 0.30/0.46 = ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ A )
% 0.30/0.46 => ( P @ X2 ) )
% 0.30/0.46 & ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ B )
% 0.30/0.46 => ( P @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ball_Un
% 0.30/0.46 thf(fact_271_Un__assoc,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 0.30/0.46 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_assoc
% 0.30/0.46 thf(fact_272_Un__assoc,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 0.30/0.46 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_assoc
% 0.30/0.46 thf(fact_273_Un__absorb,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb
% 0.30/0.46 thf(fact_274_Un__absorb,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ A @ A )
% 0.30/0.46 = A ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb
% 0.30/0.46 thf(fact_275_Un__commute,axiom,
% 0.30/0.46 ( sup_su1301156759ecy_KS
% 0.30/0.46 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_commute
% 0.30/0.46 thf(fact_276_Un__commute,axiom,
% 0.30/0.46 ( sup_su370684444chanID
% 0.30/0.46 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_commute
% 0.30/0.46 thf(fact_277_Un__left__absorb,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.30/0.46 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_absorb
% 0.30/0.46 thf(fact_278_Un__left__absorb,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 0.30/0.46 = ( sup_su370684444chanID @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_absorb
% 0.30/0.46 thf(fact_279_Un__left__commute,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 0.30/0.46 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_commute
% 0.30/0.46 thf(fact_280_Un__left__commute,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 0.30/0.46 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_commute
% 0.30/0.46 thf(fact_281_KS2Expression_Osimps_I2_J,axiom,
% 0.30/0.46 ! [M: secrecy_Secrets] :
% 0.30/0.46 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.30/0.46 = ( secrecy_sE @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS2Expression.simps(2)
% 0.30/0.46 thf(fact_282_KS_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.30/0.46 ( ( secrecy_kKS @ X1 )
% 0.30/0.46 != ( secrecy_sKS @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.distinct(1)
% 0.30/0.46 thf(fact_283_KS_Oinduct,axiom,
% 0.30/0.46 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.30/0.46 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 0.30/0.46 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 0.30/0.46 => ( P @ KS ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.induct
% 0.30/0.46 thf(fact_284_KS_Oexhaust,axiom,
% 0.30/0.46 ! [Y2: secrecy_KS] :
% 0.30/0.46 ( ! [X12: secrecy_Keys] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( secrecy_kKS @ X12 ) )
% 0.30/0.46 => ~ ! [X23: secrecy_Secrets] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( secrecy_sKS @ X23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.exhaust
% 0.30/0.46 thf(fact_285_Expression_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.30/0.46 ( ( secrecy_kE @ X1 )
% 0.30/0.46 != ( secrecy_sE @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Expression.distinct(1)
% 0.30/0.46 thf(fact_286_know_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.30/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.30/0.46 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.30/0.46 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know.simps(2)
% 0.30/0.46 thf(fact_287_singleton__Un__iff,axiom,
% 0.30/0.46 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.30/0.46 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 0.30/0.46 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.30/0.46 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.30/0.46 & ( B = bot_bo1943466239ecy_KS ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_Un_iff
% 0.30/0.46 thf(fact_288_singleton__Un__iff,axiom,
% 0.30/0.46 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.30/0.46 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 0.30/0.46 = ( sup_su1712599557specID @ A @ B ) )
% 0.30/0.46 = ( ( ( A = bot_bo1785112429specID )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.30/0.46 & ( B = bot_bo1785112429specID ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_Un_iff
% 0.30/0.46 thf(fact_289_singleton__Un__iff,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 0.30/0.46 = ( sup_su370684444chanID @ A @ B ) )
% 0.30/0.46 = ( ( ( A = bot_bo443197316chanID )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.30/0.46 & ( B = bot_bo443197316chanID ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_Un_iff
% 0.30/0.46 thf(fact_290_Un__singleton__iff,axiom,
% 0.30/0.46 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 0.30/0.46 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.30/0.46 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.30/0.46 & ( B = bot_bo1943466239ecy_KS ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_singleton_iff
% 0.30/0.46 thf(fact_291_Un__singleton__iff,axiom,
% 0.30/0.46 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 0.30/0.46 ( ( ( sup_su1712599557specID @ A @ B )
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.30/0.46 = ( ( ( A = bot_bo1785112429specID )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.30/0.46 & ( B = bot_bo1785112429specID ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_singleton_iff
% 0.30/0.46 thf(fact_292_Un__singleton__iff,axiom,
% 0.30/0.46 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 0.30/0.46 ( ( ( sup_su370684444chanID @ A @ B )
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.30/0.46 = ( ( ( A = bot_bo443197316chanID )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.30/0.46 & ( B = bot_bo443197316chanID ) )
% 0.30/0.46 | ( ( A
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_singleton_iff
% 0.30/0.46 thf(fact_293_insert__is__Un,axiom,
% 0.30/0.46 ( insert_Secrecy_KS
% 0.30/0.46 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_is_Un
% 0.30/0.46 thf(fact_294_insert__is__Un,axiom,
% 0.30/0.46 ( insert1671894227specID
% 0.30/0.46 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_is_Un
% 0.30/0.46 thf(fact_295_insert__is__Un,axiom,
% 0.30/0.46 ( insert751661162chanID
% 0.30/0.46 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_is_Un
% 0.30/0.46 thf(fact_296_LocalSecretsComposition__neg__loc__s,axiom,
% 0.30/0.46 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_loc_s
% 0.30/0.46 thf(fact_297_LocalSecretsComposition__neg__s,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_s
% 0.30/0.46 thf(fact_298_know__composition__neg__ine__s,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( knowle945212990e_know @ P @ ( secrecy_sKS @ Secret ) )
% 0.30/0.46 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know_composition_neg_ine_s
% 0.30/0.46 thf(fact_299_LocalSecretsComposition__neg1__s,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg1_s
% 0.30/0.46 thf(fact_300_LocalSecretsComposition__ine2__s,axiom,
% 0.30/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine2_s
% 0.30/0.46 thf(fact_301_LocalSecretsComposition__ine1__s,axiom,
% 0.30/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine1_s
% 0.30/0.46 thf(fact_302_LocalSecretsComposition__exprChannel__s,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.30/0.46 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 0.30/0.46 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_exprChannel_s
% 0.30/0.46 thf(fact_303_LocalSecretsComposition__neg,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ! [M4: secrecy_Keys] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_kKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.30/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_sKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg
% 0.30/0.46 thf(fact_304_LocalSecretsComposition__neg1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ! [M4: secrecy_Keys] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_kKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.30/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_sKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg1
% 0.30/0.46 thf(fact_305_sup__bot_Oright__neutral,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.right_neutral
% 0.30/0.46 thf(fact_306_sup__bot_Oright__neutral,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_specID] :
% 0.30/0.46 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.right_neutral
% 0.30/0.46 thf(fact_307_sup__bot_Oright__neutral,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.right_neutral
% 0.30/0.46 thf(fact_308_sup__bot_Oneutr__eq__iff,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.30/0.46 ( ( bot_bo1943466239ecy_KS
% 0.30/0.46 = ( sup_su1301156759ecy_KS @ A2 @ B2 ) )
% 0.30/0.46 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.30/0.46 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.neutr_eq_iff
% 0.30/0.46 thf(fact_309_sup__bot_Oneutr__eq__iff,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.30/0.46 ( ( bot_bo1785112429specID
% 0.30/0.46 = ( sup_su1712599557specID @ A2 @ B2 ) )
% 0.30/0.46 = ( ( A2 = bot_bo1785112429specID )
% 0.30/0.46 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.neutr_eq_iff
% 0.30/0.46 thf(fact_310_sup__bot_Oneutr__eq__iff,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.30/0.46 ( ( bot_bo443197316chanID
% 0.30/0.46 = ( sup_su370684444chanID @ A2 @ B2 ) )
% 0.30/0.46 = ( ( A2 = bot_bo443197316chanID )
% 0.30/0.46 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.neutr_eq_iff
% 0.30/0.46 thf(fact_311_sup__bot_Oleft__neutral,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_KS] :
% 0.30/0.46 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A2 )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.left_neutral
% 0.30/0.46 thf(fact_312_sup__bot_Oleft__neutral,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_specID] :
% 0.30/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A2 )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.left_neutral
% 0.30/0.46 thf(fact_313_sup__bot_Oleft__neutral,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_chanID] :
% 0.30/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A2 )
% 0.30/0.46 = A2 ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.left_neutral
% 0.30/0.46 thf(fact_314_sup__bot_Oeq__neutr__iff,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.30/0.46 ( ( ( sup_su1712599557specID @ A2 @ B2 )
% 0.30/0.46 = bot_bo1785112429specID )
% 0.30/0.46 = ( ( A2 = bot_bo1785112429specID )
% 0.30/0.46 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.eq_neutr_iff
% 0.30/0.46 thf(fact_315_sup__bot_Oeq__neutr__iff,axiom,
% 0.30/0.46 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ( sup_su370684444chanID @ A2 @ B2 )
% 0.30/0.46 = bot_bo443197316chanID )
% 0.30/0.46 = ( ( A2 = bot_bo443197316chanID )
% 0.30/0.46 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.eq_neutr_iff
% 0.30/0.46 thf(fact_316_ineM__Un1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,A: set_Secrecy_chanID,E2: secrecy_Expression,B: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ineM @ P @ A @ E2 )
% 0.30/0.46 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_Un1
% 0.30/0.46 thf(fact_317_notSpecKeysSecretsExpr__def,axiom,
% 0.30/0.46 ( notSpe1586871396tsExpr
% 0.30/0.46 = ( ^ [P2: secrecy_specID,E4: list_S529945141ession] :
% 0.30/0.46 ( ! [X2: secrecy_Keys] :
% 0.30/0.46 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X2 ) @ E4 )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.30/0.46 & ! [Y4: secrecy_Secrets] :
% 0.30/0.46 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y4 ) @ E4 )
% 0.30/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % notSpecKeysSecretsExpr_def
% 0.30/0.46 thf(fact_318_TBtheorem5a__empty,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( eout @ P @ E2 )
% 0.30/0.46 | ( eout @ Q @ E2 ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( ( loc @ PQ )
% 0.30/0.46 = bot_bo443197316chanID )
% 0.30/0.46 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_empty
% 0.30/0.46 thf(fact_319_correctCompositionKS__subcomp1,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.30/0.46 ( ( correctCompositionKS @ C3 )
% 0.30/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.30/0.46 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 0.30/0.46 => ? [X3: secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.30/0.46 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp1
% 0.30/0.46 thf(fact_320_TBtheorem2a,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eout @ PQ @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( eout @ P @ E2 )
% 0.30/0.46 | ( eout @ Q @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem2a
% 0.30/0.46 thf(fact_321_correctCompositionKS__subcomp3,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.30/0.46 ( ( correctCompositionKS @ C3 )
% 0.30/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.30/0.46 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.30/0.46 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp3
% 0.30/0.46 thf(fact_322_TBtheorem5a__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( eout @ P @ E2 )
% 0.30/0.46 => ( ~ ( eout @ Q @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_notP1
% 0.30/0.46 thf(fact_323_TBtheorem5a__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 0.30/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_notPQ
% 0.30/0.46 thf(fact_324_TBtheorem5a__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( eout @ Q @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_notP2
% 0.30/0.46 thf(fact_325_out__exprChannelSingle__Set,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( out_ex985543062Single @ P @ Ch @ E2 )
% 0.30/0.46 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSingle_Set
% 0.30/0.46 thf(fact_326_out__exprChannelSet__Single,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 )
% 0.30/0.46 => ( out_ex985543062Single @ P @ Ch @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSet_Single
% 0.30/0.46 thf(fact_327_TBtheorem5b__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 0.30/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.30/0.46 => ( ( M2
% 0.30/0.46 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_notPQ
% 0.30/0.46 thf(fact_328_eout__know__k,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.30/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.30/0.46 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.30/0.46 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.30/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_k
% 0.30/0.46 thf(fact_329_not__know__k__not__eout,axiom,
% 0.30/0.46 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.30/0.46 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.30/0.46 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.30/0.46 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.30/0.46 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_k_not_eout
% 0.30/0.46 thf(fact_330_not__eout__eoutM,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( eout @ P @ E2 )
% 0.30/0.46 => ~ ( eoutM @ P @ M2 @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_eout_eoutM
% 0.30/0.46 thf(fact_331_eoutM__eout,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( eoutM @ P @ M2 @ E2 )
% 0.30/0.46 => ( eout @ P @ E2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutM_eout
% 0.30/0.46 thf(fact_332_TBtheorem2b,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eoutM @ PQ @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( eoutM @ P @ M2 @ E2 )
% 0.30/0.46 | ( eoutM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem2b
% 0.30/0.46 thf(fact_333_TBtheorem5b__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.30/0.46 ( ~ ( eoutM @ Q @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_notP2
% 0.30/0.46 thf(fact_334_TBtheorem5b__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( eoutM @ P @ M2 @ E2 )
% 0.30/0.46 => ( ~ ( eoutM @ Q @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_notP1
% 0.30/0.46 thf(fact_335_eout__know__nonKS__k,axiom,
% 0.30/0.46 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.30/0.46 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.30/0.46 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 0.30/0.46 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.30/0.46 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_nonKS_k
% 0.30/0.46 thf(fact_336_eoutKnowCorrect__L1k,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.30/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.30/0.46 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.30/0.46 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.30/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutKnowCorrect_L1k
% 0.30/0.46 thf(fact_337_TBtheore54b__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eoutM @ P @ M2 @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 0.30/0.46 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheore54b_P
% 0.30/0.46 thf(fact_338_TBtheorem5b__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( eoutM @ P @ M2 @ E2 )
% 0.30/0.46 | ( eoutM @ Q @ M2 @ E2 ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.30/0.46 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.30/0.46 & ( member1967978193chanID @ Ch2 @ M2 )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_PQ
% 0.30/0.46 thf(fact_339_TBtheorem5a__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( eout @ P @ E2 )
% 0.30/0.46 | ( eout @ Q @ E2 ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.30/0.46 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_PQ
% 0.30/0.46 thf(fact_340_eout__def,axiom,
% 0.30/0.46 ( eout
% 0.30/0.46 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 0.30/0.46 ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_def
% 0.30/0.46 thf(fact_341_eoutM__def,axiom,
% 0.30/0.46 ( eoutM
% 0.30/0.46 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E3: secrecy_Expression] :
% 0.30/0.46 ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.30/0.46 & ( member1967978193chanID @ Ch3 @ M3 )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutM_def
% 0.30/0.46 thf(fact_342_out__exprChannelSet__def,axiom,
% 0.30/0.46 ( out_exprChannelSet
% 0.30/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E3: secrecy_Expression] :
% 0.30/0.46 ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 0.30/0.46 => ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 0.30/0.46 & ( exprChannel @ X2 @ E3 ) ) )
% 0.30/0.46 & ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 0.30/0.46 & ( member1967978193chanID @ X2 @ ( out @ SP ) ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSet_def
% 0.30/0.46 thf(fact_343_out__exprChannelSingle__def,axiom,
% 0.30/0.46 ( out_ex985543062Single
% 0.30/0.46 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E3 )
% 0.30/0.46 & ! [X2: secrecy_chanID,T: nat] :
% 0.30/0.46 ( ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 0.30/0.46 & ( X2 != Ch3 ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSingle_def
% 0.30/0.46 thf(fact_344_correctCompositionOut__prop1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 0.30/0.46 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 0.30/0.46 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionOut_prop1
% 0.30/0.46 thf(fact_345_TBtheorem45a__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eout @ P @ E2 )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem45a_P
% 0.30/0.46 thf(fact_346_outStream__def,axiom,
% 0.30/0.46 ( outStream
% 0.30/0.46 = ( ^ [X2: secrecy_specID] :
% 0.30/0.46 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 0.30/0.46 @ ( out @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % outStream_def
% 0.30/0.46 thf(fact_347_eout__know__nonKS__s,axiom,
% 0.30/0.46 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.30/0.46 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.30/0.46 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 0.30/0.46 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.30/0.46 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_nonKS_s
% 0.30/0.46 thf(fact_348_correctCompositionKS__subcomp4,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.30/0.46 ( ( correctCompositionKS @ C3 )
% 0.30/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.30/0.46 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 0.30/0.46 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp4
% 0.30/0.46 thf(fact_349_correctCompositionKS__subcomp2,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.30/0.46 ( ( correctCompositionKS @ C3 )
% 0.30/0.46 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.30/0.46 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 0.30/0.46 => ? [X3: secrecy_specID] :
% 0.30/0.46 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.30/0.46 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp2
% 0.30/0.46 thf(fact_350_eout__know__s,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.30/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.30/0.46 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.30/0.46 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.30/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_s
% 0.30/0.46 thf(fact_351_not__know__s__not__eout,axiom,
% 0.30/0.46 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.30/0.46 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.30/0.46 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.30/0.46 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.30/0.46 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_s_not_eout
% 0.30/0.46 thf(fact_352_eoutKnowCorrect__L1s,axiom,
% 0.30/0.46 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.30/0.46 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.30/0.46 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.30/0.46 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.30/0.46 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutKnowCorrect_L1s
% 0.30/0.46 thf(fact_353_adv__not__know2,axiom,
% 0.30/0.46 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 0.30/0.46 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 0.30/0.46 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.30/0.46 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % adv_not_know2
% 0.30/0.46 thf(fact_354_adv__not__know1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Keys] :
% 0.30/0.46 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 0.30/0.46 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.30/0.46 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % adv_not_know1
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ~ ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.46/1.49 ---- Embedded in THF ---
% 2.46/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.46/1.49 %%% Generated on Tue Feb 24 08:26:23 EST 2026
% 2.46/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.46/1.49 %%% Logic specification used:
% 2.46/1.49 %%% thf(spec, logic, $$dhol).
% 2.46/1.49
% 2.46/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2DTF19489.p
% See solution above
% 2.46/1.49 ------------------------
% 2.71/1.53 ---- Cleaned THF ---
% 2.71/1.53 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.71/1.53 list_S529945141ession: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.71/1.53 set_Secrecy_Secrets: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.71/1.53 set_Secrecy_specID: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.71/1.53 set_Secrecy_chanID: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.71/1.53 set_Secrecy_Keys: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.71/1.53 set_Secrecy_KS: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Secrecy____types__OExpression,type,
% 2.71/1.53 secrecy_Expression: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 2.71/1.53 secrecy_Secrets: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Secrecy____types__OspecID,type,
% 2.71/1.53 secrecy_specID: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Secrecy____types__OchanID,type,
% 2.71/1.53 secrecy_chanID: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Secrecy____types__OKeys,type,
% 2.71/1.53 secrecy_Keys: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Secrecy____types__OKS,type,
% 2.71/1.53 secrecy_KS: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(ty_n_t__Nat__Onat,type,
% 2.71/1.53 nat: $tType ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.71/1.53 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 2.71/1.53 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 2.71/1.53 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknows,type,
% 2.71/1.53 knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.71/1.53 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.71/1.53 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.71/1.53 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.71/1.53 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.71/1.53 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 2.71/1.53 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 2.71/1.53 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 2.71/1.53 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 2.71/1.53 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 2.71/1.53 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 2.71/1.53 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.71/1.53 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.71/1.53 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.71/1.53 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.71/1.53 bot_bo443197316chanID: set_Secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.71/1.53 bot_bo1785112429specID: set_Secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.71/1.53 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_ODecr,type,
% 2.71/1.53 decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OEnc,type,
% 2.71/1.53 enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 2.71/1.53 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OExt,type,
% 2.71/1.53 ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OSign,type,
% 2.71/1.53 sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 2.71/1.53 correctCompositionKS: secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_Oeout,type,
% 2.71/1.53 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OeoutM,type,
% 2.71/1.53 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OexprChannel,type,
% 2.71/1.53 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_Oine,type,
% 2.71/1.53 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OineM,type,
% 2.71/1.53 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 2.71/1.53 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 2.71/1.53 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 2.71/1.53 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 2.71/1.53 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 2.71/1.53 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OspecKeys,type,
% 2.71/1.53 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 2.71/1.53 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy_OspecSecrets,type,
% 2.71/1.53 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 2.71/1.53 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 2.71/1.53 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 2.71/1.53 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 2.71/1.53 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 2.71/1.53 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 2.71/1.53 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 2.71/1.53 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 2.71/1.53 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 2.71/1.53 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 2.71/1.53 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 2.71/1.53 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 2.71/1.53 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 2.71/1.53 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 2.71/1.53 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 2.71/1.53 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 2.71/1.53 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 2.71/1.53 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 2.71/1.53 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 2.71/1.53 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 2.71/1.53 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 2.71/1.53 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 2.71/1.53 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 2.71/1.53 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 2.71/1.53 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_OcorrectCompositionIn,type,
% 2.71/1.53 correctCompositionIn: secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 2.71/1.53 correc965049635ionLoc: secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_OcorrectCompositionOut,type,
% 2.71/1.53 correc990227761ionOut: secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_OinStream,type,
% 2.71/1.53 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_Oins,type,
% 2.71/1.53 ins: secrecy_specID > set_Secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_Oloc,type,
% 2.71/1.53 loc: secrecy_specID > set_Secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_OlocStream,type,
% 2.71/1.53 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_Oout,type,
% 2.71/1.53 out: secrecy_specID > set_Secrecy_chanID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_OoutStream,type,
% 2.71/1.53 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_inout_Osubcomponents,type,
% 2.71/1.53 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 2.71/1.53 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 2.71/1.53 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 2.71/1.53 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 2.71/1.53 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 2.71/1.53 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v_P,type,
% 2.71/1.53 p: secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v_PQ,type,
% 2.71/1.53 pq: secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v_Q,type,
% 2.71/1.53 q: secrecy_specID ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v_key____,type,
% 2.71/1.53 key: secrecy_Keys ).
% 2.71/1.53
% 2.71/1.53 thf(sy_v_m,type,
% 2.71/1.53 m: secrecy_KS ).
% 2.71/1.53
% 2.71/1.53 thf(fact_0_not__knowQm,axiom,
% 2.71/1.53 ~ ( knowle945212990e_know @ q @ m ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_1_a1,axiom,
% 2.71/1.53 ( m
% 2.71/1.53 = ( secrecy_kKS @ key ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_2_knowPQ,axiom,
% 2.71/1.53 knowle945212990e_know @ pq @ m ).
% 2.71/1.53
% 2.71/1.53 thf(fact_3_sg2,axiom,
% 2.71/1.53 member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ pq ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_4_KS_Oinject_I1_J,axiom,
% 2.71/1.53 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.71/1.53 ( ( ( secrecy_kKS @ X1 )
% 2.71/1.53 = ( secrecy_kKS @ Y1 ) )
% 2.71/1.53 = ( X1 = Y1 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_5_sg3a,axiom,
% 2.71/1.53 ~ ( ine @ q @ ( secrecy_kE @ key ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_6_cCompLoc,axiom,
% 2.71/1.53 correc965049635ionLoc @ pq ).
% 2.71/1.53
% 2.71/1.53 thf(fact_7_a12,axiom,
% 2.71/1.53 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_8_know_Osimps_I1_J,axiom,
% 2.71/1.53 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.71/1.53 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.71/1.53 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 2.71/1.53 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_9_subPQ,axiom,
% 2.71/1.53 ( ( subcomponents @ pq )
% 2.71/1.53 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_10_knows4,axiom,
% 2.71/1.53 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 2.71/1.53 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.71/1.53 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K2 ) )
% 2.71/1.53 & ( knowle731562421_knows @ A @ ( enc @ K1 @ E ) ) )
% 2.71/1.53 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_11_knows5,axiom,
% 2.71/1.53 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 2.71/1.53 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.71/1.53 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K1 ) )
% 2.71/1.53 & ( knowle731562421_knows @ A @ ( sign @ K2 @ E ) ) )
% 2.71/1.53 => ( knowle731562421_knows @ A @ E ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_12_knows6,axiom,
% 2.71/1.53 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 2.71/1.53 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 2.71/1.53 & ( knowle731562421_knows @ A @ E1 ) )
% 2.71/1.53 => ( knowle731562421_knows @ A @ ( enc @ K @ E1 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_13_Expression_Oinject_I1_J,axiom,
% 2.71/1.53 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.71/1.53 ( ( ( secrecy_kE @ X1 )
% 2.71/1.53 = ( secrecy_kE @ Y1 ) )
% 2.71/1.53 = ( X1 = Y1 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_14_cCompI,axiom,
% 2.71/1.53 correctCompositionIn @ pq ).
% 2.71/1.53
% 2.71/1.53 thf(fact_15_not__know__k__not__ine,axiom,
% 2.71/1.53 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.71/1.53 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.71/1.53 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_16_knows7,axiom,
% 2.71/1.53 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 2.71/1.53 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 2.71/1.53 & ( knowle731562421_knows @ A @ E1 ) )
% 2.71/1.53 => ( knowle731562421_knows @ A @ ( sign @ K @ E1 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_17_LocalSecretsComposition__ine1__k,axiom,
% 2.71/1.53 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.71/1.53 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_18_LocalSecretsComposition__ine2__k,axiom,
% 2.71/1.53 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.71/1.53 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_19_LocalSecretsComposition__neg1__k,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_20_singletonI,axiom,
% 2.71/1.53 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_21_singletonI,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_22_singletonI,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_23_singletonI,axiom,
% 2.71/1.53 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_24_singletonI,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_25_LocalSecretsComposition1,axiom,
% 2.71/1.53 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_26_know__composition__neg__ine__k,axiom,
% 2.71/1.53 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( knowle945212990e_know @ P @ ( secrecy_kKS @ Key ) )
% 2.71/1.53 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_kKS @ Key ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_27_insertCI,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 2.71/1.53 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 2.71/1.53 => ( A2 = B2 ) )
% 2.71/1.53 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_28_insertCI,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.71/1.53 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 2.71/1.53 => ( A2 = B2 ) )
% 2.71/1.53 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_29_insertCI,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.71/1.53 ( ( ~ ( member740727610specID @ A2 @ B )
% 2.71/1.53 => ( A2 = B2 ) )
% 2.71/1.53 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_30_insertCI,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 2.71/1.53 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 2.71/1.53 => ( A2 = B2 ) )
% 2.71/1.53 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_31_insertCI,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 2.71/1.53 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 2.71/1.53 => ( A2 = B2 ) )
% 2.71/1.53 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_32_insert__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 2.71/1.53 = ( ( A2 = B2 )
% 2.71/1.53 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_33_insert__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 2.71/1.53 = ( ( A2 = B2 )
% 2.71/1.53 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_34_insert__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 2.71/1.53 = ( ( A2 = B2 )
% 2.71/1.53 | ( member740727610specID @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_35_insert__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 2.71/1.53 = ( ( A2 = B2 )
% 2.71/1.53 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_36_insert__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 2.71/1.53 = ( ( A2 = B2 )
% 2.71/1.53 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_37_insert__absorb2,axiom,
% 2.71/1.53 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ X @ A ) )
% 2.71/1.53 = ( insert1671894227specID @ X @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_38_insert__absorb2,axiom,
% 2.71/1.53 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ X @ A ) )
% 2.71/1.53 = ( insert751661162chanID @ X @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_39_empty__iff,axiom,
% 2.71/1.53 ! [C: secrecy_KS] :
% 2.71/1.53 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_40_empty__iff,axiom,
% 2.71/1.53 ! [C: secrecy_Keys] :
% 2.71/1.53 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_41_empty__iff,axiom,
% 2.71/1.53 ! [C: secrecy_Secrets] :
% 2.71/1.53 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_42_empty__iff,axiom,
% 2.71/1.53 ! [C: secrecy_specID] :
% 2.71/1.53 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_43_empty__iff,axiom,
% 2.71/1.53 ! [C: secrecy_chanID] :
% 2.71/1.53 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_44_empty__Collect__eq,axiom,
% 2.71/1.53 ! [P: secrecy_specID > $o] :
% 2.71/1.53 ( ( bot_bo1785112429specID
% 2.71/1.53 = ( collec1545797240specID @ P ) )
% 2.71/1.53 = ( ! [X2: secrecy_specID] :
% 2.71/1.53 ~ ( P @ X2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_45_empty__Collect__eq,axiom,
% 2.71/1.53 ! [P: secrecy_chanID > $o] :
% 2.71/1.53 ( ( bot_bo443197316chanID
% 2.71/1.53 = ( collec625564175chanID @ P ) )
% 2.71/1.53 = ( ! [X2: secrecy_chanID] :
% 2.71/1.53 ~ ( P @ X2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_46_Collect__empty__eq,axiom,
% 2.71/1.53 ! [P: secrecy_specID > $o] :
% 2.71/1.53 ( ( ( collec1545797240specID @ P )
% 2.71/1.53 = bot_bo1785112429specID )
% 2.71/1.53 = ( ! [X2: secrecy_specID] :
% 2.71/1.53 ~ ( P @ X2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_47_Collect__empty__eq,axiom,
% 2.71/1.53 ! [P: secrecy_chanID > $o] :
% 2.71/1.53 ( ( ( collec625564175chanID @ P )
% 2.71/1.53 = bot_bo443197316chanID )
% 2.71/1.53 = ( ! [X2: secrecy_chanID] :
% 2.71/1.53 ~ ( P @ X2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_48_all__not__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS] :
% 2.71/1.53 ( ( ! [X2: secrecy_KS] :
% 2.71/1.53 ~ ( member_Secrecy_KS @ X2 @ A ) )
% 2.71/1.53 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_49_all__not__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( ! [X2: secrecy_Keys] :
% 2.71/1.53 ~ ( member_Secrecy_Keys @ X2 @ A ) )
% 2.71/1.53 = ( A = bot_bo701486667y_Keys ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_50_all__not__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( ! [X2: secrecy_Secrets] :
% 2.71/1.53 ~ ( member2138796287ecrets @ X2 @ A ) )
% 2.71/1.53 = ( A = bot_bo1124690338ecrets ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_51_all__not__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID] :
% 2.71/1.53 ( ( ! [X2: secrecy_specID] :
% 2.71/1.53 ~ ( member740727610specID @ X2 @ A ) )
% 2.71/1.53 = ( A = bot_bo1785112429specID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_52_all__not__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ! [X2: secrecy_chanID] :
% 2.71/1.53 ~ ( member1967978193chanID @ X2 @ A ) )
% 2.71/1.53 = ( A = bot_bo443197316chanID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_53_ex__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS] :
% 2.71/1.53 ( ( ? [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A ) )
% 2.71/1.53 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_54_ex__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( ? [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A ) )
% 2.71/1.53 = ( A != bot_bo701486667y_Keys ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_55_ex__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( ? [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A ) )
% 2.71/1.53 = ( A != bot_bo1124690338ecrets ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_56_ex__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID] :
% 2.71/1.53 ( ( ? [X2: secrecy_specID] : ( member740727610specID @ X2 @ A ) )
% 2.71/1.53 = ( A != bot_bo1785112429specID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_57_ex__in__conv,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ? [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A ) )
% 2.71/1.53 = ( A != bot_bo443197316chanID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_58_equals0I,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS] :
% 2.71/1.53 ( ! [Y: secrecy_KS] :
% 2.71/1.53 ~ ( member_Secrecy_KS @ Y @ A )
% 2.71/1.53 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_59_equals0I,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Keys] :
% 2.71/1.53 ( ! [Y: secrecy_Keys] :
% 2.71/1.53 ~ ( member_Secrecy_Keys @ Y @ A )
% 2.71/1.53 => ( A = bot_bo701486667y_Keys ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_60_equals0I,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ! [Y: secrecy_Secrets] :
% 2.71/1.53 ~ ( member2138796287ecrets @ Y @ A )
% 2.71/1.53 => ( A = bot_bo1124690338ecrets ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_61_equals0I,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID] :
% 2.71/1.53 ( ! [Y: secrecy_specID] :
% 2.71/1.53 ~ ( member740727610specID @ Y @ A )
% 2.71/1.53 => ( A = bot_bo1785112429specID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_62_equals0I,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ! [Y: secrecy_chanID] :
% 2.71/1.53 ~ ( member1967978193chanID @ Y @ A )
% 2.71/1.53 => ( A = bot_bo443197316chanID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_63_equals0D,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 2.71/1.53 ( ( A = bot_bo1943466239ecy_KS )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_64_equals0D,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 2.71/1.53 ( ( A = bot_bo701486667y_Keys )
% 2.71/1.53 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_65_equals0D,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 2.71/1.53 ( ( A = bot_bo1124690338ecrets )
% 2.71/1.53 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_66_equals0D,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 2.71/1.53 ( ( A = bot_bo1785112429specID )
% 2.71/1.53 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_67_equals0D,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 2.71/1.53 ( ( A = bot_bo443197316chanID )
% 2.71/1.53 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_68_emptyE,axiom,
% 2.71/1.53 ! [A2: secrecy_KS] :
% 2.71/1.53 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_69_emptyE,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys] :
% 2.71/1.53 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_70_emptyE,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets] :
% 2.71/1.53 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_71_emptyE,axiom,
% 2.71/1.53 ! [A2: secrecy_specID] :
% 2.71/1.53 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_72_emptyE,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID] :
% 2.71/1.53 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_73_mk__disjoint__insert,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ A2 @ A )
% 2.71/1.53 => ? [B3: set_Secrecy_KS] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 2.71/1.53 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_74_mk__disjoint__insert,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ A2 @ A )
% 2.71/1.53 => ? [B3: set_Secrecy_chanID] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert751661162chanID @ A2 @ B3 ) )
% 2.71/1.53 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_75_mk__disjoint__insert,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ A2 @ A )
% 2.71/1.53 => ? [B3: set_Secrecy_specID] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert1671894227specID @ A2 @ B3 ) )
% 2.71/1.53 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_76_mk__disjoint__insert,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ A2 @ A )
% 2.71/1.53 => ? [B3: set_Secrecy_Keys] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 2.71/1.53 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_77_mk__disjoint__insert,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ A2 @ A )
% 2.71/1.53 => ? [B3: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert565337510ecrets @ A2 @ B3 ) )
% 2.71/1.53 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_78_insert__commute,axiom,
% 2.71/1.53 ! [X: secrecy_specID,Y2: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( insert1671894227specID @ X @ ( insert1671894227specID @ Y2 @ A ) )
% 2.71/1.53 = ( insert1671894227specID @ Y2 @ ( insert1671894227specID @ X @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_79_insert__commute,axiom,
% 2.71/1.53 ! [X: secrecy_chanID,Y2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( insert751661162chanID @ X @ ( insert751661162chanID @ Y2 @ A ) )
% 2.71/1.53 = ( insert751661162chanID @ Y2 @ ( insert751661162chanID @ X @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_80_insert__eq__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 2.71/1.53 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 2.71/1.53 = ( insert_Secrecy_KS @ B2 @ B ) )
% 2.71/1.53 = ( ( ( A2 = B2 )
% 2.71/1.53 => ( A = B ) )
% 2.71/1.53 & ( ( A2 != B2 )
% 2.71/1.53 => ? [C2: set_Secrecy_KS] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 2.71/1.53 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 2.71/1.53 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_81_insert__eq__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( member1967978193chanID @ A2 @ A )
% 2.71/1.53 => ( ~ ( member1967978193chanID @ B2 @ B )
% 2.71/1.53 => ( ( ( insert751661162chanID @ A2 @ A )
% 2.71/1.53 = ( insert751661162chanID @ B2 @ B ) )
% 2.71/1.53 = ( ( ( A2 = B2 )
% 2.71/1.53 => ( A = B ) )
% 2.71/1.53 & ( ( A2 != B2 )
% 2.71/1.53 => ? [C2: set_Secrecy_chanID] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert751661162chanID @ B2 @ C2 ) )
% 2.71/1.53 & ~ ( member1967978193chanID @ B2 @ C2 )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert751661162chanID @ A2 @ C2 ) )
% 2.71/1.53 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_82_insert__eq__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ~ ( member740727610specID @ A2 @ A )
% 2.71/1.53 => ( ~ ( member740727610specID @ B2 @ B )
% 2.71/1.53 => ( ( ( insert1671894227specID @ A2 @ A )
% 2.71/1.53 = ( insert1671894227specID @ B2 @ B ) )
% 2.71/1.53 = ( ( ( A2 = B2 )
% 2.71/1.53 => ( A = B ) )
% 2.71/1.53 & ( ( A2 != B2 )
% 2.71/1.53 => ? [C2: set_Secrecy_specID] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert1671894227specID @ B2 @ C2 ) )
% 2.71/1.53 & ~ ( member740727610specID @ B2 @ C2 )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert1671894227specID @ A2 @ C2 ) )
% 2.71/1.53 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_83_insert__eq__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 2.71/1.53 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 2.71/1.53 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 2.71/1.53 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 2.71/1.53 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 2.71/1.53 = ( ( ( A2 = B2 )
% 2.71/1.53 => ( A = B ) )
% 2.71/1.53 & ( ( A2 != B2 )
% 2.71/1.53 => ? [C2: set_Secrecy_Keys] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 2.71/1.53 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 2.71/1.53 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_84_insert__eq__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.71/1.53 ( ~ ( member2138796287ecrets @ A2 @ A )
% 2.71/1.53 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 2.71/1.53 => ( ( ( insert565337510ecrets @ A2 @ A )
% 2.71/1.53 = ( insert565337510ecrets @ B2 @ B ) )
% 2.71/1.53 = ( ( ( A2 = B2 )
% 2.71/1.53 => ( A = B ) )
% 2.71/1.53 & ( ( A2 != B2 )
% 2.71/1.53 => ? [C2: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert565337510ecrets @ B2 @ C2 ) )
% 2.71/1.53 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert565337510ecrets @ A2 @ C2 ) )
% 2.71/1.53 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_85_insert__absorb,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ A2 @ A )
% 2.71/1.53 => ( ( insert_Secrecy_KS @ A2 @ A )
% 2.71/1.53 = A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_86_insert__absorb,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ A2 @ A )
% 2.71/1.53 => ( ( insert751661162chanID @ A2 @ A )
% 2.71/1.53 = A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_87_insert__absorb,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ A2 @ A )
% 2.71/1.53 => ( ( insert1671894227specID @ A2 @ A )
% 2.71/1.53 = A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_88_insert__absorb,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ A2 @ A )
% 2.71/1.53 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 2.71/1.53 = A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_89_insert__absorb,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ A2 @ A )
% 2.71/1.53 => ( ( insert565337510ecrets @ A2 @ A )
% 2.71/1.53 = A ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_90_insert__ident,axiom,
% 2.71/1.53 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ~ ( member_Secrecy_KS @ X @ A )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ X @ B )
% 2.71/1.53 => ( ( ( insert_Secrecy_KS @ X @ A )
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ B ) )
% 2.71/1.53 = ( A = B ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_91_insert__ident,axiom,
% 2.71/1.53 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( member1967978193chanID @ X @ A )
% 2.71/1.53 => ( ~ ( member1967978193chanID @ X @ B )
% 2.71/1.53 => ( ( ( insert751661162chanID @ X @ A )
% 2.71/1.53 = ( insert751661162chanID @ X @ B ) )
% 2.71/1.53 = ( A = B ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_92_insert__ident,axiom,
% 2.71/1.53 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ~ ( member740727610specID @ X @ A )
% 2.71/1.53 => ( ~ ( member740727610specID @ X @ B )
% 2.71/1.53 => ( ( ( insert1671894227specID @ X @ A )
% 2.71/1.53 = ( insert1671894227specID @ X @ B ) )
% 2.71/1.53 = ( A = B ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_93_insert__ident,axiom,
% 2.71/1.53 ! [X: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.71/1.53 ( ~ ( member_Secrecy_Keys @ X @ A )
% 2.71/1.53 => ( ~ ( member_Secrecy_Keys @ X @ B )
% 2.71/1.53 => ( ( ( insert_Secrecy_Keys @ X @ A )
% 2.71/1.53 = ( insert_Secrecy_Keys @ X @ B ) )
% 2.71/1.53 = ( A = B ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_94_insert__ident,axiom,
% 2.71/1.53 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.71/1.53 ( ~ ( member2138796287ecrets @ X @ A )
% 2.71/1.53 => ( ~ ( member2138796287ecrets @ X @ B )
% 2.71/1.53 => ( ( ( insert565337510ecrets @ X @ A )
% 2.71/1.53 = ( insert565337510ecrets @ X @ B ) )
% 2.71/1.53 = ( A = B ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_95_Set_Oset__insert,axiom,
% 2.71/1.53 ! [X: secrecy_KS,A: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X @ A )
% 2.71/1.53 => ~ ! [B3: set_Secrecy_KS] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ B3 ) )
% 2.71/1.53 => ( member_Secrecy_KS @ X @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_96_Set_Oset__insert,axiom,
% 2.71/1.53 ! [X: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X @ A )
% 2.71/1.53 => ~ ! [B3: set_Secrecy_chanID] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert751661162chanID @ X @ B3 ) )
% 2.71/1.53 => ( member1967978193chanID @ X @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_97_Set_Oset__insert,axiom,
% 2.71/1.53 ! [X: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ X @ A )
% 2.71/1.53 => ~ ! [B3: set_Secrecy_specID] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert1671894227specID @ X @ B3 ) )
% 2.71/1.53 => ( member740727610specID @ X @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_98_Set_Oset__insert,axiom,
% 2.71/1.53 ! [X: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ X @ A )
% 2.71/1.53 => ~ ! [B3: set_Secrecy_Keys] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert_Secrecy_Keys @ X @ B3 ) )
% 2.71/1.53 => ( member_Secrecy_Keys @ X @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_99_Set_Oset__insert,axiom,
% 2.71/1.53 ! [X: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ X @ A )
% 2.71/1.53 => ~ ! [B3: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( A
% 2.71/1.53 = ( insert565337510ecrets @ X @ B3 ) )
% 2.71/1.53 => ( member2138796287ecrets @ X @ B3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_100_insertI2,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ A2 @ B )
% 2.71/1.53 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_101_insertI2,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ A2 @ B )
% 2.71/1.53 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_102_insertI2,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ A2 @ B )
% 2.71/1.53 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_103_insertI2,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ A2 @ B )
% 2.71/1.53 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_104_insertI2,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ A2 @ B )
% 2.71/1.53 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_105_insertI1,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_106_insertI1,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_107_insertI1,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_108_insertI1,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_109_insertI1,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_110_insertE,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 2.71/1.53 => ( ( A2 != B2 )
% 2.71/1.53 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_111_insertE,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 2.71/1.53 => ( ( A2 != B2 )
% 2.71/1.53 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_112_insertE,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 2.71/1.53 => ( ( A2 != B2 )
% 2.71/1.53 => ( member740727610specID @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_113_insertE,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 2.71/1.53 => ( ( A2 != B2 )
% 2.71/1.53 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_114_insertE,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 2.71/1.53 => ( ( A2 != B2 )
% 2.71/1.53 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_115_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 2.71/1.53 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 2.71/1.53 = ( P @ A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_116_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 2.71/1.53 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 2.71/1.53 = ( P @ A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_117_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 2.71/1.53 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 2.71/1.53 = ( P @ A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_118_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 2.71/1.53 = ( P @ A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_119_mem__Collect__eq,axiom,
% 2.71/1.53 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 2.71/1.53 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 2.71/1.53 = ( P @ A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_120_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS] :
% 2.71/1.53 ( ( collect_Secrecy_KS
% 2.71/1.53 @ ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ A ) )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_121_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( collec625564175chanID
% 2.71/1.53 @ ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A ) )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_122_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID] :
% 2.71/1.53 ( ( collec1545797240specID
% 2.71/1.53 @ ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ A ) )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_123_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( collect_Secrecy_Keys
% 2.71/1.53 @ ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ A ) )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_124_Collect__mem__eq,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( collec836099393ecrets
% 2.71/1.53 @ ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ A ) )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_125_know__composition__neg1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M: secrecy_KS,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( knowle945212990e_know @ P @ M )
% 2.71/1.53 => ( ~ ( knowle945212990e_know @ Q @ M )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ~ ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_126_singleton__inject,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 2.71/1.53 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 2.71/1.53 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.71/1.53 => ( A2 = B2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_127_singleton__inject,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 2.71/1.53 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 2.71/1.53 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.71/1.53 => ( A2 = B2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_128_insert__not__empty,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( insert1671894227specID @ A2 @ A )
% 2.71/1.53 != bot_bo1785112429specID ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_129_insert__not__empty,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( insert751661162chanID @ A2 @ A )
% 2.71/1.53 != bot_bo443197316chanID ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_130_doubleton__eq__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 2.71/1.53 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.71/1.53 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 2.71/1.53 = ( ( ( A2 = C )
% 2.71/1.53 & ( B2 = D ) )
% 2.71/1.53 | ( ( A2 = D )
% 2.71/1.53 & ( B2 = C ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_131_doubleton__eq__iff,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 2.71/1.53 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.71/1.53 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 2.71/1.53 = ( ( ( A2 = C )
% 2.71/1.53 & ( B2 = D ) )
% 2.71/1.53 | ( ( A2 = D )
% 2.71/1.53 & ( B2 = C ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_132_singleton__iff,axiom,
% 2.71/1.53 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 2.71/1.53 = ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_133_singleton__iff,axiom,
% 2.71/1.53 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 2.71/1.53 = ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_134_singleton__iff,axiom,
% 2.71/1.53 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 2.71/1.53 = ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_135_singleton__iff,axiom,
% 2.71/1.53 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 2.71/1.53 = ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_136_singleton__iff,axiom,
% 2.71/1.53 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 2.71/1.53 = ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_137_singletonD,axiom,
% 2.71/1.53 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 2.71/1.53 => ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_138_singletonD,axiom,
% 2.71/1.53 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 2.71/1.53 => ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_139_singletonD,axiom,
% 2.71/1.53 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 2.71/1.53 => ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_140_singletonD,axiom,
% 2.71/1.53 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 2.71/1.53 => ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_141_singletonD,axiom,
% 2.71/1.53 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 2.71/1.53 => ( B2 = A2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_142_TBtheorem3a,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( ine @ P @ E2 )
% 2.71/1.53 => ( ~ ( ine @ Q @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_143_TBtheorem1a,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( ine @ PQ @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( ine @ P @ E2 )
% 2.71/1.53 | ( ine @ Q @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_144_the__elem__eq,axiom,
% 2.71/1.53 ! [X: secrecy_specID] :
% 2.71/1.53 ( ( the_el827131246specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.71/1.53 = X ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_145_the__elem__eq,axiom,
% 2.71/1.53 ! [X: secrecy_chanID] :
% 2.71/1.53 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.71/1.53 = X ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_146_is__singletonI,axiom,
% 2.71/1.53 ! [X: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_147_is__singletonI,axiom,
% 2.71/1.53 ! [X: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_148_KS2Expression_Osimps_I1_J,axiom,
% 2.71/1.53 ! [M: secrecy_Keys] :
% 2.71/1.53 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 2.71/1.53 = ( secrecy_kE @ M ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_149_Set_Ois__empty__def,axiom,
% 2.71/1.53 ( is_emp1849217361specID
% 2.71/1.53 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_150_Set_Ois__empty__def,axiom,
% 2.71/1.53 ( is_emp928984296chanID
% 2.71/1.53 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_151_is__singleton__def,axiom,
% 2.71/1.53 ( is_sin1501507247specID
% 2.71/1.53 = ( ^ [A3: set_Secrecy_specID] :
% 2.71/1.53 ? [X2: secrecy_specID] :
% 2.71/1.53 ( A3
% 2.71/1.53 = ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_152_is__singleton__def,axiom,
% 2.71/1.53 ( is_sin581274182chanID
% 2.71/1.53 = ( ^ [A3: set_Secrecy_chanID] :
% 2.71/1.53 ? [X2: secrecy_chanID] :
% 2.71/1.53 ( A3
% 2.71/1.53 = ( insert751661162chanID @ X2 @ bot_bo443197316chanID ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_153_is__singletonE,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID] :
% 2.71/1.53 ( ( is_sin1501507247specID @ A )
% 2.71/1.53 => ~ ! [X3: secrecy_specID] :
% 2.71/1.53 ( A
% 2.71/1.53 != ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_154_is__singletonE,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( is_sin581274182chanID @ A )
% 2.71/1.53 => ~ ! [X3: secrecy_chanID] :
% 2.71/1.53 ( A
% 2.71/1.53 != ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_155_bot__set__def,axiom,
% 2.71/1.53 ( bot_bo1785112429specID
% 2.71/1.53 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_156_bot__set__def,axiom,
% 2.71/1.53 ( bot_bo443197316chanID
% 2.71/1.53 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_157_is__singleton__the__elem,axiom,
% 2.71/1.53 ( is_sin1501507247specID
% 2.71/1.53 = ( ^ [A3: set_Secrecy_specID] :
% 2.71/1.53 ( A3
% 2.71/1.53 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_158_is__singleton__the__elem,axiom,
% 2.71/1.53 ( is_sin581274182chanID
% 2.71/1.53 = ( ^ [A3: set_Secrecy_chanID] :
% 2.71/1.53 ( A3
% 2.71/1.53 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_159_is__singletonI_H,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS] :
% 2.71/1.53 ( ( A != bot_bo1943466239ecy_KS )
% 2.71/1.53 => ( ! [X3: secrecy_KS,Y: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X3 @ A )
% 2.71/1.53 => ( ( member_Secrecy_KS @ Y @ A )
% 2.71/1.53 => ( X3 = Y ) ) )
% 2.71/1.53 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_160_is__singletonI_H,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( A != bot_bo701486667y_Keys )
% 2.71/1.53 => ( ! [X3: secrecy_Keys,Y: secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ X3 @ A )
% 2.71/1.53 => ( ( member_Secrecy_Keys @ Y @ A )
% 2.71/1.53 => ( X3 = Y ) ) )
% 2.71/1.53 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_161_is__singletonI_H,axiom,
% 2.71/1.53 ! [A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( A != bot_bo1124690338ecrets )
% 2.71/1.53 => ( ! [X3: secrecy_Secrets,Y: secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ X3 @ A )
% 2.71/1.53 => ( ( member2138796287ecrets @ Y @ A )
% 2.71/1.53 => ( X3 = Y ) ) )
% 2.71/1.53 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_162_is__singletonI_H,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID] :
% 2.71/1.53 ( ( A != bot_bo1785112429specID )
% 2.71/1.53 => ( ! [X3: secrecy_specID,Y: secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ X3 @ A )
% 2.71/1.53 => ( ( member740727610specID @ Y @ A )
% 2.71/1.53 => ( X3 = Y ) ) )
% 2.71/1.53 => ( is_sin1501507247specID @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_163_is__singletonI_H,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( A != bot_bo443197316chanID )
% 2.71/1.53 => ( ! [X3: secrecy_chanID,Y: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ A )
% 2.71/1.53 => ( ( member1967978193chanID @ Y @ A )
% 2.71/1.53 => ( X3 = Y ) ) )
% 2.71/1.53 => ( is_sin581274182chanID @ A ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_164_TBtheorem4a__empty,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ( ine @ P @ E2 )
% 2.71/1.53 | ( ine @ Q @ E2 ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( ( loc @ PQ )
% 2.71/1.53 = bot_bo443197316chanID )
% 2.71/1.53 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_165_TBtheorem1b,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( ineM @ PQ @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( ineM @ P @ M2 @ E2 )
% 2.71/1.53 | ( ineM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_166_TBtheorem3b,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( ineM @ P @ M2 @ E2 )
% 2.71/1.53 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_167_DecrEnc,axiom,
% 2.71/1.53 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list_S529945141ession] :
% 2.71/1.53 ( ( encrDecrKeys @ K12 @ K22 )
% 2.71/1.53 => ( ( decr @ K22 @ ( enc @ K12 @ E2 ) )
% 2.71/1.53 = E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_168_ExtSign,axiom,
% 2.71/1.53 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list_S529945141ession] :
% 2.71/1.53 ( ( encrDecrKeys @ K12 @ K22 )
% 2.71/1.53 => ( ( ext @ K12 @ ( sign @ K22 @ E2 ) )
% 2.71/1.53 = E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_169_correctCompositionIn__L2,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_170_correctCompositionIn__prop1,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ X @ ( ins @ P ) )
% 2.71/1.53 | ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_171_not__ine__ineM,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( ine @ P @ E2 )
% 2.71/1.53 => ~ ( ineM @ P @ M2 @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_172_ineM__ine,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( ineM @ P @ M2 @ E2 )
% 2.71/1.53 => ( ine @ P @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_173_correctCompositionIn__L1,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_174_subcomponents__loc,axiom,
% 2.71/1.53 ! [X: secrecy_specID] :
% 2.71/1.53 ( ( correc965049635ionLoc @ X )
% 2.71/1.53 => ( ( ( subcomponents @ X )
% 2.71/1.53 = bot_bo1785112429specID )
% 2.71/1.53 => ( ( loc @ X )
% 2.71/1.53 = bot_bo443197316chanID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_175_TBtheorem4b__notP1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ineM @ P @ M2 @ E2 )
% 2.71/1.53 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_176_TBtheorem4a__notP1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ine @ P @ E2 )
% 2.71/1.53 => ( ~ ( ine @ Q @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_177_TBtheorem4b__notPQ,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 2.71/1.53 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetP )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_178_TBtheorem4b__notP2,axiom,
% 2.71/1.53 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( ineM @ Q @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSet )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_179_TBtheorem4a__notPQ,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 2.71/1.53 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetP )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_180_ine__exprChannelSingle__Set,axiom,
% 2.71/1.53 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( ine_ex1303305700Single @ P @ Ch @ E2 )
% 2.71/1.53 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_181_ine__exprChannelSet__Single,axiom,
% 2.71/1.53 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 )
% 2.71/1.53 => ( ine_ex1303305700Single @ P @ Ch @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_182_ine__nonempty__exprChannelSet,axiom,
% 2.71/1.53 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 2.71/1.53 => ( ( ChSet != bot_bo443197316chanID )
% 2.71/1.53 => ( ine @ P @ E2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_183_ine__empty__exprChannelSet,axiom,
% 2.71/1.53 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 2.71/1.53 => ( ( ChSet = bot_bo443197316chanID )
% 2.71/1.53 => ~ ( ine @ P @ E2 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_184_TBtheorem4a__notP2,axiom,
% 2.71/1.53 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( ine @ Q @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSet )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_185_locStream__def,axiom,
% 2.71/1.53 ( locStream
% 2.71/1.53 = ( ^ [X2: secrecy_specID] :
% 2.71/1.53 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 2.71/1.53 @ ( loc @ X2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_186_inStream__def,axiom,
% 2.71/1.53 ( inStream
% 2.71/1.53 = ( ^ [X2: secrecy_specID] :
% 2.71/1.53 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 2.71/1.53 @ ( ins @ X2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_187_TBtheorem4b__P,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( ineM @ P @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 2.71/1.53 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_188_TBtheorem4b__PQ,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ( ineM @ P @ M2 @ E2 )
% 2.71/1.53 | ( ineM @ Q @ M2 @ E2 ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.71/1.53 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_189_TBtheorem4a__P,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( ine @ P @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_190_TBtheorem4a__PQ,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ( ine @ P @ E2 )
% 2.71/1.53 | ( ine @ Q @ E2 ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.71/1.53 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_191_ine__ins__neg1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 2.71/1.53 ( ~ ( ine @ P @ M )
% 2.71/1.53 => ( ( exprChannel @ X @ M )
% 2.71/1.53 => ~ ( member1967978193chanID @ X @ ( ins @ P ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_192_ine__def,axiom,
% 2.71/1.53 ( ine
% 2.71/1.53 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 2.71/1.53 ? [Ch3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.71/1.53 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_193_ineM__L1,axiom,
% 2.71/1.53 ! [Ch: secrecy_chanID,M2: set_Secrecy_chanID,P: secrecy_specID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch @ M2 )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ E2 )
% 2.71/1.53 => ( ineM @ P @ M2 @ E2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_194_ineM__def,axiom,
% 2.71/1.53 ( ineM
% 2.71/1.53 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E3: secrecy_Expression] :
% 2.71/1.53 ? [Ch3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.71/1.53 & ( member1967978193chanID @ Ch3 @ M3 )
% 2.71/1.53 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_195_ine__exprChannelSet__def,axiom,
% 2.71/1.53 ( ine_exprChannelSet
% 2.71/1.53 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E3: secrecy_Expression] :
% 2.71/1.53 ( ! [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 2.71/1.53 => ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 2.71/1.53 & ( exprChannel @ X2 @ E3 ) ) )
% 2.71/1.53 & ! [X2: secrecy_chanID] :
% 2.71/1.53 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 2.71/1.53 & ( member1967978193chanID @ X2 @ ( ins @ SP ) ) )
% 2.71/1.53 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_196_ine__exprChannelSingle__def,axiom,
% 2.71/1.53 ( ine_ex1303305700Single
% 2.71/1.53 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.71/1.53 & ( exprChannel @ Ch3 @ E3 )
% 2.71/1.53 & ! [X2: secrecy_chanID,T: nat] :
% 2.71/1.53 ( ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 2.71/1.53 & ( X2 != Ch3 ) )
% 2.71/1.53 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_197_LocalSecretsComposition__exprChannel__k,axiom,
% 2.71/1.53 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.71/1.53 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 2.71/1.53 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_198_correctCompositionInLoc__exprChannel,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ M )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 2.71/1.53 => ~ ( exprChannel @ X3 @ M ) )
% 2.71/1.53 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_199_TBlemma3b,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 2.71/1.53 ( ~ ( ineM @ P @ M2 @ E2 )
% 2.71/1.53 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ M2 )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.71/1.53 => ~ ( exprChannel @ Ch @ E2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_200_bot__empty__eq,axiom,
% 2.71/1.53 ( bot_bot_Secrecy_KS_o
% 2.71/1.53 = ( ^ [X2: secrecy_KS] : ( member_Secrecy_KS @ X2 @ bot_bo1943466239ecy_KS ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_201_bot__empty__eq,axiom,
% 2.71/1.53 ( bot_bo2072920570Keys_o
% 2.71/1.53 = ( ^ [X2: secrecy_Keys] : ( member_Secrecy_Keys @ X2 @ bot_bo701486667y_Keys ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_202_bot__empty__eq,axiom,
% 2.71/1.53 ( bot_bo1909946299rets_o
% 2.71/1.53 = ( ^ [X2: secrecy_Secrets] : ( member2138796287ecrets @ X2 @ bot_bo1124690338ecrets ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_203_bot__empty__eq,axiom,
% 2.71/1.53 ( bot_bo1767780696ecID_o
% 2.71/1.53 = ( ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ bot_bo1785112429specID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_204_bot__empty__eq,axiom,
% 2.71/1.53 ( bot_bo1012329985anID_o
% 2.71/1.53 = ( ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ bot_bo443197316chanID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_205_Collect__empty__eq__bot,axiom,
% 2.71/1.53 ! [P: secrecy_specID > $o] :
% 2.71/1.53 ( ( ( collec1545797240specID @ P )
% 2.71/1.53 = bot_bo1785112429specID )
% 2.71/1.53 = ( P = bot_bo1767780696ecID_o ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_206_Collect__empty__eq__bot,axiom,
% 2.71/1.53 ! [P: secrecy_chanID > $o] :
% 2.71/1.53 ( ( ( collec625564175chanID @ P )
% 2.71/1.53 = bot_bo443197316chanID )
% 2.71/1.53 = ( P = bot_bo1012329985anID_o ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_207_LocalSecretsComposition__neg__loc__k,axiom,
% 2.71/1.53 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.71/1.53 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_208_correctCompositionKS__exprChannel__k__Qex,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ? [Ch4: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_209_correctCompositionKS__exprChannel__k__Pex,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ? [Ch4: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_210_correctCompositionKS__PQ,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.71/1.53 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_211_correctCompositionKS__neg1,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_212_correctCompositionKS__negP,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_213_correctCompositionKS__negQ,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_214_know__composition,axiom,
% 2.71/1.53 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.71/1.53 => ( ( ( knowle945212990e_know @ P @ M )
% 2.71/1.53 | ( knowle945212990e_know @ Q @ M ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_215_know__composition1,axiom,
% 2.71/1.53 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.71/1.53 => ( ( knowle945212990e_know @ P @ M )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_216_know__composition2,axiom,
% 2.71/1.53 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.71/1.53 => ( ( knowle945212990e_know @ Q @ M )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_217_correctCompositionKS__exprChannel__k__P,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_218_correctCompositionKS__exprChannel__k__Q,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_219_LocalSecretsComposition__neg__k,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_220_correctCompositionKS__exprChannel__s__Qex,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ? [Ch4: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_221_correctCompositionKS__exprChannel__s__Pex,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ? [Ch4: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_222_correctCompositionKS__exprChannel__s__Q,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_223_correctCompositionKS__exprChannel__s__P,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.71/1.53 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_224_UnCI,axiom,
% 2.71/1.53 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( ~ ( member740727610specID @ C @ B )
% 2.71/1.53 => ( member740727610specID @ C @ A ) )
% 2.71/1.53 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_225_UnCI,axiom,
% 2.71/1.53 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 2.71/1.53 => ( member_Secrecy_Keys @ C @ A ) )
% 2.71/1.53 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_226_UnCI,axiom,
% 2.71/1.53 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( ~ ( member2138796287ecrets @ C @ B )
% 2.71/1.53 => ( member2138796287ecrets @ C @ A ) )
% 2.71/1.53 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_227_UnCI,axiom,
% 2.71/1.53 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 2.71/1.53 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 2.71/1.53 => ( member_Secrecy_KS @ C @ A ) )
% 2.71/1.53 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_228_UnCI,axiom,
% 2.71/1.53 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ~ ( member1967978193chanID @ C @ B )
% 2.71/1.53 => ( member1967978193chanID @ C @ A ) )
% 2.71/1.53 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_229_Un__iff,axiom,
% 2.71/1.53 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 2.71/1.53 = ( ( member740727610specID @ C @ A )
% 2.71/1.53 | ( member740727610specID @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_230_Un__iff,axiom,
% 2.71/1.53 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 2.71/1.53 = ( ( member_Secrecy_Keys @ C @ A )
% 2.71/1.53 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_231_Un__iff,axiom,
% 2.71/1.53 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 2.71/1.53 = ( ( member2138796287ecrets @ C @ A )
% 2.71/1.53 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_232_Un__iff,axiom,
% 2.71/1.53 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.71/1.53 = ( ( member_Secrecy_KS @ C @ A )
% 2.71/1.53 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_233_Un__iff,axiom,
% 2.71/1.53 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 2.71/1.53 = ( ( member1967978193chanID @ C @ A )
% 2.71/1.53 | ( member1967978193chanID @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_234_KS_Oinject_I2_J,axiom,
% 2.71/1.53 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 2.71/1.53 ( ( ( secrecy_sKS @ X22 )
% 2.71/1.53 = ( secrecy_sKS @ Y22 ) )
% 2.71/1.53 = ( X22 = Y22 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_235_Expression_Oinject_I2_J,axiom,
% 2.71/1.53 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 2.71/1.53 ( ( ( secrecy_sE @ X22 )
% 2.71/1.53 = ( secrecy_sE @ Y22 ) )
% 2.71/1.53 = ( X22 = Y22 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_236_Un__empty,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 2.71/1.53 = bot_bo1943466239ecy_KS )
% 2.71/1.53 = ( ( A = bot_bo1943466239ecy_KS )
% 2.71/1.53 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_237_Un__empty,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ( ( sup_su1712599557specID @ A @ B )
% 2.71/1.53 = bot_bo1785112429specID )
% 2.71/1.53 = ( ( A = bot_bo1785112429specID )
% 2.71/1.53 & ( B = bot_bo1785112429specID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_238_Un__empty,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ( sup_su370684444chanID @ A @ B )
% 2.71/1.53 = bot_bo443197316chanID )
% 2.71/1.53 = ( ( A = bot_bo443197316chanID )
% 2.71/1.53 & ( B = bot_bo443197316chanID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_239_Un__insert__right,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 2.71/1.53 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_240_Un__insert__right,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 2.71/1.53 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_241_Un__insert__right,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 2.71/1.53 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_242_Un__insert__left,axiom,
% 2.71/1.53 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 2.71/1.53 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 2.71/1.53 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_243_Un__insert__left,axiom,
% 2.71/1.53 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 2.71/1.53 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_244_Un__insert__left,axiom,
% 2.71/1.53 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 2.71/1.53 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_245_Un__empty__left,axiom,
% 2.71/1.53 ! [B: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 2.71/1.53 = B ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_246_Un__empty__left,axiom,
% 2.71/1.53 ! [B: set_Secrecy_specID] :
% 2.71/1.53 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 2.71/1.53 = B ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_247_Un__empty__left,axiom,
% 2.71/1.53 ! [B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 2.71/1.53 = B ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_248_Un__empty__right,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_249_Un__empty__right,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID] :
% 2.71/1.53 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_250_Un__empty__right,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_251_not__know__s__not__ine,axiom,
% 2.71/1.53 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.71/1.53 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.71/1.53 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_252_UnE,axiom,
% 2.71/1.53 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 2.71/1.53 => ( ~ ( member740727610specID @ C @ A )
% 2.71/1.53 => ( member740727610specID @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_253_UnE,axiom,
% 2.71/1.53 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 2.71/1.53 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_254_UnE,axiom,
% 2.71/1.53 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 2.71/1.53 => ( ~ ( member2138796287ecrets @ C @ A )
% 2.71/1.53 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_255_UnE,axiom,
% 2.71/1.53 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ C @ A )
% 2.71/1.53 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_256_UnE,axiom,
% 2.71/1.53 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 2.71/1.53 => ( ~ ( member1967978193chanID @ C @ A )
% 2.71/1.53 => ( member1967978193chanID @ C @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_257_UnI1,axiom,
% 2.71/1.53 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ C @ A )
% 2.71/1.53 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_258_UnI1,axiom,
% 2.71/1.53 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ C @ A )
% 2.71/1.53 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_259_UnI1,axiom,
% 2.71/1.53 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ C @ A )
% 2.71/1.53 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_260_UnI1,axiom,
% 2.71/1.53 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ C @ A )
% 2.71/1.53 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_261_UnI1,axiom,
% 2.71/1.53 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ C @ A )
% 2.71/1.53 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_262_UnI2,axiom,
% 2.71/1.53 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ C @ B )
% 2.71/1.53 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_263_UnI2,axiom,
% 2.71/1.53 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 2.71/1.53 ( ( member_Secrecy_Keys @ C @ B )
% 2.71/1.53 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_264_UnI2,axiom,
% 2.71/1.53 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.71/1.53 ( ( member2138796287ecrets @ C @ B )
% 2.71/1.53 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_265_UnI2,axiom,
% 2.71/1.53 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ C @ B )
% 2.71/1.53 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_266_UnI2,axiom,
% 2.71/1.53 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ C @ B )
% 2.71/1.53 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_267_bex__Un,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 2.71/1.53 ( ( ? [X2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.71/1.53 & ( P @ X2 ) ) )
% 2.71/1.53 = ( ? [X2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X2 @ A )
% 2.71/1.53 & ( P @ X2 ) )
% 2.71/1.53 | ? [X2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X2 @ B )
% 2.71/1.53 & ( P @ X2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_268_bex__Un,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.71/1.53 ( ( ? [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A @ B ) )
% 2.71/1.53 & ( P @ X2 ) ) )
% 2.71/1.53 = ( ? [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ A )
% 2.71/1.53 & ( P @ X2 ) )
% 2.71/1.53 | ? [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ B )
% 2.71/1.53 & ( P @ X2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_269_ball__Un,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 2.71/1.53 ( ( ! [X2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X2 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.71/1.53 => ( P @ X2 ) ) )
% 2.71/1.53 = ( ! [X2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X2 @ A )
% 2.71/1.53 => ( P @ X2 ) )
% 2.71/1.53 & ! [X2: secrecy_KS] :
% 2.71/1.53 ( ( member_Secrecy_KS @ X2 @ B )
% 2.71/1.53 => ( P @ X2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_270_ball__Un,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.71/1.53 ( ( ! [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A @ B ) )
% 2.71/1.53 => ( P @ X2 ) ) )
% 2.71/1.53 = ( ! [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ A )
% 2.71/1.53 => ( P @ X2 ) )
% 2.71/1.53 & ! [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ B )
% 2.71/1.53 => ( P @ X2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_271_Un__assoc,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 2.71/1.53 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_272_Un__assoc,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 2.71/1.53 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_273_Un__absorb,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ A @ A )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_274_Un__absorb,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ A @ A )
% 2.71/1.53 = A ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_275_Un__commute,axiom,
% 2.71/1.53 ( sup_su1301156759ecy_KS
% 2.71/1.53 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_276_Un__commute,axiom,
% 2.71/1.53 ( sup_su370684444chanID
% 2.71/1.53 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_277_Un__left__absorb,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.71/1.53 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_278_Un__left__absorb,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 2.71/1.53 = ( sup_su370684444chanID @ A @ B ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_279_Un__left__commute,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 2.71/1.53 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_280_Un__left__commute,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 2.71/1.53 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_281_KS2Expression_Osimps_I2_J,axiom,
% 2.71/1.53 ! [M: secrecy_Secrets] :
% 2.71/1.53 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 2.71/1.53 = ( secrecy_sE @ M ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_282_KS_Odistinct_I1_J,axiom,
% 2.71/1.53 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 2.71/1.53 ( ( secrecy_kKS @ X1 )
% 2.71/1.53 != ( secrecy_sKS @ X22 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_283_KS_Oinduct,axiom,
% 2.71/1.53 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 2.71/1.53 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 2.71/1.53 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 2.71/1.53 => ( P @ KS ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_284_KS_Oexhaust,axiom,
% 2.71/1.53 ! [Y2: secrecy_KS] :
% 2.71/1.53 ( ! [X12: secrecy_Keys] :
% 2.71/1.53 ( Y2
% 2.71/1.53 != ( secrecy_kKS @ X12 ) )
% 2.71/1.53 => ~ ! [X23: secrecy_Secrets] :
% 2.71/1.53 ( Y2
% 2.71/1.53 != ( secrecy_sKS @ X23 ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_285_Expression_Odistinct_I1_J,axiom,
% 2.71/1.53 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 2.71/1.53 ( ( secrecy_kE @ X1 )
% 2.71/1.53 != ( secrecy_sE @ X22 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_286_know_Osimps_I2_J,axiom,
% 2.71/1.53 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.71/1.53 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.71/1.53 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 2.71/1.53 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_287_singleton__Un__iff,axiom,
% 2.71/1.53 ! [X: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.71/1.53 ( ( ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS )
% 2.71/1.53 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.71/1.53 = ( ( ( A = bot_bo1943466239ecy_KS )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.71/1.53 & ( B = bot_bo1943466239ecy_KS ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_288_singleton__Un__iff,axiom,
% 2.71/1.53 ! [X: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.71/1.53 ( ( ( insert1671894227specID @ X @ bot_bo1785112429specID )
% 2.71/1.53 = ( sup_su1712599557specID @ A @ B ) )
% 2.71/1.53 = ( ( ( A = bot_bo1785112429specID )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.71/1.53 & ( B = bot_bo1785112429specID ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_289_singleton__Un__iff,axiom,
% 2.71/1.53 ! [X: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ( insert751661162chanID @ X @ bot_bo443197316chanID )
% 2.71/1.53 = ( sup_su370684444chanID @ A @ B ) )
% 2.71/1.53 = ( ( ( A = bot_bo443197316chanID )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.71/1.53 & ( B = bot_bo443197316chanID ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_290_Un__singleton__iff,axiom,
% 2.71/1.53 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X: secrecy_KS] :
% 2.71/1.53 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.71/1.53 = ( ( ( A = bot_bo1943466239ecy_KS )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.71/1.53 & ( B = bot_bo1943466239ecy_KS ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert_Secrecy_KS @ X @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_291_Un__singleton__iff,axiom,
% 2.71/1.53 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X: secrecy_specID] :
% 2.71/1.53 ( ( ( sup_su1712599557specID @ A @ B )
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.71/1.53 = ( ( ( A = bot_bo1785112429specID )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.71/1.53 & ( B = bot_bo1785112429specID ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_292_Un__singleton__iff,axiom,
% 2.71/1.53 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X: secrecy_chanID] :
% 2.71/1.53 ( ( ( sup_su370684444chanID @ A @ B )
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.71/1.53 = ( ( ( A = bot_bo443197316chanID )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.71/1.53 & ( B = bot_bo443197316chanID ) )
% 2.71/1.53 | ( ( A
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) )
% 2.71/1.53 & ( B
% 2.71/1.53 = ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_293_insert__is__Un,axiom,
% 2.71/1.53 ( insert_Secrecy_KS
% 2.71/1.53 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_294_insert__is__Un,axiom,
% 2.71/1.53 ( insert1671894227specID
% 2.71/1.53 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_295_insert__is__Un,axiom,
% 2.71/1.53 ( insert751661162chanID
% 2.71/1.53 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_296_LocalSecretsComposition__neg__loc__s,axiom,
% 2.71/1.53 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.71/1.53 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_297_LocalSecretsComposition__neg__s,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_298_know__composition__neg__ine__s,axiom,
% 2.71/1.53 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ~ ( knowle945212990e_know @ P @ ( secrecy_sKS @ Secret ) )
% 2.71/1.53 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correctCompositionIn @ PQ )
% 2.71/1.53 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_299_LocalSecretsComposition__neg1__s,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_300_LocalSecretsComposition__ine2__s,axiom,
% 2.71/1.53 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.71/1.53 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_301_LocalSecretsComposition__ine1__s,axiom,
% 2.71/1.53 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.71/1.53 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_302_LocalSecretsComposition__exprChannel__s,axiom,
% 2.71/1.53 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 2.71/1.53 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 2.71/1.53 => ( ~ ( member1967978193chanID @ X @ ( ins @ P ) )
% 2.71/1.53 & ~ ( member1967978193chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_303_LocalSecretsComposition__neg,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ( correctCompositionKS @ PQ )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.71/1.53 => ( ! [M4: secrecy_Keys] :
% 2.71/1.53 ( ( Ks
% 2.71/1.53 = ( secrecy_kKS @ M4 ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 2.71/1.53 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 2.71/1.53 => ( ! [M4: secrecy_Secrets] :
% 2.71/1.53 ( ( Ks
% 2.71/1.53 = ( secrecy_sKS @ M4 ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 2.71/1.53 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_304_LocalSecretsComposition__neg1,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc965049635ionLoc @ PQ )
% 2.71/1.53 => ( ! [M4: secrecy_Keys] :
% 2.71/1.53 ( ( Ks
% 2.71/1.53 = ( secrecy_kKS @ M4 ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 2.71/1.53 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 2.71/1.53 => ( ! [M4: secrecy_Secrets] :
% 2.71/1.53 ( ( Ks
% 2.71/1.53 = ( secrecy_sKS @ M4 ) )
% 2.71/1.53 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 2.71/1.53 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 2.71/1.53 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_305_sup__bot_Oright__neutral,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 2.71/1.53 = A2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_306_sup__bot_Oright__neutral,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_specID] :
% 2.71/1.53 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 2.71/1.53 = A2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_307_sup__bot_Oright__neutral,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 2.71/1.53 = A2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_308_sup__bot_Oneutr__eq__iff,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 2.71/1.53 ( ( bot_bo1943466239ecy_KS
% 2.71/1.53 = ( sup_su1301156759ecy_KS @ A2 @ B2 ) )
% 2.71/1.53 = ( ( A2 = bot_bo1943466239ecy_KS )
% 2.71/1.53 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_309_sup__bot_Oneutr__eq__iff,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 2.71/1.53 ( ( bot_bo1785112429specID
% 2.71/1.53 = ( sup_su1712599557specID @ A2 @ B2 ) )
% 2.71/1.53 = ( ( A2 = bot_bo1785112429specID )
% 2.71/1.53 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_310_sup__bot_Oneutr__eq__iff,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.71/1.53 ( ( bot_bo443197316chanID
% 2.71/1.53 = ( sup_su370684444chanID @ A2 @ B2 ) )
% 2.71/1.53 = ( ( A2 = bot_bo443197316chanID )
% 2.71/1.53 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_311_sup__bot_Oleft__neutral,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_KS] :
% 2.71/1.53 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A2 )
% 2.71/1.53 = A2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_312_sup__bot_Oleft__neutral,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_specID] :
% 2.71/1.53 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A2 )
% 2.71/1.53 = A2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_313_sup__bot_Oleft__neutral,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_chanID] :
% 2.71/1.53 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A2 )
% 2.71/1.53 = A2 ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_314_sup__bot_Oeq__neutr__iff,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 2.71/1.53 ( ( ( sup_su1712599557specID @ A2 @ B2 )
% 2.71/1.53 = bot_bo1785112429specID )
% 2.71/1.53 = ( ( A2 = bot_bo1785112429specID )
% 2.71/1.53 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_315_sup__bot_Oeq__neutr__iff,axiom,
% 2.71/1.53 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ( sup_su370684444chanID @ A2 @ B2 )
% 2.71/1.53 = bot_bo443197316chanID )
% 2.71/1.53 = ( ( A2 = bot_bo443197316chanID )
% 2.71/1.53 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_316_ineM__Un1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,A: set_Secrecy_chanID,E2: secrecy_Expression,B: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ineM @ P @ A @ E2 )
% 2.71/1.53 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_317_notSpecKeysSecretsExpr__def,axiom,
% 2.71/1.53 ( notSpe1586871396tsExpr
% 2.71/1.53 = ( ^ [P2: secrecy_specID,E4: list_S529945141ession] :
% 2.71/1.53 ( ! [X2: secrecy_Keys] :
% 2.71/1.53 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X2 ) @ E4 )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 2.71/1.53 & ! [Y4: secrecy_Secrets] :
% 2.71/1.53 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y4 ) @ E4 )
% 2.71/1.53 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_318_TBtheorem5a__empty,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ( eout @ P @ E2 )
% 2.71/1.53 | ( eout @ Q @ E2 ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( ( loc @ PQ )
% 2.71/1.53 = bot_bo443197316chanID )
% 2.71/1.53 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_319_correctCompositionKS__subcomp1,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 2.71/1.53 ( ( correctCompositionKS @ C3 )
% 2.71/1.53 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.71/1.53 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 2.71/1.53 => ? [X3: secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 2.71/1.53 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_320_TBtheorem2a,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( eout @ PQ @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( eout @ P @ E2 )
% 2.71/1.53 | ( eout @ Q @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_321_correctCompositionKS__subcomp3,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 2.71/1.53 ( ( correctCompositionKS @ C3 )
% 2.71/1.53 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.71/1.53 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 2.71/1.53 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_322_TBtheorem5a__notP1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( eout @ P @ E2 )
% 2.71/1.53 => ( ~ ( eout @ Q @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_323_TBtheorem5a__notPQ,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 2.71/1.53 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetP )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_324_TBtheorem5a__notP2,axiom,
% 2.71/1.53 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( eout @ Q @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSet )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_325_out__exprChannelSingle__Set,axiom,
% 2.71/1.53 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( out_ex985543062Single @ P @ Ch @ E2 )
% 2.71/1.53 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_326_out__exprChannelSet__Single,axiom,
% 2.71/1.53 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E2 )
% 2.71/1.53 => ( out_ex985543062Single @ P @ Ch @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_327_TBtheorem5b__notPQ,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E2: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M2: set_Secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 2.71/1.53 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 2.71/1.53 => ( ( M2
% 2.71/1.53 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetP )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSetQ )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_328_eout__know__k,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 2.71/1.53 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 2.71/1.53 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 2.71/1.53 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 2.71/1.53 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_329_not__know__k__not__eout,axiom,
% 2.71/1.53 ! [M: secrecy_Keys,A: secrecy_specID] :
% 2.71/1.53 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 2.71/1.53 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.71/1.53 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 2.71/1.53 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_330_not__eout__eoutM,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( eout @ P @ E2 )
% 2.71/1.53 => ~ ( eoutM @ P @ M2 @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_331_eoutM__eout,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.71/1.53 ( ( eoutM @ P @ M2 @ E2 )
% 2.71/1.53 => ( eout @ P @ E2 ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_332_TBtheorem2b,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( eoutM @ PQ @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( eoutM @ P @ M2 @ E2 )
% 2.71/1.53 | ( eoutM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_333_TBtheorem5b__notP2,axiom,
% 2.71/1.53 ! [Q: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.71/1.53 ( ~ ( eoutM @ Q @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 2.71/1.53 => ( ! [X3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X3 @ ChSet )
% 2.71/1.53 => ( member1967978193chanID @ X3 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_334_TBtheorem5b__notP1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( eoutM @ P @ M2 @ E2 )
% 2.71/1.53 => ( ~ ( eoutM @ Q @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_335_eout__know__nonKS__k,axiom,
% 2.71/1.53 ! [M: secrecy_Keys,A: secrecy_specID] :
% 2.71/1.53 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 2.71/1.53 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 2.71/1.53 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 2.71/1.53 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_336_eoutKnowCorrect__L1k,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 2.71/1.53 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 2.71/1.53 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 2.71/1.53 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 2.71/1.53 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_337_TBtheore54b__P,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( eoutM @ P @ M2 @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ M2 ) )
% 2.71/1.53 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_338_TBtheorem5b__PQ,axiom,
% 2.71/1.53 ! [P: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ( eoutM @ P @ M2 @ E2 )
% 2.71/1.53 | ( eoutM @ Q @ M2 @ E2 ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.71/1.53 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.71/1.53 & ( member1967978193chanID @ Ch2 @ M2 )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_339_TBtheorem5a__PQ,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.71/1.53 ( ( ( eout @ P @ E2 )
% 2.71/1.53 | ( eout @ Q @ E2 ) )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.71/1.53 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_340_eout__def,axiom,
% 2.71/1.53 ( eout
% 2.71/1.53 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 2.71/1.53 ? [Ch3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.71/1.53 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_341_eoutM__def,axiom,
% 2.71/1.53 ( eoutM
% 2.71/1.53 = ( ^ [SP: secrecy_specID,M3: set_Secrecy_chanID,E3: secrecy_Expression] :
% 2.71/1.53 ? [Ch3: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.71/1.53 & ( member1967978193chanID @ Ch3 @ M3 )
% 2.71/1.53 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_342_out__exprChannelSet__def,axiom,
% 2.71/1.53 ( out_exprChannelSet
% 2.71/1.53 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E3: secrecy_Expression] :
% 2.71/1.53 ( ! [X2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 2.71/1.53 => ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 2.71/1.53 & ( exprChannel @ X2 @ E3 ) ) )
% 2.71/1.53 & ! [X2: secrecy_chanID] :
% 2.71/1.53 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 2.71/1.53 & ( member1967978193chanID @ X2 @ ( out @ SP ) ) )
% 2.71/1.53 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_343_out__exprChannelSingle__def,axiom,
% 2.71/1.53 ( out_ex985543062Single
% 2.71/1.53 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.71/1.53 & ( exprChannel @ Ch3 @ E3 )
% 2.71/1.53 & ! [X2: secrecy_chanID,T: nat] :
% 2.71/1.53 ( ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 2.71/1.53 & ( X2 != Ch3 ) )
% 2.71/1.53 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_344_correctCompositionOut__prop1,axiom,
% 2.71/1.53 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 2.71/1.53 ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ( member1967978193chanID @ X @ ( out @ PQ ) )
% 2.71/1.53 => ( ( member1967978193chanID @ X @ ( out @ P ) )
% 2.71/1.53 | ( member1967978193chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_345_TBtheorem45a__P,axiom,
% 2.71/1.53 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.71/1.53 ( ( eout @ P @ E2 )
% 2.71/1.53 => ( ( ( subcomponents @ PQ )
% 2.71/1.53 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.71/1.53 => ( ( correc990227761ionOut @ PQ )
% 2.71/1.53 => ( ? [Ch2: secrecy_chanID] :
% 2.71/1.53 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.71/1.53 & ( exprChannel @ Ch2 @ E2 )
% 2.71/1.53 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.71/1.53 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_346_outStream__def,axiom,
% 2.71/1.53 ( outStream
% 2.71/1.53 = ( ^ [X2: secrecy_specID] :
% 2.71/1.53 ( ^ [Y3: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y3 = Z )
% 2.71/1.53 @ ( out @ X2 ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_347_eout__know__nonKS__s,axiom,
% 2.71/1.53 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 2.71/1.53 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 2.71/1.53 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 2.71/1.53 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 2.71/1.53 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_348_correctCompositionKS__subcomp4,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 2.71/1.53 ( ( correctCompositionKS @ C3 )
% 2.71/1.53 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.71/1.53 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) )
% 2.71/1.53 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_349_correctCompositionKS__subcomp2,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 2.71/1.53 ( ( correctCompositionKS @ C3 )
% 2.71/1.53 => ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.71/1.53 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 2.71/1.53 => ? [X3: secrecy_specID] :
% 2.71/1.53 ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 2.71/1.53 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_350_eout__know__s,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 2.71/1.53 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 2.71/1.53 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 2.71/1.53 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 2.71/1.53 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_351_not__know__s__not__eout,axiom,
% 2.71/1.53 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 2.71/1.53 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 2.71/1.53 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.71/1.53 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 2.71/1.53 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_352_eoutKnowCorrect__L1s,axiom,
% 2.71/1.53 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 2.71/1.53 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 2.71/1.53 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 2.71/1.53 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 2.71/1.53 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_353_adv__not__know2,axiom,
% 2.71/1.53 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 2.71/1.53 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 2.71/1.53 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.71/1.53 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(fact_354_adv__not__know1,axiom,
% 2.71/1.53 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Keys] :
% 2.71/1.53 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 2.71/1.53 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.71/1.53 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 2.71/1.53
% 2.71/1.53 thf(conj_0,conjecture,
% 2.71/1.53 ~ ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ) ).
% 2.71/1.53 ------------------------
% 2.71/1.57 % (19769)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/2Mi)
% 2.71/1.57 % (19770)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_19489 for (2999ds/2Mi)
% 2.71/1.57 % (19766)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/183Mi)
% 2.71/1.57 % (19769)Instruction limit reached!
% 2.71/1.57 % (19769)------------------------------
% 2.71/1.57 % (19769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.57 % (19769)Termination reason: Unknown
% 2.71/1.57 % (19769)Termination phase: shuffling
% 2.71/1.57
% 2.71/1.57 % (19769)Memory used [KB]: 1407
% 2.71/1.57 % (19769)Time elapsed: 0.002 s
% 2.71/1.57 % (19769)Instructions burned: 2 (million)
% 2.71/1.57 % (19769)------------------------------
% 2.71/1.57 % (19769)------------------------------
% 2.71/1.57 % (19770)Instruction limit reached!
% 2.71/1.57 % (19770)------------------------------
% 2.71/1.57 % (19770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.57 % (19770)Termination reason: Unknown
% 2.71/1.57 % (19770)Termination phase: shuffling
% 2.71/1.57
% 2.71/1.57 % (19770)Memory used [KB]: 1407
% 2.71/1.57 % (19770)Time elapsed: 0.002 s
% 2.71/1.57 % (19770)Instructions burned: 2 (million)
% 2.71/1.57 % (19770)------------------------------
% 2.71/1.57 % (19770)------------------------------
% 2.71/1.58 % (19767)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_19489 for (2999ds/4Mi)
% 2.71/1.58 % (19768)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_19489 for (2999ds/27Mi)
% 2.71/1.58 % (19771)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_19489 for (2999ds/275Mi)
% 2.71/1.58 % (19772)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/18Mi)
% 2.71/1.58 % (19773)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/3Mi)
% 2.71/1.58 % (19774)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_19489 for (2999ds/37Mi)
% 2.71/1.58 % (19767)Instruction limit reached!
% 2.71/1.58 % (19767)------------------------------
% 2.71/1.58 % (19767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.58 % (19767)Termination reason: Unknown
% 2.71/1.58 % (19767)Termination phase: shuffling
% 2.71/1.58
% 2.71/1.58 % (19767)Memory used [KB]: 1535
% 2.71/1.58 % (19767)Time elapsed: 0.005 s
% 2.71/1.58 % (19767)Instructions burned: 5 (million)
% 2.71/1.58 % (19767)------------------------------
% 2.71/1.58 % (19767)------------------------------
% 2.71/1.58 % (19773)Instruction limit reached!
% 2.71/1.58 % (19773)------------------------------
% 2.71/1.58 % (19773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.58 % (19773)Termination reason: Unknown
% 2.71/1.58 % (19773)Termination phase: shuffling
% 2.71/1.58
% 2.71/1.58 % (19773)Memory used [KB]: 1535
% 2.71/1.58 % (19773)Time elapsed: 0.003 s
% 2.71/1.58 % (19773)Instructions burned: 6 (million)
% 2.71/1.58 % (19773)------------------------------
% 2.71/1.58 % (19773)------------------------------
% 2.71/1.59 % (19772)Instruction limit reached!
% 2.71/1.59 % (19772)------------------------------
% 2.71/1.59 % (19772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.59 % (19772)Termination reason: Unknown
% 2.71/1.59 % (19772)Termination phase: shuffling
% 2.71/1.59
% 2.71/1.59 % (19772)Memory used [KB]: 1791
% 2.71/1.59 % (19772)Time elapsed: 0.014 s
% 2.71/1.59 % (19772)Instructions burned: 19 (million)
% 2.71/1.59 % (19772)------------------------------
% 2.71/1.59 % (19772)------------------------------
% 2.71/1.59 % (19774)Instruction limit reached!
% 2.71/1.59 % (19774)------------------------------
% 2.71/1.59 % (19774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.59 % (19774)Termination reason: Unknown
% 2.71/1.59 % (19774)Termination phase: shuffling
% 2.71/1.59
% 2.71/1.59 % (19774)Memory used [KB]: 2174
% 2.71/1.59 % (19774)Time elapsed: 0.012 s
% 2.71/1.59 % (19774)Instructions burned: 39 (million)
% 2.71/1.59 % (19774)------------------------------
% 2.71/1.59 % (19774)------------------------------
% 2.71/1.59 % (19776)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_19489 for (2999ds/3Mi)
% 2.71/1.59 % (19776)Instruction limit reached!
% 2.71/1.59 % (19776)------------------------------
% 2.71/1.59 % (19776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.59 % (19776)Termination reason: Unknown
% 2.71/1.59 % (19776)Termination phase: shuffling
% 2.71/1.59
% 2.71/1.59 % (19776)Memory used [KB]: 1535
% 2.71/1.59 % (19776)Time elapsed: 0.003 s
% 2.71/1.59 % (19776)Instructions burned: 5 (million)
% 2.71/1.59 % (19776)------------------------------
% 2.71/1.59 % (19776)------------------------------
% 2.71/1.60 % (19768)Instruction limit reached!
% 2.71/1.60 % (19768)------------------------------
% 2.71/1.60 % (19768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (19768)Termination reason: Unknown
% 2.71/1.60 % (19768)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (19768)Memory used [KB]: 1918
% 2.71/1.60 % (19768)Time elapsed: 0.019 s
% 2.71/1.60 % (19768)Instructions burned: 28 (million)
% 2.71/1.60 % (19768)------------------------------
% 2.71/1.60 % (19768)------------------------------
% 2.74/1.60 % (19775)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_19489 for (2999ds/15Mi)
% 2.74/1.60 % (19778)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/7Mi)
% 2.74/1.60 % (19779)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/16Mi)
% 2.74/1.61 % (19778)Instruction limit reached!
% 2.74/1.61 % (19778)------------------------------
% 2.74/1.61 % (19778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (19778)Termination reason: Unknown
% 2.74/1.61 % (19778)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (19778)Memory used [KB]: 1535
% 2.74/1.61 % (19778)Time elapsed: 0.004 s
% 2.74/1.61 % (19778)Instructions burned: 9 (million)
% 2.74/1.61 % (19778)------------------------------
% 2.74/1.61 % (19778)------------------------------
% 2.74/1.61 % (19775)Instruction limit reached!
% 2.74/1.61 % (19775)------------------------------
% 2.74/1.61 % (19775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (19775)Termination reason: Unknown
% 2.74/1.61 % (19775)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (19775)Memory used [KB]: 1663
% 2.74/1.61 % (19775)Time elapsed: 0.011 s
% 2.74/1.61 % (19775)Instructions burned: 15 (million)
% 2.74/1.61 % (19775)------------------------------
% 2.74/1.61 % (19775)------------------------------
% 2.74/1.61 % (19779)Instruction limit reached!
% 2.74/1.61 % (19779)------------------------------
% 2.74/1.61 % (19779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (19779)Termination reason: Unknown
% 2.74/1.61 % (19779)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (19779)Memory used [KB]: 1791
% 2.74/1.61 % (19779)Time elapsed: 0.006 s
% 2.74/1.61 % (19779)Instructions burned: 16 (million)
% 2.74/1.61 % (19779)------------------------------
% 2.74/1.61 % (19779)------------------------------
% 2.74/1.61 % (19777)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_19489 for (2999ds/1041Mi)
% 2.74/1.61 % (19780)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_19489 for (2999ds/3Mi)
% 2.74/1.61 % (19781)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_19489 for (2999ds/3Mi)
% 2.74/1.62 % (19781)Instruction limit reached!
% 2.74/1.62 % (19781)------------------------------
% 2.74/1.62 % (19781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (19771)Refutation not found, incomplete strategy
% 2.74/1.62 % (19771)------------------------------
% 2.74/1.62 % (19771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (19781)Termination reason: Unknown
% 2.74/1.62 % (19771)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.62
% 2.74/1.62 % (19781)Termination phase: shuffling
% 2.74/1.62
% 2.74/1.62
% 2.74/1.62 % (19781)Memory used [KB]: 1535
% 2.74/1.62 % (19781)Time elapsed: 0.002 s
% 2.74/1.62 % (19771)Memory used [KB]: 6652
% 2.74/1.62 % (19781)Instructions burned: 3 (million)
% 2.74/1.62 % (19781)------------------------------
% 2.74/1.62 % (19781)------------------------------
% 2.74/1.62 % (19771)Time elapsed: 0.038 s
% 2.74/1.62 % (19771)Instructions burned: 62 (million)
% 2.74/1.62 % (19771)------------------------------
% 2.74/1.62 % (19771)------------------------------
% 2.74/1.62 % (19780)Instruction limit reached!
% 2.74/1.62 % (19780)------------------------------
% 2.74/1.62 % (19780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (19780)Termination reason: Unknown
% 2.74/1.62 % (19780)Termination phase: shuffling
% 2.74/1.62
% 2.74/1.62 % (19780)Memory used [KB]: 1535
% 2.74/1.62 % (19780)Time elapsed: 0.004 s
% 2.74/1.62 % (19780)Instructions burned: 3 (million)
% 2.74/1.62 % (19780)------------------------------
% 2.74/1.62 % (19780)------------------------------
% 2.74/1.62 % (19783)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/3Mi)
% 2.74/1.62 % (19783)Instruction limit reached!
% 2.74/1.62 % (19783)------------------------------
% 2.74/1.62 % (19783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (19783)Termination reason: Unknown
% 2.74/1.62 % (19783)Termination phase: shuffling
% 2.74/1.62
% 2.74/1.62 % (19783)Memory used [KB]: 1407
% 2.74/1.62 % (19783)Time elapsed: 0.002 s
% 2.74/1.62 % (19783)Instructions burned: 3 (million)
% 2.74/1.62 % (19783)------------------------------
% 2.74/1.62 % (19783)------------------------------
% 2.74/1.62 % (19766)Instruction limit reached!
% 2.74/1.62 % (19766)------------------------------
% 2.74/1.62 % (19766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (19766)Termination reason: Unknown
% 2.74/1.62 % (19766)Termination phase: Saturation
% 2.74/1.62
% 2.74/1.62 % (19766)Memory used [KB]: 7419
% 2.74/1.62 % (19766)Time elapsed: 0.053 s
% 2.74/1.62 % (19766)Instructions burned: 185 (million)
% 2.74/1.62 % (19766)------------------------------
% 2.74/1.62 % (19766)------------------------------
% 2.74/1.63 % (19782)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/7Mi)
% 2.74/1.63 % (19787)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/6Mi)
% 2.74/1.63 % (19787)Instruction limit reached!
% 2.74/1.63 % (19787)------------------------------
% 2.74/1.63 % (19787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (19787)Termination reason: Unknown
% 2.74/1.63 % (19787)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (19787)Memory used [KB]: 1535
% 2.74/1.63 % (19787)Time elapsed: 0.003 s
% 2.74/1.63 % (19787)Instructions burned: 6 (million)
% 2.74/1.63 % (19787)------------------------------
% 2.74/1.63 % (19787)------------------------------
% 2.74/1.63 % (19782)Instruction limit reached!
% 2.74/1.63 % (19782)------------------------------
% 2.74/1.63 % (19782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (19782)Termination reason: Unknown
% 2.74/1.63 % (19782)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (19782)Memory used [KB]: 1535
% 2.74/1.63 % (19782)Time elapsed: 0.007 s
% 2.74/1.63 % (19782)Instructions burned: 8 (million)
% 2.74/1.63 % (19782)------------------------------
% 2.74/1.63 % (19782)------------------------------
% 2.74/1.63 % (19788)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_19489 for (2999ds/902Mi)
% 2.74/1.63 % (19784)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/4Mi)
% 2.74/1.63 % (19785)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/18Mi)
% 2.74/1.63 % (19786)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/710Mi)
% 2.74/1.64 % (19784)Instruction limit reached!
% 2.74/1.64 % (19784)------------------------------
% 2.74/1.64 % (19784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (19784)Termination reason: Unknown
% 2.74/1.64 % (19784)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (19784)Memory used [KB]: 1535
% 2.74/1.64 % (19784)Time elapsed: 0.005 s
% 2.74/1.64 % (19784)Instructions burned: 4 (million)
% 2.74/1.64 % (19784)------------------------------
% 2.74/1.64 % (19784)------------------------------
% 2.74/1.64 % (19789)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_19489 for (2999ds/21Mi)
% 2.74/1.64 % (19785)Instruction limit reached!
% 2.74/1.64 % (19785)------------------------------
% 2.74/1.64 % (19785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (19785)Termination reason: Unknown
% 2.74/1.64 % (19785)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (19785)Memory used [KB]: 1791
% 2.74/1.64 % (19785)Time elapsed: 0.013 s
% 2.74/1.64 % (19785)Instructions burned: 18 (million)
% 2.74/1.64 % (19785)------------------------------
% 2.74/1.64 % (19785)------------------------------
% 2.74/1.65 % (19789)Instruction limit reached!
% 2.74/1.65 % (19789)------------------------------
% 2.74/1.65 % (19789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (19789)Termination reason: Unknown
% 2.74/1.65 % (19789)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (19789)Memory used [KB]: 1791
% 2.74/1.65 % (19789)Time elapsed: 0.008 s
% 2.74/1.65 % (19789)Instructions burned: 22 (million)
% 2.74/1.65 % (19789)------------------------------
% 2.74/1.65 % (19789)------------------------------
% 2.74/1.65 % (19790)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19489 for (2999ds/5Mi)
% 2.74/1.65 % (19790)Instruction limit reached!
% 2.74/1.65 % (19790)------------------------------
% 2.74/1.65 % (19790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (19790)Termination reason: Unknown
% 2.74/1.65 % (19790)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (19790)Memory used [KB]: 1535
% 2.74/1.65 % (19790)Time elapsed: 0.005 s
% 2.74/1.65 % (19790)Instructions burned: 6 (million)
% 2.74/1.65 % (19790)------------------------------
% 2.74/1.65 % (19790)------------------------------
% 2.74/1.65 % (19791)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_19489 for (2999ds/6Mi)
% 2.74/1.66 % (19791)Instruction limit reached!
% 2.74/1.66 % (19791)------------------------------
% 2.74/1.66 % (19791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.66 % (19791)Termination reason: Unknown
% 2.74/1.66 % (19791)Termination phase: shuffling
% 2.74/1.66
% 2.74/1.66 % (19791)Memory used [KB]: 1535
% 2.74/1.66 % (19791)Time elapsed: 0.005 s
% 2.74/1.66 % (19791)Instructions burned: 6 (million)
% 2.74/1.66 % (19791)------------------------------
% 2.74/1.66 % (19791)------------------------------
% 2.74/1.66 % (19786)First to succeed.
% 2.74/1.66 % (19793)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_19489 for (2998ds/779Mi)
% 2.74/1.66 % (19786)Refutation found. Thanks to Tanya!
% 2.74/1.66 % SZS status Theorem for DTF2THF_19489
% 2.74/1.66 % SZS output start Proof for DTF2THF_19489
% 2.74/1.66 thf(type_def_5, type, secrecy_specID: $tType).
% 2.74/1.66 thf(type_def_6, type, set_Secrecy_KS: $tType).
% 2.74/1.66 thf(type_def_8, type, secrecy_KS: $tType).
% 2.74/1.66 thf(type_def_9, type, list_S529945141ession: $tType).
% 2.74/1.66 thf(type_def_10, type, set_Secrecy_Keys: $tType).
% 2.74/1.66 thf(type_def_11, type, set_Secrecy_Secrets: $tType).
% 2.74/1.66 thf(type_def_12, type, set_Secrecy_chanID: $tType).
% 2.74/1.66 thf(type_def_13, type, set_Secrecy_specID: $tType).
% 2.74/1.66 thf(type_def_14, type, secrecy_Expression: $tType).
% 2.74/1.66 thf(type_def_15, type, secrecy_Keys: $tType).
% 2.74/1.66 thf(type_def_16, type, secrecy_Secrets: $tType).
% 2.74/1.66 thf(type_def_17, type, secrecy_chanID: $tType).
% 2.74/1.66 thf(type_def_18, type, nat: $tType).
% 2.74/1.66 thf(func_def_0, type, list_S529945141ession: $tType).
% 2.74/1.66 thf(func_def_1, type, set_Secrecy_Secrets: $tType).
% 2.74/1.66 thf(func_def_2, type, set_Secrecy_specID: $tType).
% 2.74/1.66 thf(func_def_3, type, set_Secrecy_chanID: $tType).
% 2.74/1.66 thf(func_def_4, type, set_Secrecy_Keys: $tType).
% 2.74/1.66 thf(func_def_5, type, set_Secrecy_KS: $tType).
% 2.74/1.66 thf(func_def_6, type, secrecy_Expression: $tType).
% 2.74/1.66 thf(func_def_7, type, secrecy_Secrets: $tType).
% 2.74/1.66 thf(func_def_8, type, secrecy_specID: $tType).
% 2.74/1.66 thf(func_def_9, type, secrecy_chanID: $tType).
% 2.74/1.66 thf(func_def_10, type, secrecy_Keys: $tType).
% 2.74/1.66 thf(func_def_11, type, secrecy_KS: $tType).
% 2.74/1.66 thf(func_def_12, type, nat: $tType).
% 2.74/1.66 thf(func_def_13, type, localSecrets: secrecy_specID > set_Secrecy_KS).
% 2.74/1.66 thf(func_def_14, type, knowle233900195orrect: secrecy_specID > secrecy_KS > $o).
% 2.74/1.66 thf(func_def_15, type, knowle945212990e_know: secrecy_specID > secrecy_KS > $o).
% 2.74/1.66 thf(func_def_16, type, knowle731562421_knows: secrecy_specID > list_S529945141ession > $o).
% 2.74/1.66 thf(func_def_17, type, sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 2.74/1.66 thf(func_def_18, type, sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 2.74/1.66 thf(func_def_19, type, sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 2.74/1.66 thf(func_def_20, type, sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 2.74/1.66 thf(func_def_21, type, sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 2.74/1.66 thf(func_def_22, type, mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o).
% 2.74/1.66 thf(func_def_23, type, bot_bot_Secrecy_KS_o: secrecy_KS > $o).
% 2.74/1.66 thf(func_def_24, type, bot_bo2072920570Keys_o: secrecy_Keys > $o).
% 2.74/1.66 thf(func_def_25, type, bot_bo1909946299rets_o: secrecy_Secrets > $o).
% 2.74/1.66 thf(func_def_26, type, bot_bo1012329985anID_o: secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_27, type, bot_bo1767780696ecID_o: secrecy_specID > $o).
% 2.74/1.66 thf(func_def_28, type, bot_bo1943466239ecy_KS: set_Secrecy_KS).
% 2.74/1.66 thf(func_def_29, type, bot_bo701486667y_Keys: set_Secrecy_Keys).
% 2.74/1.66 thf(func_def_30, type, bot_bo1124690338ecrets: set_Secrecy_Secrets).
% 2.74/1.66 thf(func_def_31, type, bot_bo443197316chanID: set_Secrecy_chanID).
% 2.74/1.66 thf(func_def_32, type, bot_bo1785112429specID: set_Secrecy_specID).
% 2.74/1.66 thf(func_def_33, type, ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_34, type, decr: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 2.74/1.66 thf(func_def_35, type, enc: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 2.74/1.66 thf(func_def_36, type, encrDecrKeys: secrecy_Keys > secrecy_Keys > $o).
% 2.74/1.66 thf(func_def_37, type, ext: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 2.74/1.66 thf(func_def_38, type, sign: secrecy_Keys > list_S529945141ession > list_S529945141ession).
% 2.74/1.66 thf(func_def_39, type, correctCompositionKS: secrecy_specID > $o).
% 2.74/1.66 thf(func_def_40, type, eout: secrecy_specID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_41, type, eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_42, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_43, type, ine: secrecy_specID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_44, type, ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_45, type, ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_46, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_47, type, notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o).
% 2.74/1.66 thf(func_def_48, type, out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_49, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 2.74/1.66 thf(func_def_50, type, specKeys: secrecy_specID > set_Secrecy_Keys).
% 2.74/1.66 thf(func_def_51, type, specKeysSecrets: secrecy_specID > set_Secrecy_KS).
% 2.74/1.66 thf(func_def_52, type, specSecrets: secrecy_specID > set_Secrecy_Secrets).
% 2.74/1.66 thf(func_def_53, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 2.74/1.66 thf(func_def_54, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 2.74/1.66 thf(func_def_55, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 2.74/1.66 thf(func_def_56, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 2.74/1.66 thf(func_def_57, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 2.74/1.66 thf(func_def_58, type, collect_Secrecy_KS: (secrecy_KS > $o) > set_Secrecy_KS).
% 2.74/1.66 thf(func_def_59, type, collect_Secrecy_Keys: (secrecy_Keys > $o) > set_Secrecy_Keys).
% 2.74/1.66 thf(func_def_60, type, collec836099393ecrets: (secrecy_Secrets > $o) > set_Secrecy_Secrets).
% 2.74/1.66 thf(func_def_61, type, collec625564175chanID: (secrecy_chanID > $o) > set_Secrecy_chanID).
% 2.74/1.66 thf(func_def_62, type, collec1545797240specID: (secrecy_specID > $o) > set_Secrecy_specID).
% 2.74/1.66 thf(func_def_63, type, insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 2.74/1.66 thf(func_def_64, type, insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 2.74/1.66 thf(func_def_65, type, insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 2.74/1.66 thf(func_def_66, type, insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 2.74/1.66 thf(func_def_67, type, insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 2.74/1.66 thf(func_def_68, type, is_emp928984296chanID: set_Secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_69, type, is_emp1849217361specID: set_Secrecy_specID > $o).
% 2.74/1.66 thf(func_def_70, type, is_sin1442426433ecy_KS: set_Secrecy_KS > $o).
% 2.74/1.66 thf(func_def_71, type, is_sin1096471309y_Keys: set_Secrecy_Keys > $o).
% 2.74/1.66 thf(func_def_72, type, is_sin1002224330ecrets: set_Secrecy_Secrets > $o).
% 2.74/1.66 thf(func_def_73, type, is_sin581274182chanID: set_Secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_74, type, is_sin1501507247specID: set_Secrecy_specID > $o).
% 2.74/1.66 thf(func_def_75, type, the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID).
% 2.74/1.66 thf(func_def_76, type, the_el827131246specID: set_Secrecy_specID > secrecy_specID).
% 2.74/1.66 thf(func_def_77, type, correctCompositionIn: secrecy_specID > $o).
% 2.74/1.66 thf(func_def_78, type, correc965049635ionLoc: secrecy_specID > $o).
% 2.74/1.66 thf(func_def_79, type, correc990227761ionOut: secrecy_specID > $o).
% 2.74/1.66 thf(func_def_80, type, inStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_81, type, ins: secrecy_specID > set_Secrecy_chanID).
% 2.74/1.66 thf(func_def_82, type, loc: secrecy_specID > set_Secrecy_chanID).
% 2.74/1.66 thf(func_def_83, type, locStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_84, type, out: secrecy_specID > set_Secrecy_chanID).
% 2.74/1.66 thf(func_def_85, type, outStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_86, type, subcomponents: secrecy_specID > set_Secrecy_specID).
% 2.74/1.66 thf(func_def_87, type, member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o).
% 2.74/1.66 thf(func_def_88, type, member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o).
% 2.74/1.66 thf(func_def_89, type, member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o).
% 2.74/1.66 thf(func_def_90, type, member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o).
% 2.74/1.66 thf(func_def_91, type, member740727610specID: secrecy_specID > set_Secrecy_specID > $o).
% 2.74/1.66 thf(func_def_92, type, p: secrecy_specID).
% 2.74/1.66 thf(func_def_93, type, pq: secrecy_specID).
% 2.74/1.66 thf(func_def_94, type, q: secrecy_specID).
% 2.74/1.66 thf(func_def_95, type, key: secrecy_Keys).
% 2.74/1.66 thf(func_def_96, type, m: secrecy_KS).
% 2.74/1.66 thf(f1000,plain,(
% 2.74/1.66 $false),
% 2.74/1.66 inference(subsumption_resolution,[status(thm)],[f999,f993])).
% 2.74/1.66 thf(f993,plain,(
% 2.74/1.66 ((knowle945212990e_know @ q @ (secrecy_kKS @ key)) != $true)),
% 2.74/1.66 inference(definition_unfolding,[status(thm)],[f982,f983])).
% 2.74/1.66 thf(f983,plain,(
% 2.74/1.66 (m = (secrecy_kKS @ key))),
% 2.74/1.66 inference(cnf_transformation,[status(thm)],[f2])).
% 2.74/1.66 thf(f2,axiom,(
% 2.74/1.66 (m = (secrecy_kKS @ key))),
% 2.74/1.66 file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',fact_1_a1)).
% 2.74/1.66 thf(f982,plain,(
% 2.74/1.66 ((knowle945212990e_know @ q @ m) != $true)),
% 2.74/1.66 inference(cnf_transformation,[status(thm)],[f972])).
% 2.74/1.66 thf(f972,plain,(
% 2.74/1.66 ((knowle945212990e_know @ q @ m) != $true)),
% 2.74/1.66 inference(flattening,[status(thm)],[f836])).
% 2.74/1.66 thf(f836,plain,(
% 2.74/1.66 ~((knowle945212990e_know @ q @ m) = $true)),
% 2.74/1.66 inference(fool_elimination,[status(thm)],[f835])).
% 2.74/1.66 thf(f835,plain,(
% 2.74/1.66 ~(knowle945212990e_know @ q @ m)),
% 2.74/1.66 inference(rectify,[status(thm)],[f1])).
% 2.74/1.66 thf(f1,axiom,(
% 2.74/1.66 ~(knowle945212990e_know @ q @ m)),
% 2.74/1.66 file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',fact_0_not__knowQm)).
% 2.74/1.66 thf(f999,plain,(
% 2.74/1.66 ((knowle945212990e_know @ q @ (secrecy_kKS @ key)) = $true)),
% 2.74/1.66 inference(trivial_inequality_removal,[status(thm)],[f996])).
% 2.74/1.66 thf(f996,plain,(
% 2.74/1.66 ($true != $true) | ((knowle945212990e_know @ q @ (secrecy_kKS @ key)) = $true)),
% 2.74/1.66 inference(superposition,[status(thm)],[f991,f981])).
% 2.74/1.66 thf(f981,plain,(
% 2.74/1.66 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q)) = $true)),
% 2.74/1.66 inference(cnf_transformation,[status(thm)],[f971])).
% 2.74/1.66 thf(f971,plain,(
% 2.74/1.66 ((member_Secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q)) = $true)),
% 2.74/1.66 inference(flattening,[status(thm)],[f726])).
% 2.74/1.66 thf(f726,plain,(
% 2.74/1.66 ~~((member_Secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q)) = $true)),
% 2.74/1.66 inference(fool_elimination,[status(thm)],[f725])).
% 2.74/1.66 thf(f725,plain,(
% 2.74/1.66 ~~(member_Secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 2.74/1.66 inference(rectify,[status(thm)],[f357])).
% 2.74/1.66 thf(f357,negated_conjecture,(
% 2.74/1.66 ~~(member_Secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 2.74/1.66 inference(negated_conjecture,[status(cth)],[f356])).
% 2.74/1.66 thf(f356,conjecture,(
% 2.74/1.66 ~(member_Secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 2.74/1.66 file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',conj_0)).
% 2.74/1.66 thf(f991,plain,(
% 2.74/1.66 ( ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (((member_Secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) | ($true = (knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)))) )),
% 2.74/1.66 inference(cnf_transformation,[status(thm)],[f979])).
% 2.74/1.66 thf(f979,plain,(
% 2.74/1.66 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((($true = (knowle945212990e_know @ X0 @ (secrecy_kKS @ X1))) | (((member_Secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) & ((ine @ X0 @ (secrecy_kE @ X1)) != $true))) & (((member_Secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ((ine @ X0 @ (secrecy_kE @ X1)) = $true) | ($true != (knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)))))),
% 2.74/1.66 inference(flattening,[status(thm)],[f978])).
% 2.74/1.66 thf(f978,plain,(
% 2.74/1.66 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((($true = (knowle945212990e_know @ X0 @ (secrecy_kKS @ X1))) | (((member_Secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) & ((ine @ X0 @ (secrecy_kE @ X1)) != $true))) & ((((member_Secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ((ine @ X0 @ (secrecy_kE @ X1)) = $true)) | ($true != (knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)))))),
% 2.74/1.66 inference(nnf_transformation,[status(thm)],[f886])).
% 2.74/1.66 thf(f886,plain,(
% 2.74/1.66 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (($true = (knowle945212990e_know @ X0 @ (secrecy_kKS @ X1))) <=> (((member_Secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ((ine @ X0 @ (secrecy_kE @ X1)) = $true)))),
% 2.74/1.66 inference(fool_elimination,[status(thm)],[f885])).
% 2.74/1.66 thf(f885,plain,(
% 2.74/1.66 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((knowle945212990e_know @ X0 @ (secrecy_kKS @ X1)) = (member_Secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) | (ine @ X0 @ (secrecy_kE @ X1)))),
% 2.74/1.66 inference(rectify,[status(thm)],[f9])).
% 2.74/1.66 thf(f9,axiom,(
% 2.74/1.66 ! [X2 : secrecy_specID,X3 : secrecy_Keys] : ((knowle945212990e_know @ X2 @ (secrecy_kKS @ X3)) = (member_Secrecy_KS @ (secrecy_kKS @ X3) @ (localSecrets @ X2)) | (ine @ X2 @ (secrecy_kE @ X3)))),
% 2.74/1.66 file('/export/starexec/sandbox/tmp/tmp.n2JBi1F8LE/DTF2THF_19489.p',fact_8_know_Osimps_I1_J)).
% 2.74/1.66 % SZS output end Proof for DTF2THF_19489
% 2.74/1.66 % (19786)------------------------------
% 2.74/1.66 % (19786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.66 % (19786)Termination reason: Refutation
% 2.74/1.66
% 2.74/1.66 % (19786)Memory used [KB]: 6652
% 2.74/1.66 % (19786)Time elapsed: 0.025 s
% 2.74/1.66 % (19786)Instructions burned: 59 (million)
% 2.74/1.66 % (19786)------------------------------
% 2.74/1.66 % (19786)------------------------------
% 2.74/1.66 % (19765)Success in time 0.112 s
%------------------------------------------------------------------------------