%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP091^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 3.02s 1.88s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 26 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 188 ( 13 ~; 10 |; 7 &; 153 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 139 ( 135 usr; 13 con; 0-3 aty)
% ( 0 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 31 ( 15 ^; 14 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
secrecy_specID: $tType ).
thf(type_def_6,type,
set_Secrecy_KS: $tType ).
thf(type_def_8,type,
secrecy_KS: $tType ).
thf(type_def_9,type,
set_Secrecy_Keys: $tType ).
thf(type_def_10,type,
set_Secrecy_Secrets: $tType ).
thf(type_def_11,type,
set_Secrecy_chanID: $tType ).
thf(type_def_12,type,
set_Secrecy_specID: $tType ).
thf(type_def_13,type,
secrecy_Expression: $tType ).
thf(type_def_14,type,
list_S529945141ession: $tType ).
thf(type_def_15,type,
secrecy_Keys: $tType ).
thf(type_def_16,type,
secrecy_Secrets: $tType ).
thf(type_def_17,type,
secrecy_chanID: $tType ).
thf(type_def_18,type,
nat: $tType ).
thf(func_def_0,type,
list_S529945141ession: $tType ).
thf(func_def_1,type,
set_Secrecy_Secrets: $tType ).
thf(func_def_2,type,
set_Secrecy_specID: $tType ).
thf(func_def_3,type,
set_Secrecy_chanID: $tType ).
thf(func_def_4,type,
set_Secrecy_Keys: $tType ).
thf(func_def_5,type,
set_Secrecy_KS: $tType ).
thf(func_def_6,type,
secrecy_Expression: $tType ).
thf(func_def_7,type,
secrecy_Secrets: $tType ).
thf(func_def_8,type,
secrecy_specID: $tType ).
thf(func_def_9,type,
secrecy_chanID: $tType ).
thf(func_def_10,type,
secrecy_Keys: $tType ).
thf(func_def_11,type,
secrecy_KS: $tType ).
thf(func_def_12,type,
nat: $tType ).
thf(func_def_13,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_14,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(func_def_15,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(func_def_16,type,
sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_17,type,
sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_18,type,
sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_19,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_20,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_21,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(func_def_22,type,
bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
thf(func_def_23,type,
bot_bo2072920570Keys_o: secrecy_Keys > $o ).
thf(func_def_24,type,
bot_bo1909946299rets_o: secrecy_Secrets > $o ).
thf(func_def_25,type,
bot_bo1012329985anID_o: secrecy_chanID > $o ).
thf(func_def_26,type,
bot_bo1767780696ecID_o: secrecy_specID > $o ).
thf(func_def_27,type,
bot_bo1943466239ecy_KS: set_Secrecy_KS ).
thf(func_def_28,type,
bot_bo701486667y_Keys: set_Secrecy_Keys ).
thf(func_def_29,type,
bot_bo1124690338ecrets: set_Secrecy_Secrets ).
thf(func_def_30,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(func_def_31,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(func_def_32,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_33,type,
correctCompositionKS: secrecy_specID > $o ).
thf(func_def_34,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_35,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_36,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_37,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_38,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_39,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_40,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_41,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(func_def_42,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_43,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_44,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(func_def_45,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(func_def_46,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(func_def_47,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(func_def_48,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(func_def_49,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(func_def_50,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(func_def_51,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(func_def_52,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(func_def_53,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(func_def_54,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(func_def_55,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(func_def_56,type,
collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
thf(func_def_57,type,
insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_58,type,
insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_59,type,
insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_60,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_61,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_62,type,
is_emp928984296chanID: set_Secrecy_chanID > $o ).
thf(func_def_63,type,
is_emp1849217361specID: set_Secrecy_specID > $o ).
thf(func_def_64,type,
is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
thf(func_def_65,type,
is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
thf(func_def_66,type,
is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
thf(func_def_67,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(func_def_68,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(func_def_69,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_70,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(func_def_71,type,
correctCompositionIn: secrecy_specID > $o ).
thf(func_def_72,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(func_def_73,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(func_def_74,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_75,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_76,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_77,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_78,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_79,type,
outStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_80,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(func_def_81,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(func_def_82,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(func_def_83,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(func_def_84,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_85,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(func_def_86,type,
p: secrecy_specID ).
thf(func_def_87,type,
pq: secrecy_specID ).
thf(func_def_88,type,
q: secrecy_specID ).
thf(func_def_89,type,
m: secrecy_KS ).
thf(func_def_90,type,
secret: secrecy_Secrets ).
thf(func_def_106,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_107,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_108,type,
sK2: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_109,type,
sK3: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_110,type,
sK4: set_Secrecy_specID > secrecy_specID ).
thf(func_def_111,type,
sK5: set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_112,type,
sK6: secrecy_specID > secrecy_Keys > secrecy_specID ).
thf(func_def_113,type,
sK7: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_114,type,
sK8: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_115,type,
sK9: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_116,type,
sK10: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_117,type,
sK11: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_118,type,
sK12: secrecy_specID > secrecy_Secrets > secrecy_chanID ).
thf(func_def_119,type,
sK13: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_120,type,
sK14: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_121,type,
sK15: secrecy_Expression > secrecy_specID > secrecy_chanID ).
thf(func_def_122,type,
sK16: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_123,type,
sK17: set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_124,type,
sK18: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_125,type,
sK19: secrecy_Secrets > secrecy_specID > secrecy_chanID ).
thf(func_def_126,type,
sK20: ( secrecy_KS > $o ) > secrecy_Secrets ).
thf(func_def_127,type,
sK21: ( secrecy_KS > $o ) > secrecy_Keys ).
thf(func_def_128,type,
sK22: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_129,type,
sK23: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_130,type,
sK24: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(func_def_131,type,
sK25: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(func_def_132,type,
sK26: set_Secrecy_specID > secrecy_specID > set_Secrecy_specID ).
thf(func_def_133,type,
sK27: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_134,type,
sK28: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_135,type,
sK29: set_Secrecy_Secrets > secrecy_Secrets ).
thf(func_def_136,type,
sK30: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_137,type,
sK31: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_138,type,
sK32: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(func_def_139,type,
sK33: secrecy_specID > secrecy_Keys > secrecy_chanID ).
thf(func_def_140,type,
sK34: secrecy_specID > secrecy_Secrets > secrecy_specID ).
thf(func_def_141,type,
sK35: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_142,type,
sK36: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_143,type,
sK37: set_Secrecy_KS > secrecy_KS > set_Secrecy_KS ).
thf(func_def_144,type,
sK38: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_145,type,
sK39: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_146,type,
sK40: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets ).
thf(func_def_147,type,
sK41: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys ).
thf(func_def_148,type,
sK42: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_149,type,
sK43: set_Secrecy_specID > secrecy_specID ).
thf(func_def_150,type,
sK44: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys ).
thf(func_def_151,type,
sK45: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets ).
thf(func_def_152,type,
sK46: set_Secrecy_specID > secrecy_specID ).
thf(func_def_153,type,
sK47: set_Secrecy_specID > secrecy_specID ).
thf(func_def_154,type,
sK48: set_Secrecy_Keys > secrecy_Keys ).
thf(func_def_155,type,
sK49: secrecy_Keys > secrecy_specID > secrecy_chanID ).
thf(func_def_156,type,
sK50: secrecy_KS > secrecy_Keys ).
thf(func_def_157,type,
sK51: secrecy_KS > secrecy_Secrets ).
thf(func_def_158,type,
sK52: set_Secrecy_KS > secrecy_KS ).
thf(func_def_159,type,
sK53: set_Secrecy_KS > secrecy_KS ).
thf(func_def_160,type,
sK54: set_Secrecy_KS > secrecy_KS ).
thf(func_def_161,type,
sK55: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_163,type,
ph57:
!>[X0: $tType] : X0 ).
thf(f2536,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f2522,f2175]) ).
thf(f2175,plain,
( $true
!= ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) ) ),
inference(definition_unfolding,[status(thm)],[f1893,f1609]) ).
thf(f1609,plain,
( m
= ( secrecy_sKS @ secret ) ),
inference(cnf_transformation,[status(thm)],[f975]) ).
thf(f975,plain,
( m
= ( secrecy_sKS @ secret ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( m
= ( secrecy_sKS @ secret ) ),
file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_1_a2) ).
thf(f1893,plain,
( ( knowle945212990e_know @ q @ m )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1170]) ).
thf(f1170,plain,
( ( knowle945212990e_know @ q @ m )
!= $true ),
inference(flattening,[status(thm)],[f913]) ).
thf(f913,plain,
( ( knowle945212990e_know @ q @ m )
!= $true ),
inference(fool_elimination,[status(thm)],[f912]) ).
thf(f912,plain,
~ ( knowle945212990e_know @ q @ m ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
~ ( knowle945212990e_know @ q @ m ),
file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_0_not__knowQm) ).
thf(f2522,plain,
( $true
= ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2516]) ).
thf(f2516,plain,
( ( $false = $true )
| ( $true
= ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) ) ) ),
inference(superposition,[status(thm)],[f2377,f1081]) ).
thf(f1081,plain,
! [X2: $o,X1: $o] :
( ( ( X1
| X2 )
= $true )
| ( $false = X2 ) ),
introduced(definition,[],[logical_or_proxy_axiom]) ).
thf(f2377,plain,
( ( ( ?? @ secrecy_chanID
@ ^ [Y0: secrecy_chanID] :
( ( member1967978193chanID @ Y0 @ ( ins @ q ) )
& ( exprChannel @ Y0 @ ( secrecy_sE @ secret ) ) ) )
| $true )
= ( knowle945212990e_know @ q @ ( secrecy_sKS @ secret ) ) ),
inference(superposition,[status(thm)],[f2318,f1930]) ).
thf(f1930,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1162]) ).
thf(f1162,plain,
( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
= $true ),
inference(flattening,[status(thm)],[f876]) ).
thf(f876,plain,
~ ( ( ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f875]) ).
thf(f875,plain,
~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',conj_0) ).
thf(f2318,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( ( ?? @ secrecy_chanID
@ ^ [Y0: secrecy_chanID] :
( ( member1967978193chanID @ Y0 @ ( ins @ X1 ) )
& ( exprChannel @ Y0 @ ( secrecy_sE @ X0 ) ) ) )
| ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
= ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2166]) ).
thf(f2166,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) )
= ( ( ^ [Y0: secrecy_specID,Y1: secrecy_Expression] :
( ?? @ secrecy_chanID
@ ^ [Y2: secrecy_chanID] :
( ( member1967978193chanID @ Y2 @ ( ins @ Y0 ) )
& ( exprChannel @ Y2 @ Y1 ) ) )
@ X1
@ ( secrecy_sE @ X0 ) )
| ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1875,f1794]) ).
thf(f1794,plain,
( ine
= ( ^ [Y0: secrecy_specID,Y1: secrecy_Expression] :
( ?? @ secrecy_chanID
@ ^ [Y2: secrecy_chanID] :
( ( member1967978193chanID @ Y2 @ ( ins @ Y0 ) )
& ( exprChannel @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
thf(f396,plain,
( ine
= ( ^ [Y0: secrecy_specID,Y1: secrecy_Expression] :
( ?? @ secrecy_chanID
@ ^ [Y2: secrecy_chanID] :
( ( member1967978193chanID @ Y2 @ ( ins @ Y0 ) )
& ( exprChannel @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f395]) ).
thf(f395,plain,
( ine
= ( ^ [X0: secrecy_specID,X1: secrecy_Expression] :
? [X2: secrecy_chanID] :
( ( exprChannel @ X2 @ X1 )
& ( member1967978193chanID @ X2 @ ( ins @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f192]) ).
thf(f192,axiom,
( ine
= ( ^ [X40: secrecy_specID,X42: secrecy_Expression] :
? [X43: secrecy_chanID] :
( ( exprChannel @ X43 @ X42 )
& ( member1967978193chanID @ X43 @ ( ins @ X40 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_191_ine__def) ).
thf(f1875,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( ( ine @ X1 @ ( secrecy_sE @ X0 ) )
| ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
= ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f426]) ).
thf(f426,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( ( ine @ X1 @ ( secrecy_sE @ X0 ) )
| ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) ) )
= ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f425]) ).
thf(f425,plain,
! [X0: secrecy_Secrets,X1: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ X0 ) @ ( localSecrets @ X1 ) )
| ( ( ine @ X1 @ ( secrecy_sE @ X0 ) )
= ( knowle945212990e_know @ X1 @ ( secrecy_sKS @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X3: secrecy_Secrets,X2: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ X3 ) @ ( localSecrets @ X2 ) )
| ( ( ine @ X2 @ ( secrecy_sE @ X3 ) )
= ( knowle945212990e_know @ X2 @ ( secrecy_sKS @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_8_know_Osimps_I2_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP091^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:53 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : ITP091^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.46 % Domain : Interactive Theorem Proving
% 0.27/0.46 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_460__3295970_1
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Des21]
% 0.27/0.46 % Names : KnowledgeKeysSecrets/prob_460__3295970_1 [Des21]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % 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
% 0.27/0.46 % Syntax : Number of formulae : 447 ( 176 unt; 91 typ; 0 def)
% 0.27/0.46 % Number of atoms : 1276 ( 456 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.27/0.46 % Number of connectives : 3881 ( 291 ~; 51 |; 125 &;2855 @)
% 0.27/0.46 % ( 0 <=>; 559 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 19 ( 7 avg)
% 0.27/0.46 % Number of types : 14 ( 13 usr)
% 0.27/0.46 % Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 79 ( 78 usr; 10 con; 0-3 aty)
% 0.27/0.46 % Number of variables : 999 ( 56 ^; 898 !; 45 ?; 999 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:35:59.539
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % Could-be-implicit typings (13)
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.27/0.46 list_S529945141ession: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.27/0.46 set_Secrecy_Secrets: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.27/0.46 set_Secrecy_specID: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.27/0.46 set_Secrecy_chanID: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.27/0.46 set_Secrecy_Keys: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.27/0.46 set_Secrecy_KS: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.27/0.46 secrecy_Expression: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.27/0.46 secrecy_Secrets: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.27/0.46 secrecy_specID: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Secrecy____types__OchanID,type,
% 0.27/0.46 secrecy_chanID: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.27/0.46 secrecy_Keys: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.27/0.46 secrecy_KS: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.27/0.46 nat: $tType ).
% 0.27/0.46
% 0.27/0.46 % Explicit typings (78)
% 0.27/0.46 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.27/0.46 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.27/0.46 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.27/0.46 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.27/0.46 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.27/0.46 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.27/0.46 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.27/0.46 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.27/0.46 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.27/0.46 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 0.27/0.46 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 0.27/0.46 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 0.27/0.46 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 0.27/0.46 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 0.27/0.46 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.27/0.46 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.27/0.46 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.27/0.46 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.27/0.46 bot_bo443197316chanID: set_Secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.27/0.46 bot_bo1785112429specID: set_Secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.27/0.46 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.27/0.46 correctCompositionKS: secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_Oeout,type,
% 0.27/0.46 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OeoutM,type,
% 0.27/0.46 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OexprChannel,type,
% 0.27/0.46 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.27/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OineM,type,
% 0.27/0.46 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.27/0.46 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.27/0.46 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.27/0.46 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.27/0.46 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.27/0.46 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.27/0.46 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.27/0.46 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.27/0.46 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.27/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.27/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.27/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.27/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.27/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.27/0.46 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.27/0.46 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.27/0.46 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 0.27/0.46 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 0.27/0.46 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 0.27/0.46 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 0.27/0.46 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 0.27/0.46 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 0.27/0.46 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 0.27/0.46 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 0.27/0.46 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 0.27/0.46 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 0.27/0.46 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 0.27/0.46 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 0.27/0.46 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 0.27/0.46 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 0.27/0.46 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 0.27/0.46 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 0.27/0.46 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.27/0.46 correctCompositionIn: secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.27/0.46 correc965049635ionLoc: secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.27/0.46 correc990227761ionOut: secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_OinStream,type,
% 0.27/0.46 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_Oins,type,
% 0.27/0.46 ins: secrecy_specID > set_Secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_Oloc,type,
% 0.27/0.46 loc: secrecy_specID > set_Secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_OlocStream,type,
% 0.27/0.46 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_Oout,type,
% 0.27/0.46 out: secrecy_specID > set_Secrecy_chanID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_OoutStream,type,
% 0.27/0.46 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_inout_Osubcomponents,type,
% 0.27/0.46 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.27/0.46 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.27/0.46 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.27/0.46 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 0.27/0.46 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 0.27/0.46 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_P,type,
% 0.27/0.46 p: secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_PQ,type,
% 0.27/0.46 pq: secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_Q,type,
% 0.27/0.46 q: secrecy_specID ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_m,type,
% 0.27/0.46 m: secrecy_KS ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_secret____,type,
% 0.27/0.46 secret: secrecy_Secrets ).
% 0.27/0.46
% 0.27/0.46 % Relevant facts (355)
% 0.27/0.46 thf(fact_0_not__knowQm,axiom,
% 0.27/0.46 ~ ( knowle945212990e_know @ q @ m ) ).
% 0.27/0.46
% 0.27/0.46 % not_knowQm
% 0.27/0.46 thf(fact_1_a2,axiom,
% 0.27/0.46 ( m
% 0.27/0.46 = ( secrecy_sKS @ secret ) ) ).
% 0.27/0.46
% 0.27/0.46 % a2
% 0.27/0.46 thf(fact_2_knowPQ,axiom,
% 0.27/0.46 knowle945212990e_know @ pq @ m ).
% 0.27/0.46
% 0.27/0.46 % knowPQ
% 0.27/0.46 thf(fact_3_sg5,axiom,
% 0.27/0.46 member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ).
% 0.27/0.46
% 0.27/0.46 % sg5
% 0.27/0.46 thf(fact_4_KS_Oinject_I2_J,axiom,
% 0.27/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.27/0.46 ( ( ( secrecy_sKS @ X2 )
% 0.27/0.46 = ( secrecy_sKS @ Y2 ) )
% 0.27/0.46 = ( X2 = Y2 ) ) ).
% 0.27/0.46
% 0.27/0.46 % KS.inject(2)
% 0.27/0.46 thf(fact_5_sg6a,axiom,
% 0.27/0.46 ~ ( ine @ q @ ( secrecy_sE @ secret ) ) ).
% 0.27/0.46
% 0.27/0.46 % sg6a
% 0.27/0.46 thf(fact_6_cCompLoc,axiom,
% 0.27/0.46 correc965049635ionLoc @ pq ).
% 0.27/0.46
% 0.27/0.46 % cCompLoc
% 0.27/0.46 thf(fact_7_a22,axiom,
% 0.27/0.46 ~ ( ine @ pq @ ( secrecy_sE @ secret ) ) ).
% 0.27/0.46
% 0.27/0.46 % a22
% 0.27/0.46 thf(fact_8_know_Osimps_I2_J,axiom,
% 0.27/0.46 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.46 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.46 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.27/0.46 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % know.simps(2)
% 0.27/0.46 thf(fact_9_subPQ,axiom,
% 0.27/0.46 ( ( subcomponents @ pq )
% 0.27/0.46 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % subPQ
% 0.27/0.46 thf(fact_10_cCompI,axiom,
% 0.27/0.46 correctCompositionIn @ pq ).
% 0.27/0.46
% 0.27/0.46 % cCompI
% 0.27/0.46 thf(fact_11_KS_Odistinct_I1_J,axiom,
% 0.27/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.27/0.46 ( ( secrecy_kKS @ X1 )
% 0.27/0.46 != ( secrecy_sKS @ X2 ) ) ).
% 0.27/0.46
% 0.27/0.46 % KS.distinct(1)
% 0.27/0.46 thf(fact_12_KS_Oinduct,axiom,
% 0.27/0.46 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.27/0.46 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 0.27/0.46 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 0.27/0.46 => ( P @ KS ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % KS.induct
% 0.27/0.46 thf(fact_13_KS_Oinject_I1_J,axiom,
% 0.27/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.27/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.27/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.27/0.46 = ( X1 = Y1 ) ) ).
% 0.27/0.46
% 0.27/0.46 % KS.inject(1)
% 0.27/0.46 thf(fact_14_Expression_Oinject_I2_J,axiom,
% 0.27/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.27/0.46 ( ( ( secrecy_sE @ X2 )
% 0.27/0.46 = ( secrecy_sE @ Y2 ) )
% 0.27/0.46 = ( X2 = Y2 ) ) ).
% 0.27/0.46
% 0.27/0.46 % Expression.inject(2)
% 0.27/0.46 thf(fact_15_know__composition__neg1,axiom,
% 0.27/0.46 ! [P: secrecy_specID,M: secrecy_KS,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.46 ( ~ ( knowle945212990e_know @ P @ M )
% 0.27/0.46 => ( ~ ( knowle945212990e_know @ Q @ M )
% 0.27/0.46 => ( ( ( subcomponents @ PQ )
% 0.27/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.46 => ( ( correctCompositionIn @ PQ )
% 0.27/0.46 => ~ ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % know_composition_neg1
% 0.27/0.46 thf(fact_16_know__composition__neg__ine__s,axiom,
% 0.27/0.46 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.46 ( ~ ( knowle945212990e_know @ P @ ( secrecy_sKS @ Secret ) )
% 0.27/0.46 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 0.27/0.46 => ( ( ( subcomponents @ PQ )
% 0.27/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.46 => ( ( correctCompositionIn @ PQ )
% 0.27/0.46 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % know_composition_neg_ine_s
% 0.27/0.46 thf(fact_17_not__know__s__not__ine,axiom,
% 0.27/0.46 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.46 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.46 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % not_know_s_not_ine
% 0.27/0.46 thf(fact_18_KS_Oexhaust,axiom,
% 0.27/0.46 ! [Y: secrecy_KS] :
% 0.27/0.46 ( ! [X12: secrecy_Keys] :
% 0.27/0.46 ( Y
% 0.27/0.46 != ( secrecy_kKS @ X12 ) )
% 0.27/0.46 => ~ ! [X22: secrecy_Secrets] :
% 0.27/0.46 ( Y
% 0.27/0.46 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % KS.exhaust
% 0.27/0.46 thf(fact_19_LocalSecretsComposition__ine1__s,axiom,
% 0.27/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.46 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.27/0.46 => ( ( ( subcomponents @ PQ )
% 0.27/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.27/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.27/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.27/0.46 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % LocalSecretsComposition_ine1_s
% 0.27/0.46 thf(fact_20_LocalSecretsComposition__ine2__s,axiom,
% 0.27/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.46 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.27/0.46 => ( ( ( subcomponents @ PQ )
% 0.27/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.27/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.27/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.27/0.46 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % LocalSecretsComposition_ine2_s
% 0.27/0.46 thf(fact_21_LocalSecretsComposition__neg1__s,axiom,
% 0.27/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.27/0.46 ( ( ( subcomponents @ PQ )
% 0.27/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.27/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.27/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.27/0.46 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.27/0.46 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg1_s
% 0.27/0.47 thf(fact_22_TBtheorem1a,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( ine @ PQ @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( ine @ P @ E )
% 0.27/0.47 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem1a
% 0.27/0.47 thf(fact_23_TBtheorem3a,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ~ ( ine @ P @ E )
% 0.27/0.47 => ( ~ ( ine @ Q @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem3a
% 0.27/0.47 thf(fact_24_singletonI,axiom,
% 0.27/0.47 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonI
% 0.27/0.47 thf(fact_25_singletonI,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonI
% 0.27/0.47 thf(fact_26_singletonI,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonI
% 0.27/0.47 thf(fact_27_singletonI,axiom,
% 0.27/0.47 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonI
% 0.27/0.47 thf(fact_28_singletonI,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonI
% 0.27/0.47 thf(fact_29_LocalSecretsComposition1,axiom,
% 0.27/0.47 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition1
% 0.27/0.47 thf(fact_30_insertCI,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.27/0.47 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 0.27/0.47 => ( A2 = B2 ) )
% 0.27/0.47 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertCI
% 0.27/0.47 thf(fact_31_insertCI,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.27/0.47 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 0.27/0.47 => ( A2 = B2 ) )
% 0.27/0.47 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertCI
% 0.27/0.47 thf(fact_32_insertCI,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.27/0.47 ( ( ~ ( member740727610specID @ A2 @ B )
% 0.27/0.47 => ( A2 = B2 ) )
% 0.27/0.47 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertCI
% 0.27/0.47 thf(fact_33_insertCI,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.27/0.47 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 0.27/0.47 => ( A2 = B2 ) )
% 0.27/0.47 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertCI
% 0.27/0.47 thf(fact_34_insertCI,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.27/0.47 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 0.27/0.47 => ( A2 = B2 ) )
% 0.27/0.47 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertCI
% 0.27/0.47 thf(fact_35_insert__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.27/0.47 = ( ( A2 = B2 )
% 0.27/0.47 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_iff
% 0.27/0.47 thf(fact_36_insert__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.27/0.47 = ( ( A2 = B2 )
% 0.27/0.47 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_iff
% 0.27/0.47 thf(fact_37_insert__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.27/0.47 = ( ( A2 = B2 )
% 0.27/0.47 | ( member740727610specID @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_iff
% 0.27/0.47 thf(fact_38_insert__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.27/0.47 = ( ( A2 = B2 )
% 0.27/0.47 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_iff
% 0.27/0.47 thf(fact_39_insert__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.27/0.47 = ( ( A2 = B2 )
% 0.27/0.47 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_iff
% 0.27/0.47 thf(fact_40_insert__absorb2,axiom,
% 0.27/0.47 ! [X3: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X3 @ A ) )
% 0.27/0.47 = ( insert1671894227specID @ X3 @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_absorb2
% 0.27/0.47 thf(fact_41_insert__absorb2,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ X3 @ A ) )
% 0.27/0.47 = ( insert751661162chanID @ X3 @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_absorb2
% 0.27/0.47 thf(fact_42_empty__Collect__eq,axiom,
% 0.27/0.47 ! [P: secrecy_specID > $o] :
% 0.27/0.47 ( ( bot_bo1785112429specID
% 0.27/0.47 = ( collec1545797240specID @ P ) )
% 0.27/0.47 = ( ! [X4: secrecy_specID] :
% 0.27/0.47 ~ ( P @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % empty_Collect_eq
% 0.27/0.47 thf(fact_43_empty__Collect__eq,axiom,
% 0.27/0.47 ! [P: secrecy_chanID > $o] :
% 0.27/0.47 ( ( bot_bo443197316chanID
% 0.27/0.47 = ( collec625564175chanID @ P ) )
% 0.27/0.47 = ( ! [X4: secrecy_chanID] :
% 0.27/0.47 ~ ( P @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % empty_Collect_eq
% 0.27/0.47 thf(fact_44_Collect__empty__eq,axiom,
% 0.27/0.47 ! [P: secrecy_specID > $o] :
% 0.27/0.47 ( ( ( collec1545797240specID @ P )
% 0.27/0.47 = bot_bo1785112429specID )
% 0.27/0.47 = ( ! [X4: secrecy_specID] :
% 0.27/0.47 ~ ( P @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_empty_eq
% 0.27/0.47 thf(fact_45_Collect__empty__eq,axiom,
% 0.27/0.47 ! [P: secrecy_chanID > $o] :
% 0.27/0.47 ( ( ( collec625564175chanID @ P )
% 0.27/0.47 = bot_bo443197316chanID )
% 0.27/0.47 = ( ! [X4: secrecy_chanID] :
% 0.27/0.47 ~ ( P @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_empty_eq
% 0.27/0.47 thf(fact_46_all__not__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS] :
% 0.27/0.47 ( ( ! [X4: secrecy_KS] :
% 0.27/0.47 ~ ( member_Secrecy_KS @ X4 @ A ) )
% 0.27/0.47 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.27/0.47
% 0.27/0.47 % all_not_in_conv
% 0.27/0.47 thf(fact_47_all__not__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( ! [X4: secrecy_Keys] :
% 0.27/0.47 ~ ( member_Secrecy_Keys @ X4 @ A ) )
% 0.27/0.47 = ( A = bot_bo701486667y_Keys ) ) ).
% 0.27/0.47
% 0.27/0.47 % all_not_in_conv
% 0.27/0.47 thf(fact_48_all__not__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( ! [X4: secrecy_Secrets] :
% 0.27/0.47 ~ ( member2138796287ecrets @ X4 @ A ) )
% 0.27/0.47 = ( A = bot_bo1124690338ecrets ) ) ).
% 0.27/0.47
% 0.27/0.47 % all_not_in_conv
% 0.27/0.47 thf(fact_49_all__not__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID] :
% 0.27/0.47 ( ( ! [X4: secrecy_specID] :
% 0.27/0.47 ~ ( member740727610specID @ X4 @ A ) )
% 0.27/0.47 = ( A = bot_bo1785112429specID ) ) ).
% 0.27/0.47
% 0.27/0.47 % all_not_in_conv
% 0.27/0.47 thf(fact_50_all__not__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ! [X4: secrecy_chanID] :
% 0.27/0.47 ~ ( member1967978193chanID @ X4 @ A ) )
% 0.27/0.47 = ( A = bot_bo443197316chanID ) ) ).
% 0.27/0.47
% 0.27/0.47 % all_not_in_conv
% 0.27/0.47 thf(fact_51_empty__iff,axiom,
% 0.27/0.47 ! [C: secrecy_KS] :
% 0.27/0.47 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 0.27/0.47
% 0.27/0.47 % empty_iff
% 0.27/0.47 thf(fact_52_empty__iff,axiom,
% 0.27/0.47 ! [C: secrecy_Keys] :
% 0.27/0.47 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 0.27/0.47
% 0.27/0.47 % empty_iff
% 0.27/0.47 thf(fact_53_empty__iff,axiom,
% 0.27/0.47 ! [C: secrecy_Secrets] :
% 0.27/0.47 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 0.27/0.47
% 0.27/0.47 % empty_iff
% 0.27/0.47 thf(fact_54_empty__iff,axiom,
% 0.27/0.47 ! [C: secrecy_specID] :
% 0.27/0.47 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 0.27/0.47
% 0.27/0.47 % empty_iff
% 0.27/0.47 thf(fact_55_empty__iff,axiom,
% 0.27/0.47 ! [C: secrecy_chanID] :
% 0.27/0.47 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 0.27/0.47
% 0.27/0.47 % empty_iff
% 0.27/0.47 thf(fact_56_ex__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS] :
% 0.27/0.47 ( ( ? [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ A ) )
% 0.27/0.47 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 0.27/0.47
% 0.27/0.47 % ex_in_conv
% 0.27/0.47 thf(fact_57_ex__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( ? [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 0.27/0.47 = ( A != bot_bo701486667y_Keys ) ) ).
% 0.27/0.47
% 0.27/0.47 % ex_in_conv
% 0.27/0.47 thf(fact_58_ex__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( ? [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 0.27/0.47 = ( A != bot_bo1124690338ecrets ) ) ).
% 0.27/0.47
% 0.27/0.47 % ex_in_conv
% 0.27/0.47 thf(fact_59_ex__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID] :
% 0.27/0.47 ( ( ? [X4: secrecy_specID] : ( member740727610specID @ X4 @ A ) )
% 0.27/0.47 = ( A != bot_bo1785112429specID ) ) ).
% 0.27/0.47
% 0.27/0.47 % ex_in_conv
% 0.27/0.47 thf(fact_60_ex__in__conv,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ? [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ A ) )
% 0.27/0.47 = ( A != bot_bo443197316chanID ) ) ).
% 0.27/0.47
% 0.27/0.47 % ex_in_conv
% 0.27/0.47 thf(fact_61_equals0I,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS] :
% 0.27/0.47 ( ! [Y3: secrecy_KS] :
% 0.27/0.47 ~ ( member_Secrecy_KS @ Y3 @ A )
% 0.27/0.47 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0I
% 0.27/0.47 thf(fact_62_equals0I,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Keys] :
% 0.27/0.47 ( ! [Y3: secrecy_Keys] :
% 0.27/0.47 ~ ( member_Secrecy_Keys @ Y3 @ A )
% 0.27/0.47 => ( A = bot_bo701486667y_Keys ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0I
% 0.27/0.47 thf(fact_63_equals0I,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ! [Y3: secrecy_Secrets] :
% 0.27/0.47 ~ ( member2138796287ecrets @ Y3 @ A )
% 0.27/0.47 => ( A = bot_bo1124690338ecrets ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0I
% 0.27/0.47 thf(fact_64_equals0I,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID] :
% 0.27/0.47 ( ! [Y3: secrecy_specID] :
% 0.27/0.47 ~ ( member740727610specID @ Y3 @ A )
% 0.27/0.47 => ( A = bot_bo1785112429specID ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0I
% 0.27/0.47 thf(fact_65_equals0I,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ! [Y3: secrecy_chanID] :
% 0.27/0.47 ~ ( member1967978193chanID @ Y3 @ A )
% 0.27/0.47 => ( A = bot_bo443197316chanID ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0I
% 0.27/0.47 thf(fact_66_equals0D,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 0.27/0.47 ( ( A = bot_bo1943466239ecy_KS )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0D
% 0.27/0.47 thf(fact_67_equals0D,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 0.27/0.47 ( ( A = bot_bo701486667y_Keys )
% 0.27/0.47 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0D
% 0.27/0.47 thf(fact_68_equals0D,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 0.27/0.47 ( ( A = bot_bo1124690338ecrets )
% 0.27/0.47 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0D
% 0.27/0.47 thf(fact_69_equals0D,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 0.27/0.47 ( ( A = bot_bo1785112429specID )
% 0.27/0.47 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0D
% 0.27/0.47 thf(fact_70_equals0D,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 0.27/0.47 ( ( A = bot_bo443197316chanID )
% 0.27/0.47 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % equals0D
% 0.27/0.47 thf(fact_71_emptyE,axiom,
% 0.27/0.47 ! [A2: secrecy_KS] :
% 0.27/0.47 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 0.27/0.47
% 0.27/0.47 % emptyE
% 0.27/0.47 thf(fact_72_emptyE,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys] :
% 0.27/0.47 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 0.27/0.47
% 0.27/0.47 % emptyE
% 0.27/0.47 thf(fact_73_emptyE,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets] :
% 0.27/0.47 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 0.27/0.47
% 0.27/0.47 % emptyE
% 0.27/0.47 thf(fact_74_emptyE,axiom,
% 0.27/0.47 ! [A2: secrecy_specID] :
% 0.27/0.47 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 0.27/0.47
% 0.27/0.47 % emptyE
% 0.27/0.47 thf(fact_75_emptyE,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID] :
% 0.27/0.47 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 0.27/0.47
% 0.27/0.47 % emptyE
% 0.27/0.47 thf(fact_76_mk__disjoint__insert,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ A2 @ A )
% 0.27/0.47 => ? [B3: set_Secrecy_KS] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 0.27/0.47 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mk_disjoint_insert
% 0.27/0.47 thf(fact_77_mk__disjoint__insert,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ A2 @ A )
% 0.27/0.47 => ? [B3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert751661162chanID @ A2 @ B3 ) )
% 0.27/0.47 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mk_disjoint_insert
% 0.27/0.47 thf(fact_78_mk__disjoint__insert,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ A2 @ A )
% 0.27/0.47 => ? [B3: set_Secrecy_specID] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert1671894227specID @ A2 @ B3 ) )
% 0.27/0.47 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mk_disjoint_insert
% 0.27/0.47 thf(fact_79_mk__disjoint__insert,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.27/0.47 => ? [B3: set_Secrecy_Keys] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 0.27/0.47 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mk_disjoint_insert
% 0.27/0.47 thf(fact_80_mk__disjoint__insert,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ A2 @ A )
% 0.27/0.47 => ? [B3: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert565337510ecrets @ A2 @ B3 ) )
% 0.27/0.47 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % mk_disjoint_insert
% 0.27/0.47 thf(fact_81_insert__commute,axiom,
% 0.27/0.47 ! [X3: secrecy_specID,Y: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ Y @ A ) )
% 0.27/0.47 = ( insert1671894227specID @ Y @ ( insert1671894227specID @ X3 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_commute
% 0.27/0.47 thf(fact_82_insert__commute,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID,Y: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ Y @ A ) )
% 0.27/0.47 = ( insert751661162chanID @ Y @ ( insert751661162chanID @ X3 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_commute
% 0.27/0.47 thf(fact_83_insert__eq__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 0.27/0.47 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 0.27/0.47 = ( insert_Secrecy_KS @ B2 @ B ) )
% 0.27/0.47 = ( ( ( A2 = B2 )
% 0.27/0.47 => ( A = B ) )
% 0.27/0.47 & ( ( A2 != B2 )
% 0.27/0.47 => ? [C2: set_Secrecy_KS] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 0.27/0.47 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 0.27/0.47 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_eq_iff
% 0.27/0.47 thf(fact_84_insert__eq__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( member1967978193chanID @ A2 @ A )
% 0.27/0.47 => ( ~ ( member1967978193chanID @ B2 @ B )
% 0.27/0.47 => ( ( ( insert751661162chanID @ A2 @ A )
% 0.27/0.47 = ( insert751661162chanID @ B2 @ B ) )
% 0.27/0.47 = ( ( ( A2 = B2 )
% 0.27/0.47 => ( A = B ) )
% 0.27/0.47 & ( ( A2 != B2 )
% 0.27/0.47 => ? [C2: set_Secrecy_chanID] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert751661162chanID @ B2 @ C2 ) )
% 0.27/0.47 & ~ ( member1967978193chanID @ B2 @ C2 )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert751661162chanID @ A2 @ C2 ) )
% 0.27/0.47 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_eq_iff
% 0.27/0.47 thf(fact_85_insert__eq__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ~ ( member740727610specID @ A2 @ A )
% 0.27/0.47 => ( ~ ( member740727610specID @ B2 @ B )
% 0.27/0.47 => ( ( ( insert1671894227specID @ A2 @ A )
% 0.27/0.47 = ( insert1671894227specID @ B2 @ B ) )
% 0.27/0.47 = ( ( ( A2 = B2 )
% 0.27/0.47 => ( A = B ) )
% 0.27/0.47 & ( ( A2 != B2 )
% 0.27/0.47 => ? [C2: set_Secrecy_specID] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert1671894227specID @ B2 @ C2 ) )
% 0.27/0.47 & ~ ( member740727610specID @ B2 @ C2 )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert1671894227specID @ A2 @ C2 ) )
% 0.27/0.47 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_eq_iff
% 0.27/0.47 thf(fact_86_insert__eq__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 0.27/0.47 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 0.27/0.47 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 0.27/0.47 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.27/0.47 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 0.27/0.47 = ( ( ( A2 = B2 )
% 0.27/0.47 => ( A = B ) )
% 0.27/0.47 & ( ( A2 != B2 )
% 0.27/0.47 => ? [C2: set_Secrecy_Keys] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 0.27/0.47 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 0.27/0.47 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_eq_iff
% 0.27/0.47 thf(fact_87_insert__eq__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.27/0.47 ( ~ ( member2138796287ecrets @ A2 @ A )
% 0.27/0.47 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 0.27/0.47 => ( ( ( insert565337510ecrets @ A2 @ A )
% 0.27/0.47 = ( insert565337510ecrets @ B2 @ B ) )
% 0.27/0.47 = ( ( ( A2 = B2 )
% 0.27/0.47 => ( A = B ) )
% 0.27/0.47 & ( ( A2 != B2 )
% 0.27/0.47 => ? [C2: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert565337510ecrets @ B2 @ C2 ) )
% 0.27/0.47 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert565337510ecrets @ A2 @ C2 ) )
% 0.27/0.47 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_eq_iff
% 0.27/0.47 thf(fact_88_insert__absorb,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ A2 @ A )
% 0.27/0.47 => ( ( insert_Secrecy_KS @ A2 @ A )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_absorb
% 0.27/0.47 thf(fact_89_insert__absorb,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ A2 @ A )
% 0.27/0.47 => ( ( insert751661162chanID @ A2 @ A )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_absorb
% 0.27/0.47 thf(fact_90_insert__absorb,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ A2 @ A )
% 0.27/0.47 => ( ( insert1671894227specID @ A2 @ A )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_absorb
% 0.27/0.47 thf(fact_91_insert__absorb,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.27/0.47 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_absorb
% 0.27/0.47 thf(fact_92_insert__absorb,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ A2 @ A )
% 0.27/0.47 => ( ( insert565337510ecrets @ A2 @ A )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_absorb
% 0.27/0.47 thf(fact_93_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 0.27/0.47 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 0.27/0.47 = ( P @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_94_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 0.27/0.47 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 0.27/0.47 = ( P @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_95_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 0.27/0.47 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 0.27/0.47 = ( P @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_96_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 0.27/0.47 = ( P @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_97_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.27/0.47 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 0.27/0.47 = ( P @ A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_98_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS] :
% 0.27/0.47 ( ( collect_Secrecy_KS
% 0.27/0.47 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ A ) )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_99_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( collec625564175chanID
% 0.27/0.47 @ ^ [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ A ) )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_100_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID] :
% 0.27/0.47 ( ( collec1545797240specID
% 0.27/0.47 @ ^ [X4: secrecy_specID] : ( member740727610specID @ X4 @ A ) )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_101_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( collect_Secrecy_Keys
% 0.27/0.47 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_102_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( collec836099393ecrets
% 0.27/0.47 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_103_insert__ident,axiom,
% 0.27/0.47 ! [X3: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ~ ( member_Secrecy_KS @ X3 @ A )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ X3 @ B )
% 0.27/0.47 => ( ( ( insert_Secrecy_KS @ X3 @ A )
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ B ) )
% 0.27/0.47 = ( A = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_ident
% 0.27/0.47 thf(fact_104_insert__ident,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( member1967978193chanID @ X3 @ A )
% 0.27/0.47 => ( ~ ( member1967978193chanID @ X3 @ B )
% 0.27/0.47 => ( ( ( insert751661162chanID @ X3 @ A )
% 0.27/0.47 = ( insert751661162chanID @ X3 @ B ) )
% 0.27/0.47 = ( A = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_ident
% 0.27/0.47 thf(fact_105_insert__ident,axiom,
% 0.27/0.47 ! [X3: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ~ ( member740727610specID @ X3 @ A )
% 0.27/0.47 => ( ~ ( member740727610specID @ X3 @ B )
% 0.27/0.47 => ( ( ( insert1671894227specID @ X3 @ A )
% 0.27/0.47 = ( insert1671894227specID @ X3 @ B ) )
% 0.27/0.47 = ( A = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_ident
% 0.27/0.47 thf(fact_106_insert__ident,axiom,
% 0.27/0.47 ! [X3: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.27/0.47 ( ~ ( member_Secrecy_Keys @ X3 @ A )
% 0.27/0.47 => ( ~ ( member_Secrecy_Keys @ X3 @ B )
% 0.27/0.47 => ( ( ( insert_Secrecy_Keys @ X3 @ A )
% 0.27/0.47 = ( insert_Secrecy_Keys @ X3 @ B ) )
% 0.27/0.47 = ( A = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_ident
% 0.27/0.47 thf(fact_107_insert__ident,axiom,
% 0.27/0.47 ! [X3: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.27/0.47 ( ~ ( member2138796287ecrets @ X3 @ A )
% 0.27/0.47 => ( ~ ( member2138796287ecrets @ X3 @ B )
% 0.27/0.47 => ( ( ( insert565337510ecrets @ X3 @ A )
% 0.27/0.47 = ( insert565337510ecrets @ X3 @ B ) )
% 0.27/0.47 = ( A = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_ident
% 0.27/0.47 thf(fact_108_Set_Oset__insert,axiom,
% 0.27/0.47 ! [X3: secrecy_KS,A: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X3 @ A )
% 0.27/0.47 => ~ ! [B3: set_Secrecy_KS] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ B3 ) )
% 0.27/0.47 => ( member_Secrecy_KS @ X3 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Set.set_insert
% 0.27/0.47 thf(fact_109_Set_Oset__insert,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X3 @ A )
% 0.27/0.47 => ~ ! [B3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert751661162chanID @ X3 @ B3 ) )
% 0.27/0.47 => ( member1967978193chanID @ X3 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Set.set_insert
% 0.27/0.47 thf(fact_110_Set_Oset__insert,axiom,
% 0.27/0.47 ! [X3: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ X3 @ A )
% 0.27/0.47 => ~ ! [B3: set_Secrecy_specID] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert1671894227specID @ X3 @ B3 ) )
% 0.27/0.47 => ( member740727610specID @ X3 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Set.set_insert
% 0.27/0.47 thf(fact_111_Set_Oset__insert,axiom,
% 0.27/0.47 ! [X3: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ X3 @ A )
% 0.27/0.47 => ~ ! [B3: set_Secrecy_Keys] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert_Secrecy_Keys @ X3 @ B3 ) )
% 0.27/0.47 => ( member_Secrecy_Keys @ X3 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Set.set_insert
% 0.27/0.47 thf(fact_112_Set_Oset__insert,axiom,
% 0.27/0.47 ! [X3: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ X3 @ A )
% 0.27/0.47 => ~ ! [B3: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( insert565337510ecrets @ X3 @ B3 ) )
% 0.27/0.47 => ( member2138796287ecrets @ X3 @ B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Set.set_insert
% 0.27/0.47 thf(fact_113_insertI2,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ A2 @ B )
% 0.27/0.47 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI2
% 0.27/0.47 thf(fact_114_insertI2,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ A2 @ B )
% 0.27/0.47 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI2
% 0.27/0.47 thf(fact_115_insertI2,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ A2 @ B )
% 0.27/0.47 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI2
% 0.27/0.47 thf(fact_116_insertI2,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ A2 @ B )
% 0.27/0.47 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI2
% 0.27/0.47 thf(fact_117_insertI2,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ A2 @ B )
% 0.27/0.47 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI2
% 0.27/0.47 thf(fact_118_insertI1,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI1
% 0.27/0.47 thf(fact_119_insertI1,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI1
% 0.27/0.47 thf(fact_120_insertI1,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI1
% 0.27/0.47 thf(fact_121_insertI1,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI1
% 0.27/0.47 thf(fact_122_insertI1,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertI1
% 0.27/0.47 thf(fact_123_insertE,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertE
% 0.27/0.47 thf(fact_124_insertE,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertE
% 0.27/0.47 thf(fact_125_insertE,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( member740727610specID @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertE
% 0.27/0.47 thf(fact_126_insertE,axiom,
% 0.27/0.47 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertE
% 0.27/0.47 thf(fact_127_insertE,axiom,
% 0.27/0.47 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.27/0.47 => ( ( A2 != B2 )
% 0.27/0.47 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insertE
% 0.27/0.47 thf(fact_128_singleton__inject,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 0.27/0.47 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 0.27/0.47 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.27/0.47 => ( A2 = B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_inject
% 0.27/0.47 thf(fact_129_singleton__inject,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 0.27/0.47 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 0.27/0.47 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.27/0.47 => ( A2 = B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_inject
% 0.27/0.47 thf(fact_130_insert__not__empty,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( insert1671894227specID @ A2 @ A )
% 0.27/0.47 != bot_bo1785112429specID ) ).
% 0.27/0.47
% 0.27/0.47 % insert_not_empty
% 0.27/0.47 thf(fact_131_insert__not__empty,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( insert751661162chanID @ A2 @ A )
% 0.27/0.47 != bot_bo443197316chanID ) ).
% 0.27/0.47
% 0.27/0.47 % insert_not_empty
% 0.27/0.47 thf(fact_132_doubleton__eq__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 0.27/0.47 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.27/0.47 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 0.27/0.47 = ( ( ( A2 = C )
% 0.27/0.47 & ( B2 = D ) )
% 0.27/0.47 | ( ( A2 = D )
% 0.27/0.47 & ( B2 = C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % doubleton_eq_iff
% 0.27/0.47 thf(fact_133_doubleton__eq__iff,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 0.27/0.47 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.27/0.47 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 0.27/0.47 = ( ( ( A2 = C )
% 0.27/0.47 & ( B2 = D ) )
% 0.27/0.47 | ( ( A2 = D )
% 0.27/0.47 & ( B2 = C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % doubleton_eq_iff
% 0.27/0.47 thf(fact_134_singleton__iff,axiom,
% 0.27/0.47 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.27/0.47 = ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_iff
% 0.27/0.47 thf(fact_135_singleton__iff,axiom,
% 0.27/0.47 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.27/0.47 = ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_iff
% 0.27/0.47 thf(fact_136_singleton__iff,axiom,
% 0.27/0.47 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.27/0.47 = ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_iff
% 0.27/0.47 thf(fact_137_singleton__iff,axiom,
% 0.27/0.47 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.27/0.47 = ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_iff
% 0.27/0.47 thf(fact_138_singleton__iff,axiom,
% 0.27/0.47 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.27/0.47 = ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_iff
% 0.27/0.47 thf(fact_139_singletonD,axiom,
% 0.27/0.47 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.27/0.47 => ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonD
% 0.27/0.47 thf(fact_140_singletonD,axiom,
% 0.27/0.47 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.27/0.47 => ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonD
% 0.27/0.47 thf(fact_141_singletonD,axiom,
% 0.27/0.47 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.27/0.47 => ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonD
% 0.27/0.47 thf(fact_142_singletonD,axiom,
% 0.27/0.47 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.27/0.47 => ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonD
% 0.27/0.47 thf(fact_143_singletonD,axiom,
% 0.27/0.47 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.27/0.47 => ( B2 = A2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % singletonD
% 0.27/0.47 thf(fact_144_LocalSecretsComposition__neg1,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.47 => ( ! [M2: secrecy_Keys] :
% 0.27/0.47 ( ( Ks
% 0.27/0.47 = ( secrecy_kKS @ M2 ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 0.27/0.47 & ~ ( ine @ Q @ ( secrecy_kE @ M2 ) ) ) )
% 0.27/0.47 => ( ! [M2: secrecy_Secrets] :
% 0.27/0.47 ( ( Ks
% 0.27/0.47 = ( secrecy_sKS @ M2 ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 0.27/0.47 & ~ ( ine @ Q @ ( secrecy_sE @ M2 ) ) ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg1
% 0.27/0.47 thf(fact_145_the__elem__eq,axiom,
% 0.27/0.47 ! [X3: secrecy_specID] :
% 0.27/0.47 ( ( the_el827131246specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % the_elem_eq
% 0.27/0.47 thf(fact_146_the__elem__eq,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID] :
% 0.27/0.47 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % the_elem_eq
% 0.27/0.47 thf(fact_147_LocalSecretsComposition__neg1__k,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.27/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg1_k
% 0.27/0.47 thf(fact_148_LocalSecretsComposition__ine2__k,axiom,
% 0.27/0.47 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.27/0.47 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_ine2_k
% 0.27/0.47 thf(fact_149_LocalSecretsComposition__ine1__k,axiom,
% 0.27/0.47 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.27/0.47 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_ine1_k
% 0.27/0.47 thf(fact_150_know__composition__neg__ine__k,axiom,
% 0.27/0.47 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ~ ( knowle945212990e_know @ P @ ( secrecy_kKS @ Key ) )
% 0.27/0.47 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_kKS @ Key ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % know_composition_neg_ine_k
% 0.27/0.47 thf(fact_151_is__singletonI,axiom,
% 0.27/0.47 ! [X3: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonI
% 0.27/0.47 thf(fact_152_is__singletonI,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonI
% 0.27/0.47 thf(fact_153_KS2Expression_Osimps_I2_J,axiom,
% 0.27/0.47 ! [M: secrecy_Secrets] :
% 0.27/0.47 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.27/0.47 = ( secrecy_sE @ M ) ) ).
% 0.27/0.47
% 0.27/0.47 % KS2Expression.simps(2)
% 0.27/0.47 thf(fact_154_Expression_Oinject_I1_J,axiom,
% 0.27/0.47 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.27/0.47 ( ( ( secrecy_kE @ X1 )
% 0.27/0.47 = ( secrecy_kE @ Y1 ) )
% 0.27/0.47 = ( X1 = Y1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Expression.inject(1)
% 0.27/0.47 thf(fact_155_KS2Expression_Osimps_I1_J,axiom,
% 0.27/0.47 ! [M: secrecy_Keys] :
% 0.27/0.47 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.27/0.47 = ( secrecy_kE @ M ) ) ).
% 0.27/0.47
% 0.27/0.47 % KS2Expression.simps(1)
% 0.27/0.47 thf(fact_156_bot__set__def,axiom,
% 0.27/0.47 ( bot_bo1785112429specID
% 0.27/0.47 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_set_def
% 0.27/0.47 thf(fact_157_bot__set__def,axiom,
% 0.27/0.47 ( bot_bo443197316chanID
% 0.27/0.47 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_set_def
% 0.27/0.47 thf(fact_158_Expression_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.27/0.47 ( ( secrecy_kE @ X1 )
% 0.27/0.47 != ( secrecy_sE @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Expression.distinct(1)
% 0.27/0.47 thf(fact_159_is__singleton__the__elem,axiom,
% 0.27/0.47 ( is_sin1501507247specID
% 0.27/0.47 = ( ^ [A3: set_Secrecy_specID] :
% 0.27/0.47 ( A3
% 0.27/0.47 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singleton_the_elem
% 0.27/0.47 thf(fact_160_is__singleton__the__elem,axiom,
% 0.27/0.47 ( is_sin581274182chanID
% 0.27/0.47 = ( ^ [A3: set_Secrecy_chanID] :
% 0.27/0.47 ( A3
% 0.27/0.47 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singleton_the_elem
% 0.27/0.47 thf(fact_161_is__singletonI_H,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS] :
% 0.27/0.47 ( ( A != bot_bo1943466239ecy_KS )
% 0.27/0.47 => ( ! [X: secrecy_KS,Y3: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X @ A )
% 0.27/0.47 => ( ( member_Secrecy_KS @ Y3 @ A )
% 0.27/0.47 => ( X = Y3 ) ) )
% 0.27/0.47 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonI'
% 0.27/0.47 thf(fact_162_is__singletonI_H,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( A != bot_bo701486667y_Keys )
% 0.27/0.47 => ( ! [X: secrecy_Keys,Y3: secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ X @ A )
% 0.27/0.47 => ( ( member_Secrecy_Keys @ Y3 @ A )
% 0.27/0.47 => ( X = Y3 ) ) )
% 0.27/0.47 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonI'
% 0.27/0.47 thf(fact_163_is__singletonI_H,axiom,
% 0.27/0.47 ! [A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( A != bot_bo1124690338ecrets )
% 0.27/0.47 => ( ! [X: secrecy_Secrets,Y3: secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ X @ A )
% 0.27/0.47 => ( ( member2138796287ecrets @ Y3 @ A )
% 0.27/0.47 => ( X = Y3 ) ) )
% 0.27/0.47 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonI'
% 0.27/0.47 thf(fact_164_is__singletonI_H,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID] :
% 0.27/0.47 ( ( A != bot_bo1785112429specID )
% 0.27/0.47 => ( ! [X: secrecy_specID,Y3: secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ X @ A )
% 0.27/0.47 => ( ( member740727610specID @ Y3 @ A )
% 0.27/0.47 => ( X = Y3 ) ) )
% 0.27/0.47 => ( is_sin1501507247specID @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonI'
% 0.27/0.47 thf(fact_165_is__singletonI_H,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( A != bot_bo443197316chanID )
% 0.27/0.47 => ( ! [X: secrecy_chanID,Y3: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ A )
% 0.27/0.47 => ( ( member1967978193chanID @ Y3 @ A )
% 0.27/0.47 => ( X = Y3 ) ) )
% 0.27/0.47 => ( is_sin581274182chanID @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonI'
% 0.27/0.47 thf(fact_166_not__know__k__not__ine,axiom,
% 0.27/0.47 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.47 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.47 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_know_k_not_ine
% 0.27/0.47 thf(fact_167_is__singletonE,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID] :
% 0.27/0.47 ( ( is_sin1501507247specID @ A )
% 0.27/0.47 => ~ ! [X: secrecy_specID] :
% 0.27/0.47 ( A
% 0.27/0.47 != ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonE
% 0.27/0.47 thf(fact_168_is__singletonE,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( is_sin581274182chanID @ A )
% 0.27/0.47 => ~ ! [X: secrecy_chanID] :
% 0.27/0.47 ( A
% 0.27/0.47 != ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singletonE
% 0.27/0.47 thf(fact_169_is__singleton__def,axiom,
% 0.27/0.47 ( is_sin1501507247specID
% 0.27/0.47 = ( ^ [A3: set_Secrecy_specID] :
% 0.27/0.47 ? [X4: secrecy_specID] :
% 0.27/0.47 ( A3
% 0.27/0.47 = ( insert1671894227specID @ X4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singleton_def
% 0.27/0.47 thf(fact_170_is__singleton__def,axiom,
% 0.27/0.47 ( is_sin581274182chanID
% 0.27/0.47 = ( ^ [A3: set_Secrecy_chanID] :
% 0.27/0.47 ? [X4: secrecy_chanID] :
% 0.27/0.47 ( A3
% 0.27/0.47 = ( insert751661162chanID @ X4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % is_singleton_def
% 0.27/0.47 thf(fact_171_know_Osimps_I1_J,axiom,
% 0.27/0.47 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.47 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.47 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.27/0.47 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % know.simps(1)
% 0.27/0.47 thf(fact_172_TBtheorem4a__empty,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ( ine @ P @ E )
% 0.27/0.47 | ( ine @ Q @ E ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( ( loc @ PQ )
% 0.27/0.47 = bot_bo443197316chanID )
% 0.27/0.47 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4a_empty
% 0.27/0.47 thf(fact_173_TBtheorem1b,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( ineM @ PQ @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( ineM @ P @ M3 @ E )
% 0.27/0.47 | ( ineM @ Q @ M3 @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem1b
% 0.27/0.47 thf(fact_174_TBtheorem3b,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ~ ( ineM @ P @ M3 @ E )
% 0.27/0.47 => ( ~ ( ineM @ Q @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem3b
% 0.27/0.47 thf(fact_175_Set_Ois__empty__def,axiom,
% 0.27/0.47 ( is_emp1849217361specID
% 0.27/0.47 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Set.is_empty_def
% 0.27/0.47 thf(fact_176_Set_Ois__empty__def,axiom,
% 0.27/0.47 ( is_emp928984296chanID
% 0.27/0.47 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Set.is_empty_def
% 0.27/0.47 thf(fact_177_correctCompositionIn__L2,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionIn_L2
% 0.27/0.47 thf(fact_178_correctCompositionIn__prop1,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 0.27/0.47 | ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionIn_prop1
% 0.27/0.47 thf(fact_179_TBtheorem4a__notP1,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ine @ P @ E )
% 0.27/0.47 => ( ~ ( ine @ Q @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4a_notP1
% 0.27/0.47 thf(fact_180_not__ine__ineM,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,M3: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( ine @ P @ E )
% 0.27/0.47 => ~ ( ineM @ P @ M3 @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_ine_ineM
% 0.27/0.47 thf(fact_181_ineM__ine,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( ineM @ P @ M3 @ E )
% 0.27/0.47 => ( ine @ P @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % ineM_ine
% 0.27/0.47 thf(fact_182_TBtheorem4b__notP1,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ineM @ P @ M3 @ E )
% 0.27/0.47 => ( ~ ( ineM @ Q @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4b_notP1
% 0.27/0.47 thf(fact_183_correctCompositionIn__L1,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionIn_L1
% 0.27/0.47 thf(fact_184_subcomponents__loc,axiom,
% 0.27/0.47 ! [X3: secrecy_specID] :
% 0.27/0.47 ( ( correc965049635ionLoc @ X3 )
% 0.27/0.47 => ( ( ( subcomponents @ X3 )
% 0.27/0.47 = bot_bo1785112429specID )
% 0.27/0.47 => ( ( loc @ X3 )
% 0.27/0.47 = bot_bo443197316chanID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subcomponents_loc
% 0.27/0.47 thf(fact_185_TBtheorem4b__notPQ,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.27/0.47 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetP )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4b_notPQ
% 0.27/0.47 thf(fact_186_TBtheorem4b__notP2,axiom,
% 0.27/0.47 ! [Q: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( ineM @ Q @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSet )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4b_notP2
% 0.27/0.47 thf(fact_187_TBtheorem4a__notPQ,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.27/0.47 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetP )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4a_notPQ
% 0.27/0.47 thf(fact_188_TBtheorem4a__notP2,axiom,
% 0.27/0.47 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( ine @ Q @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSet )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4a_notP2
% 0.27/0.47 thf(fact_189_TBtheorem4b__PQ,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ( ineM @ P @ M3 @ E )
% 0.27/0.47 | ( ineM @ Q @ M3 @ E ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.27/0.47 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4b_PQ
% 0.27/0.47 thf(fact_190_ine__exprChannelSet__def,axiom,
% 0.27/0.47 ( ine_exprChannelSet
% 0.27/0.47 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.27/0.47 ( ! [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ ChSet2 )
% 0.27/0.47 => ( ( member1967978193chanID @ X4 @ ( ins @ SP ) )
% 0.27/0.47 & ( exprChannel @ X4 @ E2 ) ) )
% 0.27/0.47 & ! [X4: secrecy_chanID] :
% 0.27/0.47 ( ( ~ ( member1967978193chanID @ X4 @ ChSet2 )
% 0.27/0.47 & ( member1967978193chanID @ X4 @ ( ins @ SP ) ) )
% 0.27/0.47 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_exprChannelSet_def
% 0.27/0.47 thf(fact_191_ine__def,axiom,
% 0.27/0.47 ( ine
% 0.27/0.47 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.27/0.47 ? [Ch3: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.27/0.47 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_def
% 0.27/0.47 thf(fact_192_ine__ins__neg1,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M: secrecy_Expression,X3: secrecy_chanID] :
% 0.27/0.47 ( ~ ( ine @ P @ M )
% 0.27/0.47 => ( ( exprChannel @ X3 @ M )
% 0.27/0.47 => ~ ( member1967978193chanID @ X3 @ ( ins @ P ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_ins_neg1
% 0.27/0.47 thf(fact_193_ineM__def,axiom,
% 0.27/0.47 ( ineM
% 0.27/0.47 = ( ^ [SP: secrecy_specID,M4: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.27/0.47 ? [Ch3: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.27/0.47 & ( member1967978193chanID @ Ch3 @ M4 )
% 0.27/0.47 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ineM_def
% 0.27/0.47 thf(fact_194_ineM__L1,axiom,
% 0.27/0.47 ! [Ch: secrecy_chanID,M3: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch @ M3 )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ E )
% 0.27/0.47 => ( ineM @ P @ M3 @ E ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ineM_L1
% 0.27/0.47 thf(fact_195_ine__exprChannelSingle__def,axiom,
% 0.27/0.47 ( ine_ex1303305700Single
% 0.27/0.47 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.27/0.47 & ( exprChannel @ Ch3 @ E2 )
% 0.27/0.47 & ! [X4: secrecy_chanID,T: nat] :
% 0.27/0.47 ( ( ( member1967978193chanID @ X4 @ ( ins @ SP ) )
% 0.27/0.47 & ( X4 != Ch3 ) )
% 0.27/0.47 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_exprChannelSingle_def
% 0.27/0.47 thf(fact_196_LocalSecretsComposition__exprChannel__s,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( exprChannel @ X3 @ ( secrecy_sE @ Secrets ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.27/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.27/0.47 => ( ~ ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 0.27/0.47 & ~ ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_exprChannel_s
% 0.27/0.47 thf(fact_197_LocalSecretsComposition__exprChannel__k,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( exprChannel @ X3 @ ( secrecy_kE @ Keys ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.27/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.27/0.47 => ( ~ ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 0.27/0.47 & ~ ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_exprChannel_k
% 0.27/0.47 thf(fact_198_ine__nonempty__exprChannelSet,axiom,
% 0.27/0.47 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.27/0.47 => ( ( ChSet != bot_bo443197316chanID )
% 0.27/0.47 => ( ine @ P @ E ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_nonempty_exprChannelSet
% 0.27/0.47 thf(fact_199_ine__empty__exprChannelSet,axiom,
% 0.27/0.47 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.27/0.47 => ( ( ChSet = bot_bo443197316chanID )
% 0.27/0.47 => ~ ( ine @ P @ E ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_empty_exprChannelSet
% 0.27/0.47 thf(fact_200_ine__exprChannelSingle__Set,axiom,
% 0.27/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.27/0.47 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_exprChannelSingle_Set
% 0.27/0.47 thf(fact_201_ine__exprChannelSet__Single,axiom,
% 0.27/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.27/0.47 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % ine_exprChannelSet_Single
% 0.27/0.47 thf(fact_202_correctCompositionInLoc__exprChannel,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ M )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 0.27/0.47 => ~ ( exprChannel @ X @ M ) )
% 0.27/0.47 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionInLoc_exprChannel
% 0.27/0.47 thf(fact_203_TBlemma3b,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.27/0.47 ( ~ ( ineM @ P @ M3 @ E )
% 0.27/0.47 => ( ~ ( ineM @ Q @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ M3 )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.27/0.47 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBlemma3b
% 0.27/0.47 thf(fact_204_TBtheorem4a__P,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( ine @ P @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4a_P
% 0.27/0.47 thf(fact_205_TBtheorem4a__PQ,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ( ine @ P @ E )
% 0.27/0.47 | ( ine @ Q @ E ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.27/0.47 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4a_PQ
% 0.27/0.47 thf(fact_206_TBtheorem4b__P,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( ineM @ P @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ M3 ) )
% 0.27/0.47 => ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem4b_P
% 0.27/0.47 thf(fact_207_locStream__def,axiom,
% 0.27/0.47 ( locStream
% 0.27/0.47 = ( ^ [X4: secrecy_specID] :
% 0.27/0.47 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.27/0.47 @ ( loc @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % locStream_def
% 0.27/0.47 thf(fact_208_inStream__def,axiom,
% 0.27/0.47 ( inStream
% 0.27/0.47 = ( ^ [X4: secrecy_specID] :
% 0.27/0.47 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.27/0.47 @ ( ins @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % inStream_def
% 0.27/0.47 thf(fact_209_Collect__empty__eq__bot,axiom,
% 0.27/0.47 ! [P: secrecy_specID > $o] :
% 0.27/0.47 ( ( ( collec1545797240specID @ P )
% 0.27/0.47 = bot_bo1785112429specID )
% 0.27/0.47 = ( P = bot_bo1767780696ecID_o ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_empty_eq_bot
% 0.27/0.47 thf(fact_210_Collect__empty__eq__bot,axiom,
% 0.27/0.47 ! [P: secrecy_chanID > $o] :
% 0.27/0.47 ( ( ( collec625564175chanID @ P )
% 0.27/0.47 = bot_bo443197316chanID )
% 0.27/0.47 = ( P = bot_bo1012329985anID_o ) ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_empty_eq_bot
% 0.27/0.47 thf(fact_211_bot__empty__eq,axiom,
% 0.27/0.47 ( bot_bot_Secrecy_KS_o
% 0.27/0.47 = ( ^ [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ bot_bo1943466239ecy_KS ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_empty_eq
% 0.27/0.47 thf(fact_212_bot__empty__eq,axiom,
% 0.27/0.47 ( bot_bo2072920570Keys_o
% 0.27/0.47 = ( ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ bot_bo701486667y_Keys ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_empty_eq
% 0.27/0.47 thf(fact_213_bot__empty__eq,axiom,
% 0.27/0.47 ( bot_bo1909946299rets_o
% 0.27/0.47 = ( ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ bot_bo1124690338ecrets ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_empty_eq
% 0.27/0.47 thf(fact_214_bot__empty__eq,axiom,
% 0.27/0.47 ( bot_bo1767780696ecID_o
% 0.27/0.47 = ( ^ [X4: secrecy_specID] : ( member740727610specID @ X4 @ bot_bo1785112429specID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_empty_eq
% 0.27/0.47 thf(fact_215_bot__empty__eq,axiom,
% 0.27/0.47 ( bot_bo1012329985anID_o
% 0.27/0.47 = ( ^ [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ bot_bo443197316chanID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_empty_eq
% 0.27/0.47 thf(fact_216_LocalSecretsComposition__neg__loc__s,axiom,
% 0.27/0.47 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.27/0.47 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg_loc_s
% 0.27/0.47 thf(fact_217_LocalSecretsComposition__neg__loc__k,axiom,
% 0.27/0.47 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.27/0.47 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg_loc_k
% 0.27/0.47 thf(fact_218_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ? [Ch4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_s_Qex
% 0.27/0.47 thf(fact_219_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ? [Ch4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_s_Pex
% 0.27/0.47 thf(fact_220_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_s_Q
% 0.27/0.47 thf(fact_221_correctCompositionKS__exprChannel__s__P,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_s_P
% 0.27/0.47 thf(fact_222_correctCompositionKS__PQ,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.27/0.47 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_PQ
% 0.27/0.47 thf(fact_223_correctCompositionKS__neg1,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_neg1
% 0.27/0.47 thf(fact_224_correctCompositionKS__negP,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_negP
% 0.27/0.47 thf(fact_225_correctCompositionKS__negQ,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_negQ
% 0.27/0.47 thf(fact_226_know__composition,axiom,
% 0.27/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.27/0.47 => ( ( ( knowle945212990e_know @ P @ M )
% 0.27/0.47 | ( knowle945212990e_know @ Q @ M ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % know_composition
% 0.27/0.47 thf(fact_227_know__composition1,axiom,
% 0.27/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.27/0.47 => ( ( knowle945212990e_know @ P @ M )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % know_composition1
% 0.27/0.47 thf(fact_228_know__composition2,axiom,
% 0.27/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.27/0.47 => ( ( knowle945212990e_know @ Q @ M )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % know_composition2
% 0.27/0.47 thf(fact_229_correctCompositionKS__exprChannel__k__P,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_k_P
% 0.27/0.47 thf(fact_230_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_k_Q
% 0.27/0.47 thf(fact_231_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ? [Ch4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_k_Pex
% 0.27/0.47 thf(fact_232_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.27/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.27/0.47 => ( ( correctCompositionIn @ PQ )
% 0.27/0.47 => ? [Ch4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.27/0.47 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_exprChannel_k_Qex
% 0.27/0.47 thf(fact_233_LocalSecretsComposition__neg,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.27/0.47 => ( ! [M2: secrecy_Keys] :
% 0.27/0.47 ( ( Ks
% 0.27/0.47 = ( secrecy_kKS @ M2 ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 0.27/0.47 & ~ ( ine @ Q @ ( secrecy_kE @ M2 ) ) ) )
% 0.27/0.47 => ( ! [M2: secrecy_Secrets] :
% 0.27/0.47 ( ( Ks
% 0.27/0.47 = ( secrecy_sKS @ M2 ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 0.27/0.47 & ~ ( ine @ Q @ ( secrecy_sE @ M2 ) ) ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg
% 0.27/0.47 thf(fact_234_LocalSecretsComposition__neg__s,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.27/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg_s
% 0.27/0.47 thf(fact_235_LocalSecretsComposition__neg__k,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.27/0.47 => ( ( correctCompositionKS @ PQ )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.27/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.27/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % LocalSecretsComposition_neg_k
% 0.27/0.47 thf(fact_236_notSpecKeysSecretsExpr__def,axiom,
% 0.27/0.47 ( notSpe1586871396tsExpr
% 0.27/0.47 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 0.27/0.47 ( ! [X4: secrecy_Keys] :
% 0.27/0.47 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E3 )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.27/0.47 & ! [Y5: secrecy_Secrets] :
% 0.27/0.47 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y5 ) @ E3 )
% 0.27/0.47 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y5 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % notSpecKeysSecretsExpr_def
% 0.27/0.47 thf(fact_237_UnCI,axiom,
% 0.27/0.47 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( ~ ( member740727610specID @ C @ B )
% 0.27/0.47 => ( member740727610specID @ C @ A ) )
% 0.27/0.47 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnCI
% 0.27/0.47 thf(fact_238_UnCI,axiom,
% 0.27/0.47 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 0.27/0.47 => ( member_Secrecy_Keys @ C @ A ) )
% 0.27/0.47 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnCI
% 0.27/0.47 thf(fact_239_UnCI,axiom,
% 0.27/0.47 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( ~ ( member2138796287ecrets @ C @ B )
% 0.27/0.47 => ( member2138796287ecrets @ C @ A ) )
% 0.27/0.47 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnCI
% 0.27/0.47 thf(fact_240_UnCI,axiom,
% 0.27/0.47 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.27/0.47 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 0.27/0.47 => ( member_Secrecy_KS @ C @ A ) )
% 0.27/0.47 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnCI
% 0.27/0.47 thf(fact_241_UnCI,axiom,
% 0.27/0.47 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ~ ( member1967978193chanID @ C @ B )
% 0.27/0.47 => ( member1967978193chanID @ C @ A ) )
% 0.27/0.47 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnCI
% 0.27/0.47 thf(fact_242_Un__iff,axiom,
% 0.27/0.47 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.27/0.47 = ( ( member740727610specID @ C @ A )
% 0.27/0.47 | ( member740727610specID @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_iff
% 0.27/0.47 thf(fact_243_Un__iff,axiom,
% 0.27/0.47 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.27/0.47 = ( ( member_Secrecy_Keys @ C @ A )
% 0.27/0.47 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_iff
% 0.27/0.47 thf(fact_244_Un__iff,axiom,
% 0.27/0.47 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.27/0.47 = ( ( member2138796287ecrets @ C @ A )
% 0.27/0.47 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_iff
% 0.27/0.47 thf(fact_245_Un__iff,axiom,
% 0.27/0.47 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.27/0.47 = ( ( member_Secrecy_KS @ C @ A )
% 0.27/0.47 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_iff
% 0.27/0.47 thf(fact_246_Un__iff,axiom,
% 0.27/0.47 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.27/0.47 = ( ( member1967978193chanID @ C @ A )
% 0.27/0.47 | ( member1967978193chanID @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_iff
% 0.27/0.47 thf(fact_247_Un__empty,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.27/0.47 = bot_bo1943466239ecy_KS )
% 0.27/0.47 = ( ( A = bot_bo1943466239ecy_KS )
% 0.27/0.47 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty
% 0.27/0.47 thf(fact_248_Un__empty,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ( ( sup_su1712599557specID @ A @ B )
% 0.27/0.47 = bot_bo1785112429specID )
% 0.27/0.47 = ( ( A = bot_bo1785112429specID )
% 0.27/0.47 & ( B = bot_bo1785112429specID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty
% 0.27/0.47 thf(fact_249_Un__empty,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ( sup_su370684444chanID @ A @ B )
% 0.27/0.47 = bot_bo443197316chanID )
% 0.27/0.47 = ( ( A = bot_bo443197316chanID )
% 0.27/0.47 & ( B = bot_bo443197316chanID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty
% 0.27/0.47 thf(fact_250_Un__insert__right,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 0.27/0.47 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_insert_right
% 0.27/0.47 thf(fact_251_Un__insert__right,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 0.27/0.47 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_insert_right
% 0.27/0.47 thf(fact_252_Un__insert__right,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 0.27/0.47 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_insert_right
% 0.27/0.47 thf(fact_253_Un__insert__left,axiom,
% 0.27/0.47 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 0.27/0.47 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_insert_left
% 0.27/0.47 thf(fact_254_Un__insert__left,axiom,
% 0.27/0.47 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 0.27/0.47 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_insert_left
% 0.27/0.47 thf(fact_255_Un__insert__left,axiom,
% 0.27/0.47 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 0.27/0.47 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_insert_left
% 0.27/0.47 thf(fact_256_UnE,axiom,
% 0.27/0.47 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.27/0.47 => ( ~ ( member740727610specID @ C @ A )
% 0.27/0.47 => ( member740727610specID @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnE
% 0.27/0.47 thf(fact_257_UnE,axiom,
% 0.27/0.47 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 0.27/0.47 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnE
% 0.27/0.47 thf(fact_258_UnE,axiom,
% 0.27/0.47 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.27/0.47 => ( ~ ( member2138796287ecrets @ C @ A )
% 0.27/0.47 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnE
% 0.27/0.47 thf(fact_259_UnE,axiom,
% 0.27/0.47 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.27/0.47 => ( ~ ( member_Secrecy_KS @ C @ A )
% 0.27/0.47 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnE
% 0.27/0.47 thf(fact_260_UnE,axiom,
% 0.27/0.47 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.27/0.47 => ( ~ ( member1967978193chanID @ C @ A )
% 0.27/0.47 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnE
% 0.27/0.47 thf(fact_261_UnI1,axiom,
% 0.27/0.47 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ C @ A )
% 0.27/0.47 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI1
% 0.27/0.47 thf(fact_262_UnI1,axiom,
% 0.27/0.47 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ C @ A )
% 0.27/0.47 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI1
% 0.27/0.47 thf(fact_263_UnI1,axiom,
% 0.27/0.47 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ C @ A )
% 0.27/0.47 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI1
% 0.27/0.47 thf(fact_264_UnI1,axiom,
% 0.27/0.47 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ C @ A )
% 0.27/0.47 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI1
% 0.27/0.47 thf(fact_265_UnI1,axiom,
% 0.27/0.47 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ C @ A )
% 0.27/0.47 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI1
% 0.27/0.47 thf(fact_266_UnI2,axiom,
% 0.27/0.47 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ C @ B )
% 0.27/0.47 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI2
% 0.27/0.47 thf(fact_267_UnI2,axiom,
% 0.27/0.47 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.27/0.47 ( ( member_Secrecy_Keys @ C @ B )
% 0.27/0.47 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI2
% 0.27/0.47 thf(fact_268_UnI2,axiom,
% 0.27/0.47 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.27/0.47 ( ( member2138796287ecrets @ C @ B )
% 0.27/0.47 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI2
% 0.27/0.47 thf(fact_269_UnI2,axiom,
% 0.27/0.47 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ C @ B )
% 0.27/0.47 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI2
% 0.27/0.47 thf(fact_270_UnI2,axiom,
% 0.27/0.47 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ C @ B )
% 0.27/0.47 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % UnI2
% 0.27/0.47 thf(fact_271_bex__Un,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.27/0.47 ( ( ? [X4: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X4 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.27/0.47 & ( P @ X4 ) ) )
% 0.27/0.47 = ( ? [X4: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X4 @ A )
% 0.27/0.47 & ( P @ X4 ) )
% 0.27/0.47 | ? [X4: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X4 @ B )
% 0.27/0.47 & ( P @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % bex_Un
% 0.27/0.47 thf(fact_272_bex__Un,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.27/0.47 ( ( ? [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ ( sup_su370684444chanID @ A @ B ) )
% 0.27/0.47 & ( P @ X4 ) ) )
% 0.27/0.47 = ( ? [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ A )
% 0.27/0.47 & ( P @ X4 ) )
% 0.27/0.47 | ? [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ B )
% 0.27/0.47 & ( P @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % bex_Un
% 0.27/0.47 thf(fact_273_ball__Un,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.27/0.47 ( ( ! [X4: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X4 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.27/0.47 => ( P @ X4 ) ) )
% 0.27/0.47 = ( ! [X4: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X4 @ A )
% 0.27/0.47 => ( P @ X4 ) )
% 0.27/0.47 & ! [X4: secrecy_KS] :
% 0.27/0.47 ( ( member_Secrecy_KS @ X4 @ B )
% 0.27/0.47 => ( P @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ball_Un
% 0.27/0.47 thf(fact_274_ball__Un,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.27/0.47 ( ( ! [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ ( sup_su370684444chanID @ A @ B ) )
% 0.27/0.47 => ( P @ X4 ) ) )
% 0.27/0.47 = ( ! [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ A )
% 0.27/0.47 => ( P @ X4 ) )
% 0.27/0.47 & ! [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ B )
% 0.27/0.47 => ( P @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ball_Un
% 0.27/0.47 thf(fact_275_Un__assoc,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 0.27/0.47 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_assoc
% 0.27/0.47 thf(fact_276_Un__assoc,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 0.27/0.47 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_assoc
% 0.27/0.47 thf(fact_277_Un__absorb,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ A @ A )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Un_absorb
% 0.27/0.47 thf(fact_278_Un__absorb,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ A @ A )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Un_absorb
% 0.27/0.47 thf(fact_279_Un__commute,axiom,
% 0.27/0.47 ( sup_su1301156759ecy_KS
% 0.27/0.47 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_commute
% 0.27/0.47 thf(fact_280_Un__commute,axiom,
% 0.27/0.47 ( sup_su370684444chanID
% 0.27/0.47 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_commute
% 0.27/0.47 thf(fact_281_Un__left__absorb,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.27/0.47 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_left_absorb
% 0.27/0.47 thf(fact_282_Un__left__absorb,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 0.27/0.47 = ( sup_su370684444chanID @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_left_absorb
% 0.27/0.47 thf(fact_283_Un__left__commute,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 0.27/0.47 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_left_commute
% 0.27/0.47 thf(fact_284_Un__left__commute,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 0.27/0.47 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_left_commute
% 0.27/0.47 thf(fact_285_Un__empty__left,axiom,
% 0.27/0.47 ! [B: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 0.27/0.47 = B ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty_left
% 0.27/0.47 thf(fact_286_Un__empty__left,axiom,
% 0.27/0.47 ! [B: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 0.27/0.47 = B ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty_left
% 0.27/0.47 thf(fact_287_Un__empty__left,axiom,
% 0.27/0.47 ! [B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 0.27/0.47 = B ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty_left
% 0.27/0.47 thf(fact_288_Un__empty__right,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty_right
% 0.27/0.47 thf(fact_289_Un__empty__right,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty_right
% 0.27/0.47 thf(fact_290_Un__empty__right,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % Un_empty_right
% 0.27/0.47 thf(fact_291_singleton__Un__iff,axiom,
% 0.27/0.47 ! [X3: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.27/0.47 ( ( ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS )
% 0.27/0.47 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.27/0.47 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.27/0.47 & ( B = bot_bo1943466239ecy_KS ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_Un_iff
% 0.27/0.47 thf(fact_292_singleton__Un__iff,axiom,
% 0.27/0.47 ! [X3: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.27/0.47 ( ( ( insert1671894227specID @ X3 @ bot_bo1785112429specID )
% 0.27/0.47 = ( sup_su1712599557specID @ A @ B ) )
% 0.27/0.47 = ( ( ( A = bot_bo1785112429specID )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.27/0.47 & ( B = bot_bo1785112429specID ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_Un_iff
% 0.27/0.47 thf(fact_293_singleton__Un__iff,axiom,
% 0.27/0.47 ! [X3: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ( insert751661162chanID @ X3 @ bot_bo443197316chanID )
% 0.27/0.47 = ( sup_su370684444chanID @ A @ B ) )
% 0.27/0.47 = ( ( ( A = bot_bo443197316chanID )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.27/0.47 & ( B = bot_bo443197316chanID ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % singleton_Un_iff
% 0.27/0.47 thf(fact_294_Un__singleton__iff,axiom,
% 0.27/0.47 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.47 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.27/0.47 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.27/0.47 & ( B = bot_bo1943466239ecy_KS ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_singleton_iff
% 0.27/0.47 thf(fact_295_Un__singleton__iff,axiom,
% 0.27/0.47 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X3: secrecy_specID] :
% 0.27/0.47 ( ( ( sup_su1712599557specID @ A @ B )
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.27/0.47 = ( ( ( A = bot_bo1785112429specID )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.27/0.47 & ( B = bot_bo1785112429specID ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_singleton_iff
% 0.27/0.47 thf(fact_296_Un__singleton__iff,axiom,
% 0.27/0.47 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X3: secrecy_chanID] :
% 0.27/0.47 ( ( ( sup_su370684444chanID @ A @ B )
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.27/0.47 = ( ( ( A = bot_bo443197316chanID )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.27/0.47 & ( B = bot_bo443197316chanID ) )
% 0.27/0.47 | ( ( A
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.27/0.47 & ( B
% 0.27/0.47 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Un_singleton_iff
% 0.27/0.47 thf(fact_297_insert__is__Un,axiom,
% 0.27/0.47 ( insert_Secrecy_KS
% 0.27/0.47 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_is_Un
% 0.27/0.47 thf(fact_298_insert__is__Un,axiom,
% 0.27/0.47 ( insert1671894227specID
% 0.27/0.47 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_is_Un
% 0.27/0.47 thf(fact_299_insert__is__Un,axiom,
% 0.27/0.47 ( insert751661162chanID
% 0.27/0.47 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_is_Un
% 0.27/0.47 thf(fact_300_sup__bot_Oright__neutral,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 0.27/0.47 = A2 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.right_neutral
% 0.27/0.47 thf(fact_301_sup__bot_Oright__neutral,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 0.27/0.47 = A2 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.right_neutral
% 0.27/0.47 thf(fact_302_sup__bot_Oright__neutral,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 0.27/0.47 = A2 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.right_neutral
% 0.27/0.47 thf(fact_303_sup__bot_Oneutr__eq__iff,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.27/0.47 ( ( bot_bo1943466239ecy_KS
% 0.27/0.47 = ( sup_su1301156759ecy_KS @ A2 @ B2 ) )
% 0.27/0.47 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.27/0.47 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.neutr_eq_iff
% 0.27/0.47 thf(fact_304_sup__bot_Oneutr__eq__iff,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.27/0.47 ( ( bot_bo1785112429specID
% 0.27/0.47 = ( sup_su1712599557specID @ A2 @ B2 ) )
% 0.27/0.47 = ( ( A2 = bot_bo1785112429specID )
% 0.27/0.47 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.neutr_eq_iff
% 0.27/0.47 thf(fact_305_sup__bot_Oneutr__eq__iff,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.27/0.47 ( ( bot_bo443197316chanID
% 0.27/0.47 = ( sup_su370684444chanID @ A2 @ B2 ) )
% 0.27/0.47 = ( ( A2 = bot_bo443197316chanID )
% 0.27/0.47 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.neutr_eq_iff
% 0.27/0.47 thf(fact_306_sup__bot_Oleft__neutral,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A2 )
% 0.27/0.47 = A2 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.left_neutral
% 0.27/0.47 thf(fact_307_sup__bot_Oleft__neutral,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A2 )
% 0.27/0.47 = A2 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.left_neutral
% 0.27/0.47 thf(fact_308_sup__bot_Oleft__neutral,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A2 )
% 0.27/0.47 = A2 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.left_neutral
% 0.27/0.47 thf(fact_309_sup__bot_Oeq__neutr__iff,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.27/0.47 ( ( ( sup_su1301156759ecy_KS @ A2 @ B2 )
% 0.27/0.47 = bot_bo1943466239ecy_KS )
% 0.27/0.47 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.27/0.47 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.eq_neutr_iff
% 0.27/0.47 thf(fact_310_sup__bot_Oeq__neutr__iff,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.27/0.47 ( ( ( sup_su1712599557specID @ A2 @ B2 )
% 0.27/0.47 = bot_bo1785112429specID )
% 0.27/0.47 = ( ( A2 = bot_bo1785112429specID )
% 0.27/0.47 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.eq_neutr_iff
% 0.27/0.47 thf(fact_311_sup__bot_Oeq__neutr__iff,axiom,
% 0.27/0.47 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ( sup_su370684444chanID @ A2 @ B2 )
% 0.27/0.47 = bot_bo443197316chanID )
% 0.27/0.47 = ( ( A2 = bot_bo443197316chanID )
% 0.27/0.47 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot.eq_neutr_iff
% 0.27/0.47 thf(fact_312_sup__bot__left,axiom,
% 0.27/0.47 ! [X3: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X3 )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot_left
% 0.27/0.47 thf(fact_313_sup__bot__left,axiom,
% 0.27/0.47 ! [X3: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X3 )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot_left
% 0.27/0.47 thf(fact_314_sup__bot__left,axiom,
% 0.27/0.47 ! [X3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X3 )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot_left
% 0.27/0.47 thf(fact_315_sup__bot__right,axiom,
% 0.27/0.47 ! [X3: set_Secrecy_KS] :
% 0.27/0.47 ( ( sup_su1301156759ecy_KS @ X3 @ bot_bo1943466239ecy_KS )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot_right
% 0.27/0.47 thf(fact_316_sup__bot__right,axiom,
% 0.27/0.47 ! [X3: set_Secrecy_specID] :
% 0.27/0.47 ( ( sup_su1712599557specID @ X3 @ bot_bo1785112429specID )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot_right
% 0.27/0.47 thf(fact_317_sup__bot__right,axiom,
% 0.27/0.47 ! [X3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( sup_su370684444chanID @ X3 @ bot_bo443197316chanID )
% 0.27/0.47 = X3 ) ).
% 0.27/0.47
% 0.27/0.47 % sup_bot_right
% 0.27/0.47 thf(fact_318_ineM__Un1,axiom,
% 0.27/0.47 ! [P: secrecy_specID,A: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ineM @ P @ A @ E )
% 0.27/0.47 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % ineM_Un1
% 0.27/0.47 thf(fact_319_TBtheorem5a__empty,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ( eout @ P @ E )
% 0.27/0.47 | ( eout @ Q @ E ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( ( loc @ PQ )
% 0.27/0.47 = bot_bo443197316chanID )
% 0.27/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5a_empty
% 0.27/0.47 thf(fact_320_correctCompositionKS__subcomp1,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Keys] :
% 0.27/0.47 ( ( correctCompositionKS @ C3 )
% 0.27/0.47 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.27/0.47 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 0.27/0.47 => ? [X: secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.27/0.47 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_subcomp1
% 0.27/0.47 thf(fact_321_correctCompositionKS__subcomp2,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Secrets] :
% 0.27/0.47 ( ( correctCompositionKS @ C3 )
% 0.27/0.47 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.27/0.47 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 0.27/0.47 => ? [X: secrecy_specID] :
% 0.27/0.47 ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.27/0.47 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_subcomp2
% 0.27/0.47 thf(fact_322_TBtheorem2a,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( eout @ PQ @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( eout @ P @ E )
% 0.27/0.47 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem2a
% 0.27/0.47 thf(fact_323_correctCompositionKS__subcomp4,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Secrets] :
% 0.27/0.47 ( ( correctCompositionKS @ C3 )
% 0.27/0.47 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.27/0.47 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X3 ) )
% 0.27/0.47 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_subcomp4
% 0.27/0.47 thf(fact_324_correctCompositionKS__subcomp3,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Keys] :
% 0.27/0.47 ( ( correctCompositionKS @ C3 )
% 0.27/0.47 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.27/0.47 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X3 ) )
% 0.27/0.47 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionKS_subcomp3
% 0.27/0.47 thf(fact_325_TBtheorem5a__notP1,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( eout @ P @ E )
% 0.27/0.47 => ( ~ ( eout @ Q @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5a_notP1
% 0.27/0.47 thf(fact_326_TBtheorem5a__notPQ,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.27/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetP )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5a_notPQ
% 0.27/0.47 thf(fact_327_TBtheorem5a__notP2,axiom,
% 0.27/0.47 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( eout @ Q @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSet )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5a_notP2
% 0.27/0.47 thf(fact_328_out__exprChannelSingle__Set,axiom,
% 0.27/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.27/0.47 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % out_exprChannelSingle_Set
% 0.27/0.47 thf(fact_329_out__exprChannelSet__Single,axiom,
% 0.27/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.27/0.47 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % out_exprChannelSet_Single
% 0.27/0.47 thf(fact_330_TBtheorem5b__notPQ,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M3: set_Secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.27/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.27/0.47 => ( ( M3
% 0.27/0.47 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetP )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5b_notPQ
% 0.27/0.47 thf(fact_331_eout__know__s,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.27/0.47 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.27/0.47 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.27/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eout_know_s
% 0.27/0.47 thf(fact_332_not__know__s__not__eout,axiom,
% 0.27/0.47 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.27/0.47 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.27/0.47 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.47 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_know_s_not_eout
% 0.27/0.47 thf(fact_333_not__eout__eoutM,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,M3: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( eout @ P @ E )
% 0.27/0.47 => ~ ( eoutM @ P @ M3 @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_eout_eoutM
% 0.27/0.47 thf(fact_334_eoutM__eout,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.27/0.47 ( ( eoutM @ P @ M3 @ E )
% 0.27/0.47 => ( eout @ P @ E ) ) ).
% 0.27/0.47
% 0.27/0.47 % eoutM_eout
% 0.27/0.47 thf(fact_335_TBtheorem2b,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( eoutM @ PQ @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( eoutM @ P @ M3 @ E )
% 0.27/0.47 | ( eoutM @ Q @ M3 @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem2b
% 0.27/0.47 thf(fact_336_TBtheorem5b__notP2,axiom,
% 0.27/0.47 ! [Q: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.27/0.47 ( ~ ( eoutM @ Q @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.27/0.47 => ( ! [X: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X @ ChSet )
% 0.27/0.47 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5b_notP2
% 0.27/0.47 thf(fact_337_TBtheorem5b__notP1,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( eoutM @ P @ M3 @ E )
% 0.27/0.47 => ( ~ ( eoutM @ Q @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5b_notP1
% 0.27/0.47 thf(fact_338_eout__know__nonKS__k,axiom,
% 0.27/0.47 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.27/0.47 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.27/0.47 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 0.27/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.47 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eout_know_nonKS_k
% 0.27/0.47 thf(fact_339_eoutKnowCorrect__L1k,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.27/0.47 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.27/0.47 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.27/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eoutKnowCorrect_L1k
% 0.27/0.47 thf(fact_340_not__know__k__not__eout,axiom,
% 0.27/0.47 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.27/0.47 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.27/0.47 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.47 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_know_k_not_eout
% 0.27/0.47 thf(fact_341_eout__know__k,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.27/0.47 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.27/0.47 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.27/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eout_know_k
% 0.27/0.47 thf(fact_342_eout__know__nonKS__s,axiom,
% 0.27/0.47 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.27/0.47 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.27/0.47 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 0.27/0.47 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.47 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eout_know_nonKS_s
% 0.27/0.47 thf(fact_343_eoutKnowCorrect__L1s,axiom,
% 0.27/0.47 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.47 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.27/0.47 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.27/0.47 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.27/0.47 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eoutKnowCorrect_L1s
% 0.27/0.47 thf(fact_344_TBtheore54b__P,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( eoutM @ P @ M3 @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ M3 ) )
% 0.27/0.47 => ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheore54b_P
% 0.27/0.47 thf(fact_345_TBtheorem5b__PQ,axiom,
% 0.27/0.47 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ( eoutM @ P @ M3 @ E )
% 0.27/0.47 | ( eoutM @ Q @ M3 @ E ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.27/0.47 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.27/0.47 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5b_PQ
% 0.27/0.47 thf(fact_346_TBtheorem45a__P,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.27/0.47 ( ( eout @ P @ E )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem45a_P
% 0.27/0.47 thf(fact_347_eout__def,axiom,
% 0.27/0.47 ( eout
% 0.27/0.47 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.27/0.47 ? [Ch3: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.27/0.47 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eout_def
% 0.27/0.47 thf(fact_348_eoutM__def,axiom,
% 0.27/0.47 ( eoutM
% 0.27/0.47 = ( ^ [SP: secrecy_specID,M4: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.27/0.47 ? [Ch3: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.27/0.47 & ( member1967978193chanID @ Ch3 @ M4 )
% 0.27/0.47 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eoutM_def
% 0.27/0.47 thf(fact_349_out__exprChannelSet__def,axiom,
% 0.27/0.47 ( out_exprChannelSet
% 0.27/0.47 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.27/0.47 ( ! [X4: secrecy_chanID] :
% 0.27/0.47 ( ( member1967978193chanID @ X4 @ ChSet2 )
% 0.27/0.47 => ( ( member1967978193chanID @ X4 @ ( out @ SP ) )
% 0.27/0.47 & ( exprChannel @ X4 @ E2 ) ) )
% 0.27/0.47 & ! [X4: secrecy_chanID] :
% 0.27/0.47 ( ( ~ ( member1967978193chanID @ X4 @ ChSet2 )
% 0.27/0.47 & ( member1967978193chanID @ X4 @ ( out @ SP ) ) )
% 0.27/0.47 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % out_exprChannelSet_def
% 0.27/0.47 thf(fact_350_out__exprChannelSingle__def,axiom,
% 0.27/0.47 ( out_ex985543062Single
% 0.27/0.47 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.27/0.47 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.27/0.47 & ( exprChannel @ Ch3 @ E2 )
% 0.27/0.47 & ! [X4: secrecy_chanID,T: nat] :
% 0.27/0.47 ( ( ( member1967978193chanID @ X4 @ ( out @ SP ) )
% 0.27/0.47 & ( X4 != Ch3 ) )
% 0.27/0.47 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % out_exprChannelSingle_def
% 0.27/0.47 thf(fact_351_correctCompositionOut__prop1,axiom,
% 0.27/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.27/0.47 ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ( member1967978193chanID @ X3 @ ( out @ PQ ) )
% 0.27/0.47 => ( ( member1967978193chanID @ X3 @ ( out @ P ) )
% 0.27/0.47 | ( member1967978193chanID @ X3 @ ( out @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % correctCompositionOut_prop1
% 0.27/0.47 thf(fact_352_TBtheorem5a__PQ,axiom,
% 0.27/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.27/0.47 ( ( ( eout @ P @ E )
% 0.27/0.47 | ( eout @ Q @ E ) )
% 0.27/0.47 => ( ( ( subcomponents @ PQ )
% 0.27/0.47 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.27/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.27/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.27/0.47 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.27/0.47 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.27/0.47 & ( exprChannel @ Ch2 @ E )
% 0.27/0.47 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.27/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % TBtheorem5a_PQ
% 0.27/0.47 thf(fact_353_outStream__def,axiom,
% 0.27/0.47 ( outStream
% 0.27/0.47 = ( ^ [X4: secrecy_specID] :
% 0.27/0.47 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.27/0.47 @ ( out @ X4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % outStream_def
% 0.27/0.47 thf(fact_354_adv__not__know2,axiom,
% 0.27/0.47 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.47 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 0.27/0.47 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.47 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % adv_not_know2
% 0.27/0.47
% 0.27/0.47 % Conjectures (1)
% 0.27/0.47 thf(conj_0,conjecture,
% 0.27/0.47 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.96/1.52 ---- Embedded in THF ---
% 2.96/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.96/1.52 %%% Generated on Tue Feb 24 08:25:54 EST 2026
% 2.96/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.96/1.52 %%% Logic specification used:
% 2.96/1.52 %%% thf(spec, logic, $$dhol).
% 2.96/1.52
% 2.96/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2DTF14089.p
% See solution above
% 2.96/1.52 ------------------------
% 2.96/1.55 ---- Cleaned THF ---
% 2.96/1.55 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 2.96/1.55 list_S529945141ession: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.96/1.55 set_Secrecy_Secrets: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.96/1.55 set_Secrecy_specID: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.96/1.55 set_Secrecy_chanID: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.96/1.55 set_Secrecy_Keys: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.96/1.55 set_Secrecy_KS: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Secrecy____types__OExpression,type,
% 2.96/1.55 secrecy_Expression: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 2.96/1.55 secrecy_Secrets: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Secrecy____types__OspecID,type,
% 2.96/1.55 secrecy_specID: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Secrecy____types__OchanID,type,
% 2.96/1.55 secrecy_chanID: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Secrecy____types__OKeys,type,
% 2.96/1.55 secrecy_Keys: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Secrecy____types__OKS,type,
% 2.96/1.55 secrecy_KS: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(ty_n_t__Nat__Onat,type,
% 2.96/1.55 nat: $tType ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.96/1.55 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 2.96/1.55 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 2.96/1.55 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.96/1.55 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.96/1.55 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.96/1.55 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.96/1.55 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.96/1.55 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 2.96/1.55 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 2.96/1.55 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 2.96/1.55 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 2.96/1.55 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 2.96/1.55 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 2.96/1.55 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 2.96/1.55 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 2.96/1.55 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 2.96/1.55 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.96/1.55 bot_bo443197316chanID: set_Secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.96/1.55 bot_bo1785112429specID: set_Secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.96/1.55 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 2.96/1.55 correctCompositionKS: secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_Oeout,type,
% 2.96/1.55 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OeoutM,type,
% 2.96/1.55 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OexprChannel,type,
% 2.96/1.55 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_Oine,type,
% 2.96/1.55 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OineM,type,
% 2.96/1.55 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 2.96/1.55 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 2.96/1.55 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 2.96/1.55 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 2.96/1.55 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 2.96/1.55 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OspecKeys,type,
% 2.96/1.55 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 2.96/1.55 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy_OspecSecrets,type,
% 2.96/1.55 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 2.96/1.55 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 2.96/1.55 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 2.96/1.55 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 2.96/1.55 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 2.96/1.55 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 2.96/1.55 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 2.96/1.55 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 2.96/1.55 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 2.96/1.55 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 2.96/1.55 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 2.96/1.55 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 2.96/1.55 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 2.96/1.55 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 2.96/1.55 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 2.96/1.55 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 2.96/1.55 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 2.96/1.55 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 2.96/1.55 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 2.96/1.55 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 2.96/1.55 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 2.96/1.55 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 2.96/1.55 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 2.96/1.55 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 2.96/1.55 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_OcorrectCompositionIn,type,
% 2.96/1.55 correctCompositionIn: secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 2.96/1.55 correc965049635ionLoc: secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_OcorrectCompositionOut,type,
% 2.96/1.55 correc990227761ionOut: secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_OinStream,type,
% 2.96/1.55 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_Oins,type,
% 2.96/1.55 ins: secrecy_specID > set_Secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_Oloc,type,
% 2.96/1.55 loc: secrecy_specID > set_Secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_OlocStream,type,
% 2.96/1.55 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_Oout,type,
% 2.96/1.55 out: secrecy_specID > set_Secrecy_chanID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_OoutStream,type,
% 2.96/1.55 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_inout_Osubcomponents,type,
% 2.96/1.55 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 2.96/1.55 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 2.96/1.55 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 2.96/1.55 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 2.96/1.55 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 2.96/1.55 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 2.96/1.55
% 2.96/1.55 thf(sy_v_P,type,
% 2.96/1.55 p: secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_v_PQ,type,
% 2.96/1.55 pq: secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_v_Q,type,
% 2.96/1.55 q: secrecy_specID ).
% 2.96/1.55
% 2.96/1.55 thf(sy_v_m,type,
% 2.96/1.55 m: secrecy_KS ).
% 2.96/1.55
% 2.96/1.55 thf(sy_v_secret____,type,
% 2.96/1.55 secret: secrecy_Secrets ).
% 2.96/1.55
% 2.96/1.55 thf(fact_0_not__knowQm,axiom,
% 2.96/1.55 ~ ( knowle945212990e_know @ q @ m ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_1_a2,axiom,
% 2.96/1.55 ( m
% 2.96/1.55 = ( secrecy_sKS @ secret ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_2_knowPQ,axiom,
% 2.96/1.55 knowle945212990e_know @ pq @ m ).
% 2.96/1.55
% 2.96/1.55 thf(fact_3_sg5,axiom,
% 2.96/1.55 member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_4_KS_Oinject_I2_J,axiom,
% 2.96/1.55 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.96/1.55 ( ( ( secrecy_sKS @ X2 )
% 2.96/1.55 = ( secrecy_sKS @ Y2 ) )
% 2.96/1.55 = ( X2 = Y2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_5_sg6a,axiom,
% 2.96/1.55 ~ ( ine @ q @ ( secrecy_sE @ secret ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_6_cCompLoc,axiom,
% 2.96/1.55 correc965049635ionLoc @ pq ).
% 2.96/1.55
% 2.96/1.55 thf(fact_7_a22,axiom,
% 2.96/1.55 ~ ( ine @ pq @ ( secrecy_sE @ secret ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_8_know_Osimps_I2_J,axiom,
% 2.96/1.55 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.96/1.55 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.96/1.55 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 2.96/1.55 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_9_subPQ,axiom,
% 2.96/1.55 ( ( subcomponents @ pq )
% 2.96/1.55 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_10_cCompI,axiom,
% 2.96/1.55 correctCompositionIn @ pq ).
% 2.96/1.55
% 2.96/1.55 thf(fact_11_KS_Odistinct_I1_J,axiom,
% 2.96/1.55 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.96/1.55 ( ( secrecy_kKS @ X1 )
% 2.96/1.55 != ( secrecy_sKS @ X2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_12_KS_Oinduct,axiom,
% 2.96/1.55 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 2.96/1.55 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 2.96/1.55 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 2.96/1.55 => ( P @ KS ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_13_KS_Oinject_I1_J,axiom,
% 2.96/1.55 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.96/1.55 ( ( ( secrecy_kKS @ X1 )
% 2.96/1.55 = ( secrecy_kKS @ Y1 ) )
% 2.96/1.55 = ( X1 = Y1 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_14_Expression_Oinject_I2_J,axiom,
% 2.96/1.55 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.96/1.55 ( ( ( secrecy_sE @ X2 )
% 2.96/1.55 = ( secrecy_sE @ Y2 ) )
% 2.96/1.55 = ( X2 = Y2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_15_know__composition__neg1,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M: secrecy_KS,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( knowle945212990e_know @ P @ M )
% 2.96/1.55 => ( ~ ( knowle945212990e_know @ Q @ M )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ~ ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_16_know__composition__neg__ine__s,axiom,
% 2.96/1.55 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( knowle945212990e_know @ P @ ( secrecy_sKS @ Secret ) )
% 2.96/1.55 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_17_not__know__s__not__ine,axiom,
% 2.96/1.55 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 2.96/1.55 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.96/1.55 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_18_KS_Oexhaust,axiom,
% 2.96/1.55 ! [Y: secrecy_KS] :
% 2.96/1.55 ( ! [X12: secrecy_Keys] :
% 2.96/1.55 ( Y
% 2.96/1.55 != ( secrecy_kKS @ X12 ) )
% 2.96/1.55 => ~ ! [X22: secrecy_Secrets] :
% 2.96/1.55 ( Y
% 2.96/1.55 != ( secrecy_sKS @ X22 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_19_LocalSecretsComposition__ine1__s,axiom,
% 2.96/1.55 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.96/1.55 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_20_LocalSecretsComposition__ine2__s,axiom,
% 2.96/1.55 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.96/1.55 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_21_LocalSecretsComposition__neg1__s,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_22_TBtheorem1a,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( ine @ PQ @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( ine @ P @ E )
% 2.96/1.55 | ( ine @ Q @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_23_TBtheorem3a,axiom,
% 2.96/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( ine @ P @ E )
% 2.96/1.55 => ( ~ ( ine @ Q @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_24_singletonI,axiom,
% 2.96/1.55 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_25_singletonI,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_26_singletonI,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_27_singletonI,axiom,
% 2.96/1.55 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_28_singletonI,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_29_LocalSecretsComposition1,axiom,
% 2.96/1.55 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_30_insertCI,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 2.96/1.55 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 2.96/1.55 => ( A2 = B2 ) )
% 2.96/1.55 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_31_insertCI,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.96/1.55 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 2.96/1.55 => ( A2 = B2 ) )
% 2.96/1.55 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_32_insertCI,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.96/1.55 ( ( ~ ( member740727610specID @ A2 @ B )
% 2.96/1.55 => ( A2 = B2 ) )
% 2.96/1.55 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_33_insertCI,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 2.96/1.55 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 2.96/1.55 => ( A2 = B2 ) )
% 2.96/1.55 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_34_insertCI,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 2.96/1.55 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 2.96/1.55 => ( A2 = B2 ) )
% 2.96/1.55 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_35_insert__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 2.96/1.55 = ( ( A2 = B2 )
% 2.96/1.55 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_36_insert__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 2.96/1.55 = ( ( A2 = B2 )
% 2.96/1.55 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_37_insert__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 2.96/1.55 = ( ( A2 = B2 )
% 2.96/1.55 | ( member740727610specID @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_38_insert__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 2.96/1.55 = ( ( A2 = B2 )
% 2.96/1.55 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_39_insert__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 2.96/1.55 = ( ( A2 = B2 )
% 2.96/1.55 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_40_insert__absorb2,axiom,
% 2.96/1.55 ! [X3: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X3 @ A ) )
% 2.96/1.55 = ( insert1671894227specID @ X3 @ A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_41_insert__absorb2,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ X3 @ A ) )
% 2.96/1.55 = ( insert751661162chanID @ X3 @ A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_42_empty__Collect__eq,axiom,
% 2.96/1.55 ! [P: secrecy_specID > $o] :
% 2.96/1.55 ( ( bot_bo1785112429specID
% 2.96/1.55 = ( collec1545797240specID @ P ) )
% 2.96/1.55 = ( ! [X4: secrecy_specID] :
% 2.96/1.55 ~ ( P @ X4 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_43_empty__Collect__eq,axiom,
% 2.96/1.55 ! [P: secrecy_chanID > $o] :
% 2.96/1.55 ( ( bot_bo443197316chanID
% 2.96/1.55 = ( collec625564175chanID @ P ) )
% 2.96/1.55 = ( ! [X4: secrecy_chanID] :
% 2.96/1.55 ~ ( P @ X4 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_44_Collect__empty__eq,axiom,
% 2.96/1.55 ! [P: secrecy_specID > $o] :
% 2.96/1.55 ( ( ( collec1545797240specID @ P )
% 2.96/1.55 = bot_bo1785112429specID )
% 2.96/1.55 = ( ! [X4: secrecy_specID] :
% 2.96/1.55 ~ ( P @ X4 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_45_Collect__empty__eq,axiom,
% 2.96/1.55 ! [P: secrecy_chanID > $o] :
% 2.96/1.55 ( ( ( collec625564175chanID @ P )
% 2.96/1.55 = bot_bo443197316chanID )
% 2.96/1.55 = ( ! [X4: secrecy_chanID] :
% 2.96/1.55 ~ ( P @ X4 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_46_all__not__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS] :
% 2.96/1.55 ( ( ! [X4: secrecy_KS] :
% 2.96/1.55 ~ ( member_Secrecy_KS @ X4 @ A ) )
% 2.96/1.55 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_47_all__not__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( ! [X4: secrecy_Keys] :
% 2.96/1.55 ~ ( member_Secrecy_Keys @ X4 @ A ) )
% 2.96/1.55 = ( A = bot_bo701486667y_Keys ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_48_all__not__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( ! [X4: secrecy_Secrets] :
% 2.96/1.55 ~ ( member2138796287ecrets @ X4 @ A ) )
% 2.96/1.55 = ( A = bot_bo1124690338ecrets ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_49_all__not__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID] :
% 2.96/1.55 ( ( ! [X4: secrecy_specID] :
% 2.96/1.55 ~ ( member740727610specID @ X4 @ A ) )
% 2.96/1.55 = ( A = bot_bo1785112429specID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_50_all__not__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( ! [X4: secrecy_chanID] :
% 2.96/1.55 ~ ( member1967978193chanID @ X4 @ A ) )
% 2.96/1.55 = ( A = bot_bo443197316chanID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_51_empty__iff,axiom,
% 2.96/1.55 ! [C: secrecy_KS] :
% 2.96/1.55 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_52_empty__iff,axiom,
% 2.96/1.55 ! [C: secrecy_Keys] :
% 2.96/1.55 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_53_empty__iff,axiom,
% 2.96/1.55 ! [C: secrecy_Secrets] :
% 2.96/1.55 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_54_empty__iff,axiom,
% 2.96/1.55 ! [C: secrecy_specID] :
% 2.96/1.55 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_55_empty__iff,axiom,
% 2.96/1.55 ! [C: secrecy_chanID] :
% 2.96/1.55 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_56_ex__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS] :
% 2.96/1.55 ( ( ? [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ A ) )
% 2.96/1.55 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_57_ex__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( ? [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 2.96/1.55 = ( A != bot_bo701486667y_Keys ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_58_ex__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( ? [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 2.96/1.55 = ( A != bot_bo1124690338ecrets ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_59_ex__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID] :
% 2.96/1.55 ( ( ? [X4: secrecy_specID] : ( member740727610specID @ X4 @ A ) )
% 2.96/1.55 = ( A != bot_bo1785112429specID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_60_ex__in__conv,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( ? [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ A ) )
% 2.96/1.55 = ( A != bot_bo443197316chanID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_61_equals0I,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS] :
% 2.96/1.55 ( ! [Y3: secrecy_KS] :
% 2.96/1.55 ~ ( member_Secrecy_KS @ Y3 @ A )
% 2.96/1.55 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_62_equals0I,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Keys] :
% 2.96/1.55 ( ! [Y3: secrecy_Keys] :
% 2.96/1.55 ~ ( member_Secrecy_Keys @ Y3 @ A )
% 2.96/1.55 => ( A = bot_bo701486667y_Keys ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_63_equals0I,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ! [Y3: secrecy_Secrets] :
% 2.96/1.55 ~ ( member2138796287ecrets @ Y3 @ A )
% 2.96/1.55 => ( A = bot_bo1124690338ecrets ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_64_equals0I,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID] :
% 2.96/1.55 ( ! [Y3: secrecy_specID] :
% 2.96/1.55 ~ ( member740727610specID @ Y3 @ A )
% 2.96/1.55 => ( A = bot_bo1785112429specID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_65_equals0I,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID] :
% 2.96/1.55 ( ! [Y3: secrecy_chanID] :
% 2.96/1.55 ~ ( member1967978193chanID @ Y3 @ A )
% 2.96/1.55 => ( A = bot_bo443197316chanID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_66_equals0D,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 2.96/1.55 ( ( A = bot_bo1943466239ecy_KS )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_67_equals0D,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 2.96/1.55 ( ( A = bot_bo701486667y_Keys )
% 2.96/1.55 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_68_equals0D,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 2.96/1.55 ( ( A = bot_bo1124690338ecrets )
% 2.96/1.55 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_69_equals0D,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 2.96/1.55 ( ( A = bot_bo1785112429specID )
% 2.96/1.55 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_70_equals0D,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 2.96/1.55 ( ( A = bot_bo443197316chanID )
% 2.96/1.55 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_71_emptyE,axiom,
% 2.96/1.55 ! [A2: secrecy_KS] :
% 2.96/1.55 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_72_emptyE,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys] :
% 2.96/1.55 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_73_emptyE,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets] :
% 2.96/1.55 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_74_emptyE,axiom,
% 2.96/1.55 ! [A2: secrecy_specID] :
% 2.96/1.55 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_75_emptyE,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID] :
% 2.96/1.55 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_76_mk__disjoint__insert,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ A2 @ A )
% 2.96/1.55 => ? [B3: set_Secrecy_KS] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 2.96/1.55 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_77_mk__disjoint__insert,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ A2 @ A )
% 2.96/1.55 => ? [B3: set_Secrecy_chanID] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert751661162chanID @ A2 @ B3 ) )
% 2.96/1.55 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_78_mk__disjoint__insert,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ A2 @ A )
% 2.96/1.55 => ? [B3: set_Secrecy_specID] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert1671894227specID @ A2 @ B3 ) )
% 2.96/1.55 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_79_mk__disjoint__insert,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ A2 @ A )
% 2.96/1.55 => ? [B3: set_Secrecy_Keys] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 2.96/1.55 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_80_mk__disjoint__insert,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ A2 @ A )
% 2.96/1.55 => ? [B3: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert565337510ecrets @ A2 @ B3 ) )
% 2.96/1.55 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_81_insert__commute,axiom,
% 2.96/1.55 ! [X3: secrecy_specID,Y: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ Y @ A ) )
% 2.96/1.55 = ( insert1671894227specID @ Y @ ( insert1671894227specID @ X3 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_82_insert__commute,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID,Y: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ Y @ A ) )
% 2.96/1.55 = ( insert751661162chanID @ Y @ ( insert751661162chanID @ X3 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_83_insert__eq__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.55 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 2.96/1.55 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 2.96/1.55 = ( insert_Secrecy_KS @ B2 @ B ) )
% 2.96/1.55 = ( ( ( A2 = B2 )
% 2.96/1.55 => ( A = B ) )
% 2.96/1.55 & ( ( A2 != B2 )
% 2.96/1.55 => ? [C2: set_Secrecy_KS] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 2.96/1.55 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 2.96/1.55 & ( B
% 2.96/1.55 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 2.96/1.55 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_84_insert__eq__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.55 ( ~ ( member1967978193chanID @ A2 @ A )
% 2.96/1.55 => ( ~ ( member1967978193chanID @ B2 @ B )
% 2.96/1.55 => ( ( ( insert751661162chanID @ A2 @ A )
% 2.96/1.55 = ( insert751661162chanID @ B2 @ B ) )
% 2.96/1.55 = ( ( ( A2 = B2 )
% 2.96/1.55 => ( A = B ) )
% 2.96/1.55 & ( ( A2 != B2 )
% 2.96/1.55 => ? [C2: set_Secrecy_chanID] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert751661162chanID @ B2 @ C2 ) )
% 2.96/1.55 & ~ ( member1967978193chanID @ B2 @ C2 )
% 2.96/1.55 & ( B
% 2.96/1.55 = ( insert751661162chanID @ A2 @ C2 ) )
% 2.96/1.55 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_85_insert__eq__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.55 ( ~ ( member740727610specID @ A2 @ A )
% 2.96/1.55 => ( ~ ( member740727610specID @ B2 @ B )
% 2.96/1.55 => ( ( ( insert1671894227specID @ A2 @ A )
% 2.96/1.55 = ( insert1671894227specID @ B2 @ B ) )
% 2.96/1.55 = ( ( ( A2 = B2 )
% 2.96/1.55 => ( A = B ) )
% 2.96/1.55 & ( ( A2 != B2 )
% 2.96/1.55 => ? [C2: set_Secrecy_specID] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert1671894227specID @ B2 @ C2 ) )
% 2.96/1.55 & ~ ( member740727610specID @ B2 @ C2 )
% 2.96/1.55 & ( B
% 2.96/1.55 = ( insert1671894227specID @ A2 @ C2 ) )
% 2.96/1.55 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_86_insert__eq__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 2.96/1.55 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 2.96/1.55 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 2.96/1.55 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 2.96/1.55 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 2.96/1.55 = ( ( ( A2 = B2 )
% 2.96/1.55 => ( A = B ) )
% 2.96/1.55 & ( ( A2 != B2 )
% 2.96/1.55 => ? [C2: set_Secrecy_Keys] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 2.96/1.55 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 2.96/1.55 & ( B
% 2.96/1.55 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 2.96/1.55 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_87_insert__eq__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.96/1.55 ( ~ ( member2138796287ecrets @ A2 @ A )
% 2.96/1.55 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 2.96/1.55 => ( ( ( insert565337510ecrets @ A2 @ A )
% 2.96/1.55 = ( insert565337510ecrets @ B2 @ B ) )
% 2.96/1.55 = ( ( ( A2 = B2 )
% 2.96/1.55 => ( A = B ) )
% 2.96/1.55 & ( ( A2 != B2 )
% 2.96/1.55 => ? [C2: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert565337510ecrets @ B2 @ C2 ) )
% 2.96/1.55 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 2.96/1.55 & ( B
% 2.96/1.55 = ( insert565337510ecrets @ A2 @ C2 ) )
% 2.96/1.55 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_88_insert__absorb,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ A2 @ A )
% 2.96/1.55 => ( ( insert_Secrecy_KS @ A2 @ A )
% 2.96/1.55 = A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_89_insert__absorb,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ A2 @ A )
% 2.96/1.55 => ( ( insert751661162chanID @ A2 @ A )
% 2.96/1.55 = A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_90_insert__absorb,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ A2 @ A )
% 2.96/1.55 => ( ( insert1671894227specID @ A2 @ A )
% 2.96/1.55 = A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_91_insert__absorb,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ A2 @ A )
% 2.96/1.55 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 2.96/1.55 = A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_92_insert__absorb,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ A2 @ A )
% 2.96/1.55 => ( ( insert565337510ecrets @ A2 @ A )
% 2.96/1.55 = A ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_93_mem__Collect__eq,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 2.96/1.55 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 2.96/1.55 = ( P @ A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_94_mem__Collect__eq,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 2.96/1.55 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 2.96/1.55 = ( P @ A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_95_mem__Collect__eq,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 2.96/1.55 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 2.96/1.55 = ( P @ A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_96_mem__Collect__eq,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 2.96/1.55 = ( P @ A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_97_mem__Collect__eq,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 2.96/1.55 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 2.96/1.55 = ( P @ A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_98_Collect__mem__eq,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS] :
% 2.96/1.55 ( ( collect_Secrecy_KS
% 2.96/1.55 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ A ) )
% 2.96/1.55 = A ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_99_Collect__mem__eq,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( collec625564175chanID
% 2.96/1.55 @ ^ [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ A ) )
% 2.96/1.55 = A ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_100_Collect__mem__eq,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID] :
% 2.96/1.55 ( ( collec1545797240specID
% 2.96/1.55 @ ^ [X4: secrecy_specID] : ( member740727610specID @ X4 @ A ) )
% 2.96/1.55 = A ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_101_Collect__mem__eq,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( collect_Secrecy_Keys
% 2.96/1.55 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 2.96/1.55 = A ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_102_Collect__mem__eq,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( collec836099393ecrets
% 2.96/1.55 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 2.96/1.55 = A ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_103_insert__ident,axiom,
% 2.96/1.55 ! [X3: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.55 ( ~ ( member_Secrecy_KS @ X3 @ A )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ X3 @ B )
% 2.96/1.55 => ( ( ( insert_Secrecy_KS @ X3 @ A )
% 2.96/1.55 = ( insert_Secrecy_KS @ X3 @ B ) )
% 2.96/1.55 = ( A = B ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_104_insert__ident,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.55 ( ~ ( member1967978193chanID @ X3 @ A )
% 2.96/1.55 => ( ~ ( member1967978193chanID @ X3 @ B )
% 2.96/1.55 => ( ( ( insert751661162chanID @ X3 @ A )
% 2.96/1.55 = ( insert751661162chanID @ X3 @ B ) )
% 2.96/1.55 = ( A = B ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_105_insert__ident,axiom,
% 2.96/1.55 ! [X3: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.55 ( ~ ( member740727610specID @ X3 @ A )
% 2.96/1.55 => ( ~ ( member740727610specID @ X3 @ B )
% 2.96/1.55 => ( ( ( insert1671894227specID @ X3 @ A )
% 2.96/1.55 = ( insert1671894227specID @ X3 @ B ) )
% 2.96/1.55 = ( A = B ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_106_insert__ident,axiom,
% 2.96/1.55 ! [X3: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.96/1.55 ( ~ ( member_Secrecy_Keys @ X3 @ A )
% 2.96/1.55 => ( ~ ( member_Secrecy_Keys @ X3 @ B )
% 2.96/1.55 => ( ( ( insert_Secrecy_Keys @ X3 @ A )
% 2.96/1.55 = ( insert_Secrecy_Keys @ X3 @ B ) )
% 2.96/1.55 = ( A = B ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_107_insert__ident,axiom,
% 2.96/1.55 ! [X3: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.96/1.55 ( ~ ( member2138796287ecrets @ X3 @ A )
% 2.96/1.55 => ( ~ ( member2138796287ecrets @ X3 @ B )
% 2.96/1.55 => ( ( ( insert565337510ecrets @ X3 @ A )
% 2.96/1.55 = ( insert565337510ecrets @ X3 @ B ) )
% 2.96/1.55 = ( A = B ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_108_Set_Oset__insert,axiom,
% 2.96/1.55 ! [X3: secrecy_KS,A: set_Secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ X3 @ A )
% 2.96/1.55 => ~ ! [B3: set_Secrecy_KS] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert_Secrecy_KS @ X3 @ B3 ) )
% 2.96/1.55 => ( member_Secrecy_KS @ X3 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_109_Set_Oset__insert,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X3 @ A )
% 2.96/1.55 => ~ ! [B3: set_Secrecy_chanID] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert751661162chanID @ X3 @ B3 ) )
% 2.96/1.55 => ( member1967978193chanID @ X3 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_110_Set_Oset__insert,axiom,
% 2.96/1.55 ! [X3: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ X3 @ A )
% 2.96/1.55 => ~ ! [B3: set_Secrecy_specID] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert1671894227specID @ X3 @ B3 ) )
% 2.96/1.55 => ( member740727610specID @ X3 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_111_Set_Oset__insert,axiom,
% 2.96/1.55 ! [X3: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ X3 @ A )
% 2.96/1.55 => ~ ! [B3: set_Secrecy_Keys] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert_Secrecy_Keys @ X3 @ B3 ) )
% 2.96/1.55 => ( member_Secrecy_Keys @ X3 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_112_Set_Oset__insert,axiom,
% 2.96/1.55 ! [X3: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ X3 @ A )
% 2.96/1.55 => ~ ! [B3: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( A
% 2.96/1.55 = ( insert565337510ecrets @ X3 @ B3 ) )
% 2.96/1.55 => ( member2138796287ecrets @ X3 @ B3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_113_insertI2,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ A2 @ B )
% 2.96/1.55 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_114_insertI2,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ A2 @ B )
% 2.96/1.55 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_115_insertI2,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ A2 @ B )
% 2.96/1.55 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_116_insertI2,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ A2 @ B )
% 2.96/1.55 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_117_insertI2,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ A2 @ B )
% 2.96/1.55 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_118_insertI1,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_119_insertI1,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_120_insertI1,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_121_insertI1,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_122_insertI1,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_123_insertE,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 2.96/1.55 => ( ( A2 != B2 )
% 2.96/1.55 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_124_insertE,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 2.96/1.55 => ( ( A2 != B2 )
% 2.96/1.55 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_125_insertE,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 2.96/1.55 => ( ( A2 != B2 )
% 2.96/1.55 => ( member740727610specID @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_126_insertE,axiom,
% 2.96/1.55 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 2.96/1.55 => ( ( A2 != B2 )
% 2.96/1.55 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_127_insertE,axiom,
% 2.96/1.55 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 2.96/1.55 => ( ( A2 != B2 )
% 2.96/1.55 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_128_singleton__inject,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 2.96/1.55 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 2.96/1.55 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.96/1.55 => ( A2 = B2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_129_singleton__inject,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 2.96/1.55 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 2.96/1.55 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.96/1.55 => ( A2 = B2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_130_insert__not__empty,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( insert1671894227specID @ A2 @ A )
% 2.96/1.55 != bot_bo1785112429specID ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_131_insert__not__empty,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( insert751661162chanID @ A2 @ A )
% 2.96/1.55 != bot_bo443197316chanID ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_132_doubleton__eq__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 2.96/1.55 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.96/1.55 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 2.96/1.55 = ( ( ( A2 = C )
% 2.96/1.55 & ( B2 = D ) )
% 2.96/1.55 | ( ( A2 = D )
% 2.96/1.55 & ( B2 = C ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_133_doubleton__eq__iff,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 2.96/1.55 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.96/1.55 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 2.96/1.55 = ( ( ( A2 = C )
% 2.96/1.55 & ( B2 = D ) )
% 2.96/1.55 | ( ( A2 = D )
% 2.96/1.55 & ( B2 = C ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_134_singleton__iff,axiom,
% 2.96/1.55 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 2.96/1.55 = ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_135_singleton__iff,axiom,
% 2.96/1.55 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 2.96/1.55 = ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_136_singleton__iff,axiom,
% 2.96/1.55 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 2.96/1.55 = ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_137_singleton__iff,axiom,
% 2.96/1.55 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 2.96/1.55 = ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_138_singleton__iff,axiom,
% 2.96/1.55 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 2.96/1.55 = ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_139_singletonD,axiom,
% 2.96/1.55 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 2.96/1.55 => ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_140_singletonD,axiom,
% 2.96/1.55 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 2.96/1.55 => ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_141_singletonD,axiom,
% 2.96/1.55 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 2.96/1.55 => ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_142_singletonD,axiom,
% 2.96/1.55 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 2.96/1.55 => ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_143_singletonD,axiom,
% 2.96/1.55 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 2.96/1.55 => ( B2 = A2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_144_LocalSecretsComposition__neg1,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ! [M2: secrecy_Keys] :
% 2.96/1.55 ( ( Ks
% 2.96/1.55 = ( secrecy_kKS @ M2 ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 2.96/1.55 & ~ ( ine @ Q @ ( secrecy_kE @ M2 ) ) ) )
% 2.96/1.55 => ( ! [M2: secrecy_Secrets] :
% 2.96/1.55 ( ( Ks
% 2.96/1.55 = ( secrecy_sKS @ M2 ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 2.96/1.55 & ~ ( ine @ Q @ ( secrecy_sE @ M2 ) ) ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_145_the__elem__eq,axiom,
% 2.96/1.55 ! [X3: secrecy_specID] :
% 2.96/1.55 ( ( the_el827131246specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.96/1.55 = X3 ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_146_the__elem__eq,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID] :
% 2.96/1.55 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.96/1.55 = X3 ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_147_LocalSecretsComposition__neg1__k,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_148_LocalSecretsComposition__ine2__k,axiom,
% 2.96/1.55 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.96/1.55 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_149_LocalSecretsComposition__ine1__k,axiom,
% 2.96/1.55 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.96/1.55 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_150_know__composition__neg__ine__k,axiom,
% 2.96/1.55 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( knowle945212990e_know @ P @ ( secrecy_kKS @ Key ) )
% 2.96/1.55 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_kKS @ Key ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_151_is__singletonI,axiom,
% 2.96/1.55 ! [X3: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_152_is__singletonI,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_153_KS2Expression_Osimps_I2_J,axiom,
% 2.96/1.55 ! [M: secrecy_Secrets] :
% 2.96/1.55 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 2.96/1.55 = ( secrecy_sE @ M ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_154_Expression_Oinject_I1_J,axiom,
% 2.96/1.55 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.96/1.55 ( ( ( secrecy_kE @ X1 )
% 2.96/1.55 = ( secrecy_kE @ Y1 ) )
% 2.96/1.55 = ( X1 = Y1 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_155_KS2Expression_Osimps_I1_J,axiom,
% 2.96/1.55 ! [M: secrecy_Keys] :
% 2.96/1.55 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 2.96/1.55 = ( secrecy_kE @ M ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_156_bot__set__def,axiom,
% 2.96/1.55 ( bot_bo1785112429specID
% 2.96/1.55 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_157_bot__set__def,axiom,
% 2.96/1.55 ( bot_bo443197316chanID
% 2.96/1.55 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_158_Expression_Odistinct_I1_J,axiom,
% 2.96/1.55 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.96/1.55 ( ( secrecy_kE @ X1 )
% 2.96/1.55 != ( secrecy_sE @ X2 ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_159_is__singleton__the__elem,axiom,
% 2.96/1.55 ( is_sin1501507247specID
% 2.96/1.55 = ( ^ [A3: set_Secrecy_specID] :
% 2.96/1.55 ( A3
% 2.96/1.55 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_160_is__singleton__the__elem,axiom,
% 2.96/1.55 ( is_sin581274182chanID
% 2.96/1.55 = ( ^ [A3: set_Secrecy_chanID] :
% 2.96/1.55 ( A3
% 2.96/1.55 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_161_is__singletonI_H,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS] :
% 2.96/1.55 ( ( A != bot_bo1943466239ecy_KS )
% 2.96/1.55 => ( ! [X: secrecy_KS,Y3: secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ X @ A )
% 2.96/1.55 => ( ( member_Secrecy_KS @ Y3 @ A )
% 2.96/1.55 => ( X = Y3 ) ) )
% 2.96/1.55 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_162_is__singletonI_H,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( A != bot_bo701486667y_Keys )
% 2.96/1.55 => ( ! [X: secrecy_Keys,Y3: secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ X @ A )
% 2.96/1.55 => ( ( member_Secrecy_Keys @ Y3 @ A )
% 2.96/1.55 => ( X = Y3 ) ) )
% 2.96/1.55 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_163_is__singletonI_H,axiom,
% 2.96/1.55 ! [A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( A != bot_bo1124690338ecrets )
% 2.96/1.55 => ( ! [X: secrecy_Secrets,Y3: secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ X @ A )
% 2.96/1.55 => ( ( member2138796287ecrets @ Y3 @ A )
% 2.96/1.55 => ( X = Y3 ) ) )
% 2.96/1.55 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_164_is__singletonI_H,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID] :
% 2.96/1.55 ( ( A != bot_bo1785112429specID )
% 2.96/1.55 => ( ! [X: secrecy_specID,Y3: secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ X @ A )
% 2.96/1.55 => ( ( member740727610specID @ Y3 @ A )
% 2.96/1.55 => ( X = Y3 ) ) )
% 2.96/1.55 => ( is_sin1501507247specID @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_165_is__singletonI_H,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( A != bot_bo443197316chanID )
% 2.96/1.55 => ( ! [X: secrecy_chanID,Y3: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ A )
% 2.96/1.55 => ( ( member1967978193chanID @ Y3 @ A )
% 2.96/1.55 => ( X = Y3 ) ) )
% 2.96/1.55 => ( is_sin581274182chanID @ A ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_166_not__know__k__not__ine,axiom,
% 2.96/1.55 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.96/1.55 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.96/1.55 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_167_is__singletonE,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID] :
% 2.96/1.55 ( ( is_sin1501507247specID @ A )
% 2.96/1.55 => ~ ! [X: secrecy_specID] :
% 2.96/1.55 ( A
% 2.96/1.55 != ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_168_is__singletonE,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( is_sin581274182chanID @ A )
% 2.96/1.55 => ~ ! [X: secrecy_chanID] :
% 2.96/1.55 ( A
% 2.96/1.55 != ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_169_is__singleton__def,axiom,
% 2.96/1.55 ( is_sin1501507247specID
% 2.96/1.55 = ( ^ [A3: set_Secrecy_specID] :
% 2.96/1.55 ? [X4: secrecy_specID] :
% 2.96/1.55 ( A3
% 2.96/1.55 = ( insert1671894227specID @ X4 @ bot_bo1785112429specID ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_170_is__singleton__def,axiom,
% 2.96/1.55 ( is_sin581274182chanID
% 2.96/1.55 = ( ^ [A3: set_Secrecy_chanID] :
% 2.96/1.55 ? [X4: secrecy_chanID] :
% 2.96/1.55 ( A3
% 2.96/1.55 = ( insert751661162chanID @ X4 @ bot_bo443197316chanID ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_171_know_Osimps_I1_J,axiom,
% 2.96/1.55 ! [A: secrecy_specID,M: secrecy_Keys] :
% 2.96/1.55 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.96/1.55 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 2.96/1.55 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_172_TBtheorem4a__empty,axiom,
% 2.96/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ( ( ine @ P @ E )
% 2.96/1.55 | ( ine @ Q @ E ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( ( loc @ PQ )
% 2.96/1.55 = bot_bo443197316chanID )
% 2.96/1.55 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_173_TBtheorem1b,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( ineM @ PQ @ M3 @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( ineM @ P @ M3 @ E )
% 2.96/1.55 | ( ineM @ Q @ M3 @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_174_TBtheorem3b,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( ineM @ P @ M3 @ E )
% 2.96/1.55 => ( ~ ( ineM @ Q @ M3 @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_175_Set_Ois__empty__def,axiom,
% 2.96/1.55 ( is_emp1849217361specID
% 2.96/1.55 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_176_Set_Ois__empty__def,axiom,
% 2.96/1.55 ( is_emp928984296chanID
% 2.96/1.55 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_177_correctCompositionIn__L2,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_178_correctCompositionIn__prop1,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 2.96/1.55 | ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_179_TBtheorem4a__notP1,axiom,
% 2.96/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ( ine @ P @ E )
% 2.96/1.55 => ( ~ ( ine @ Q @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.55 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 2.96/1.55 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_180_not__ine__ineM,axiom,
% 2.96/1.55 ! [P: secrecy_specID,E: secrecy_Expression,M3: set_Secrecy_chanID] :
% 2.96/1.55 ( ~ ( ine @ P @ E )
% 2.96/1.55 => ~ ( ineM @ P @ M3 @ E ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_181_ineM__ine,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.55 ( ( ineM @ P @ M3 @ E )
% 2.96/1.55 => ( ine @ P @ E ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_182_TBtheorem4b__notP1,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ( ineM @ P @ M3 @ E )
% 2.96/1.55 => ( ~ ( ineM @ Q @ M3 @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.55 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 2.96/1.55 & ( member1967978193chanID @ Ch2 @ M3 )
% 2.96/1.55 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.55 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_183_correctCompositionIn__L1,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_184_subcomponents__loc,axiom,
% 2.96/1.55 ! [X3: secrecy_specID] :
% 2.96/1.55 ( ( correc965049635ionLoc @ X3 )
% 2.96/1.55 => ( ( ( subcomponents @ X3 )
% 2.96/1.55 = bot_bo1785112429specID )
% 2.96/1.55 => ( ( loc @ X3 )
% 2.96/1.55 = bot_bo443197316chanID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_185_TBtheorem4b__notPQ,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M3: set_Secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.96/1.55 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.96/1.55 => ( ! [X: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ ChSetP )
% 2.96/1.55 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.55 => ( ! [X: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ ChSetQ )
% 2.96/1.55 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.55 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_186_TBtheorem4b__notP2,axiom,
% 2.96/1.55 ! [Q: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.96/1.55 ( ~ ( ineM @ Q @ M3 @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.96/1.55 => ( ! [X: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ ChSet )
% 2.96/1.55 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.55 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_187_TBtheorem4a__notPQ,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.96/1.55 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.96/1.55 => ( ! [X: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ ChSetP )
% 2.96/1.55 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.55 => ( ! [X: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ ChSetQ )
% 2.96/1.55 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_188_TBtheorem4a__notP2,axiom,
% 2.96/1.55 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.96/1.55 ( ~ ( ine @ Q @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.96/1.55 => ( ! [X: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ ChSet )
% 2.96/1.55 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_189_TBtheorem4b__PQ,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ( ( ineM @ P @ M3 @ E )
% 2.96/1.55 | ( ineM @ Q @ M3 @ E ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.55 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.96/1.55 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.96/1.55 & ( member1967978193chanID @ Ch2 @ M3 )
% 2.96/1.55 & ( exprChannel @ Ch2 @ E )
% 2.96/1.55 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.55 => ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_190_ine__exprChannelSet__def,axiom,
% 2.96/1.55 ( ine_exprChannelSet
% 2.96/1.55 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.96/1.55 ( ! [X4: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X4 @ ChSet2 )
% 2.96/1.55 => ( ( member1967978193chanID @ X4 @ ( ins @ SP ) )
% 2.96/1.55 & ( exprChannel @ X4 @ E2 ) ) )
% 2.96/1.55 & ! [X4: secrecy_chanID] :
% 2.96/1.55 ( ( ~ ( member1967978193chanID @ X4 @ ChSet2 )
% 2.96/1.55 & ( member1967978193chanID @ X4 @ ( ins @ SP ) ) )
% 2.96/1.55 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_191_ine__def,axiom,
% 2.96/1.55 ( ine
% 2.96/1.55 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.96/1.55 ? [Ch3: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.96/1.55 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_192_ine__ins__neg1,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M: secrecy_Expression,X3: secrecy_chanID] :
% 2.96/1.55 ( ~ ( ine @ P @ M )
% 2.96/1.55 => ( ( exprChannel @ X3 @ M )
% 2.96/1.55 => ~ ( member1967978193chanID @ X3 @ ( ins @ P ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_193_ineM__def,axiom,
% 2.96/1.55 ( ineM
% 2.96/1.55 = ( ^ [SP: secrecy_specID,M4: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.96/1.55 ? [Ch3: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.96/1.55 & ( member1967978193chanID @ Ch3 @ M4 )
% 2.96/1.55 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_194_ineM__L1,axiom,
% 2.96/1.55 ! [Ch: secrecy_chanID,M3: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch @ M3 )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ E )
% 2.96/1.55 => ( ineM @ P @ M3 @ E ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_195_ine__exprChannelSingle__def,axiom,
% 2.96/1.55 ( ine_ex1303305700Single
% 2.96/1.55 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.96/1.55 & ( exprChannel @ Ch3 @ E2 )
% 2.96/1.55 & ! [X4: secrecy_chanID,T: nat] :
% 2.96/1.55 ( ( ( member1967978193chanID @ X4 @ ( ins @ SP ) )
% 2.96/1.55 & ( X4 != Ch3 ) )
% 2.96/1.55 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_196_LocalSecretsComposition__exprChannel__s,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( exprChannel @ X3 @ ( secrecy_sE @ Secrets ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 2.96/1.55 => ( ~ ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 2.96/1.55 & ~ ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_197_LocalSecretsComposition__exprChannel__k,axiom,
% 2.96/1.55 ! [X3: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( exprChannel @ X3 @ ( secrecy_kE @ Keys ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.96/1.55 => ( ~ ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 2.96/1.55 & ~ ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_198_ine__nonempty__exprChannelSet,axiom,
% 2.96/1.55 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.55 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.96/1.55 => ( ( ChSet != bot_bo443197316chanID )
% 2.96/1.55 => ( ine @ P @ E ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_199_ine__empty__exprChannelSet,axiom,
% 2.96/1.55 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.55 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.96/1.55 => ( ( ChSet = bot_bo443197316chanID )
% 2.96/1.55 => ~ ( ine @ P @ E ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_200_ine__exprChannelSingle__Set,axiom,
% 2.96/1.55 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.55 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 2.96/1.55 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_201_ine__exprChannelSet__Single,axiom,
% 2.96/1.55 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.55 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 2.96/1.55 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_202_correctCompositionInLoc__exprChannel,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ M )
% 2.96/1.55 => ( ! [X: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 2.96/1.55 => ~ ( exprChannel @ X @ M ) )
% 2.96/1.55 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_203_TBlemma3b,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 2.96/1.55 ( ~ ( ineM @ P @ M3 @ E )
% 2.96/1.55 => ( ~ ( ineM @ Q @ M3 @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ M3 )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.96/1.55 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_204_TBtheorem4a__P,axiom,
% 2.96/1.55 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( ine @ P @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.96/1.55 & ( exprChannel @ Ch2 @ E )
% 2.96/1.55 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.55 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_205_TBtheorem4a__PQ,axiom,
% 2.96/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ( ( ine @ P @ E )
% 2.96/1.55 | ( ine @ Q @ E ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.55 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.96/1.55 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.96/1.55 & ( exprChannel @ Ch2 @ E )
% 2.96/1.55 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.55 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_206_TBtheorem4b__P,axiom,
% 2.96/1.55 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.55 ( ( ineM @ P @ M3 @ E )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 2.96/1.55 & ( exprChannel @ Ch2 @ E )
% 2.96/1.55 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.96/1.55 & ( member1967978193chanID @ Ch2 @ M3 ) )
% 2.96/1.55 => ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_207_locStream__def,axiom,
% 2.96/1.55 ( locStream
% 2.96/1.55 = ( ^ [X4: secrecy_specID] :
% 2.96/1.55 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 2.96/1.55 @ ( loc @ X4 ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_208_inStream__def,axiom,
% 2.96/1.55 ( inStream
% 2.96/1.55 = ( ^ [X4: secrecy_specID] :
% 2.96/1.55 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 2.96/1.55 @ ( ins @ X4 ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_209_Collect__empty__eq__bot,axiom,
% 2.96/1.55 ! [P: secrecy_specID > $o] :
% 2.96/1.55 ( ( ( collec1545797240specID @ P )
% 2.96/1.55 = bot_bo1785112429specID )
% 2.96/1.55 = ( P = bot_bo1767780696ecID_o ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_210_Collect__empty__eq__bot,axiom,
% 2.96/1.55 ! [P: secrecy_chanID > $o] :
% 2.96/1.55 ( ( ( collec625564175chanID @ P )
% 2.96/1.55 = bot_bo443197316chanID )
% 2.96/1.55 = ( P = bot_bo1012329985anID_o ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_211_bot__empty__eq,axiom,
% 2.96/1.55 ( bot_bot_Secrecy_KS_o
% 2.96/1.55 = ( ^ [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ bot_bo1943466239ecy_KS ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_212_bot__empty__eq,axiom,
% 2.96/1.55 ( bot_bo2072920570Keys_o
% 2.96/1.55 = ( ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ bot_bo701486667y_Keys ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_213_bot__empty__eq,axiom,
% 2.96/1.55 ( bot_bo1909946299rets_o
% 2.96/1.55 = ( ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ bot_bo1124690338ecrets ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_214_bot__empty__eq,axiom,
% 2.96/1.55 ( bot_bo1767780696ecID_o
% 2.96/1.55 = ( ^ [X4: secrecy_specID] : ( member740727610specID @ X4 @ bot_bo1785112429specID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_215_bot__empty__eq,axiom,
% 2.96/1.55 ( bot_bo1012329985anID_o
% 2.96/1.55 = ( ^ [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ bot_bo443197316chanID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_216_LocalSecretsComposition__neg__loc__s,axiom,
% 2.96/1.55 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.96/1.55 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_217_LocalSecretsComposition__neg__loc__k,axiom,
% 2.96/1.55 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.96/1.55 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_218_correctCompositionKS__exprChannel__s__Qex,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ? [Ch4: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_219_correctCompositionKS__exprChannel__s__Pex,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ? [Ch4: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_220_correctCompositionKS__exprChannel__s__Q,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_221_correctCompositionKS__exprChannel__s__P,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_222_correctCompositionKS__PQ,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.96/1.55 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_223_correctCompositionKS__neg1,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_224_correctCompositionKS__negP,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_225_correctCompositionKS__negQ,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_226_know__composition,axiom,
% 2.96/1.55 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.96/1.55 => ( ( ( knowle945212990e_know @ P @ M )
% 2.96/1.55 | ( knowle945212990e_know @ Q @ M ) )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_227_know__composition1,axiom,
% 2.96/1.55 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.96/1.55 => ( ( knowle945212990e_know @ P @ M )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_228_know__composition2,axiom,
% 2.96/1.55 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.55 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.96/1.55 => ( ( knowle945212990e_know @ Q @ M )
% 2.96/1.55 => ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_229_correctCompositionKS__exprChannel__k__P,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_230_correctCompositionKS__exprChannel__k__Q,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_231_correctCompositionKS__exprChannel__k__Pex,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ? [Ch4: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_232_correctCompositionKS__exprChannel__k__Qex,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.96/1.55 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 2.96/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.96/1.55 => ( ( correctCompositionIn @ PQ )
% 2.96/1.55 => ? [Ch4: secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 2.96/1.55 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_233_LocalSecretsComposition__neg,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.96/1.55 => ( ! [M2: secrecy_Keys] :
% 2.96/1.55 ( ( Ks
% 2.96/1.55 = ( secrecy_kKS @ M2 ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 2.96/1.55 & ~ ( ine @ Q @ ( secrecy_kE @ M2 ) ) ) )
% 2.96/1.55 => ( ! [M2: secrecy_Secrets] :
% 2.96/1.55 ( ( Ks
% 2.96/1.55 = ( secrecy_sKS @ M2 ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 2.96/1.55 & ~ ( ine @ Q @ ( secrecy_sE @ M2 ) ) ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_234_LocalSecretsComposition__neg__s,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_235_LocalSecretsComposition__neg__k,axiom,
% 2.96/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 2.96/1.55 ( ( ( subcomponents @ PQ )
% 2.96/1.55 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.55 => ( ( correc965049635ionLoc @ PQ )
% 2.96/1.55 => ( ( correctCompositionKS @ PQ )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.96/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 2.96/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 2.96/1.55 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_236_notSpecKeysSecretsExpr__def,axiom,
% 2.96/1.55 ( notSpe1586871396tsExpr
% 2.96/1.55 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 2.96/1.55 ( ! [X4: secrecy_Keys] :
% 2.96/1.55 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E3 )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P2 ) ) )
% 2.96/1.55 & ! [Y5: secrecy_Secrets] :
% 2.96/1.55 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y5 ) @ E3 )
% 2.96/1.55 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y5 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_237_UnCI,axiom,
% 2.96/1.55 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.55 ( ( ~ ( member740727610specID @ C @ B )
% 2.96/1.55 => ( member740727610specID @ C @ A ) )
% 2.96/1.55 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_238_UnCI,axiom,
% 2.96/1.55 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 2.96/1.55 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 2.96/1.55 => ( member_Secrecy_Keys @ C @ A ) )
% 2.96/1.55 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_239_UnCI,axiom,
% 2.96/1.55 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( ~ ( member2138796287ecrets @ C @ B )
% 2.96/1.55 => ( member2138796287ecrets @ C @ A ) )
% 2.96/1.55 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_240_UnCI,axiom,
% 2.96/1.55 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 2.96/1.55 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 2.96/1.55 => ( member_Secrecy_KS @ C @ A ) )
% 2.96/1.55 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_241_UnCI,axiom,
% 2.96/1.55 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.55 ( ( ~ ( member1967978193chanID @ C @ B )
% 2.96/1.55 => ( member1967978193chanID @ C @ A ) )
% 2.96/1.55 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_242_Un__iff,axiom,
% 2.96/1.55 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 2.96/1.55 = ( ( member740727610specID @ C @ A )
% 2.96/1.55 | ( member740727610specID @ C @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_243_Un__iff,axiom,
% 2.96/1.55 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 2.96/1.55 = ( ( member_Secrecy_Keys @ C @ A )
% 2.96/1.55 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_244_Un__iff,axiom,
% 2.96/1.55 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.96/1.55 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 2.96/1.55 = ( ( member2138796287ecrets @ C @ A )
% 2.96/1.55 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_245_Un__iff,axiom,
% 2.96/1.55 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.55 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.96/1.55 = ( ( member_Secrecy_KS @ C @ A )
% 2.96/1.55 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_246_Un__iff,axiom,
% 2.96/1.55 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.55 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 2.96/1.55 = ( ( member1967978193chanID @ C @ A )
% 2.96/1.55 | ( member1967978193chanID @ C @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_247_Un__empty,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.55 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 2.96/1.55 = bot_bo1943466239ecy_KS )
% 2.96/1.55 = ( ( A = bot_bo1943466239ecy_KS )
% 2.96/1.55 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_248_Un__empty,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.55 ( ( ( sup_su1712599557specID @ A @ B )
% 2.96/1.55 = bot_bo1785112429specID )
% 2.96/1.55 = ( ( A = bot_bo1785112429specID )
% 2.96/1.55 & ( B = bot_bo1785112429specID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_249_Un__empty,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.55 ( ( ( sup_su370684444chanID @ A @ B )
% 2.96/1.55 = bot_bo443197316chanID )
% 2.96/1.55 = ( ( A = bot_bo443197316chanID )
% 2.96/1.55 & ( B = bot_bo443197316chanID ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_250_Un__insert__right,axiom,
% 2.96/1.55 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.55 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 2.96/1.55 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_251_Un__insert__right,axiom,
% 2.96/1.55 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.55 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 2.96/1.55 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_252_Un__insert__right,axiom,
% 2.96/1.55 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.55 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 2.96/1.55 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_253_Un__insert__left,axiom,
% 2.96/1.55 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 2.96/1.55 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 2.96/1.55 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_254_Un__insert__left,axiom,
% 2.96/1.55 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.96/1.55 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 2.96/1.55 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_255_Un__insert__left,axiom,
% 2.96/1.55 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.96/1.55 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 2.96/1.55 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_256_UnE,axiom,
% 2.96/1.55 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.55 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 2.96/1.55 => ( ~ ( member740727610specID @ C @ A )
% 2.96/1.55 => ( member740727610specID @ C @ B ) ) ) ).
% 2.96/1.55
% 2.96/1.55 thf(fact_257_UnE,axiom,
% 2.96/1.55 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.96/1.55 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 2.96/1.56 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 2.96/1.56 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_258_UnE,axiom,
% 2.96/1.56 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.96/1.56 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 2.96/1.56 => ( ~ ( member2138796287ecrets @ C @ A )
% 2.96/1.56 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_259_UnE,axiom,
% 2.96/1.56 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.96/1.56 => ( ~ ( member_Secrecy_KS @ C @ A )
% 2.96/1.56 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_260_UnE,axiom,
% 2.96/1.56 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 2.96/1.56 => ( ~ ( member1967978193chanID @ C @ A )
% 2.96/1.56 => ( member1967978193chanID @ C @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_261_UnI1,axiom,
% 2.96/1.56 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.56 ( ( member740727610specID @ C @ A )
% 2.96/1.56 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_262_UnI1,axiom,
% 2.96/1.56 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 2.96/1.56 ( ( member_Secrecy_Keys @ C @ A )
% 2.96/1.56 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_263_UnI1,axiom,
% 2.96/1.56 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 2.96/1.56 ( ( member2138796287ecrets @ C @ A )
% 2.96/1.56 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_264_UnI1,axiom,
% 2.96/1.56 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ C @ A )
% 2.96/1.56 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_265_UnI1,axiom,
% 2.96/1.56 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ C @ A )
% 2.96/1.56 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_266_UnI2,axiom,
% 2.96/1.56 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 2.96/1.56 ( ( member740727610specID @ C @ B )
% 2.96/1.56 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_267_UnI2,axiom,
% 2.96/1.56 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 2.96/1.56 ( ( member_Secrecy_Keys @ C @ B )
% 2.96/1.56 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_268_UnI2,axiom,
% 2.96/1.56 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 2.96/1.56 ( ( member2138796287ecrets @ C @ B )
% 2.96/1.56 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_269_UnI2,axiom,
% 2.96/1.56 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ C @ B )
% 2.96/1.56 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_270_UnI2,axiom,
% 2.96/1.56 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ C @ B )
% 2.96/1.56 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_271_bex__Un,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 2.96/1.56 ( ( ? [X4: secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ X4 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.96/1.56 & ( P @ X4 ) ) )
% 2.96/1.56 = ( ? [X4: secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ X4 @ A )
% 2.96/1.56 & ( P @ X4 ) )
% 2.96/1.56 | ? [X4: secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ X4 @ B )
% 2.96/1.56 & ( P @ X4 ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_272_bex__Un,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.96/1.56 ( ( ? [X4: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X4 @ ( sup_su370684444chanID @ A @ B ) )
% 2.96/1.56 & ( P @ X4 ) ) )
% 2.96/1.56 = ( ? [X4: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X4 @ A )
% 2.96/1.56 & ( P @ X4 ) )
% 2.96/1.56 | ? [X4: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X4 @ B )
% 2.96/1.56 & ( P @ X4 ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_273_ball__Un,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 2.96/1.56 ( ( ! [X4: secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ X4 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.96/1.56 => ( P @ X4 ) ) )
% 2.96/1.56 = ( ! [X4: secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ X4 @ A )
% 2.96/1.56 => ( P @ X4 ) )
% 2.96/1.56 & ! [X4: secrecy_KS] :
% 2.96/1.56 ( ( member_Secrecy_KS @ X4 @ B )
% 2.96/1.56 => ( P @ X4 ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_274_ball__Un,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.96/1.56 ( ( ! [X4: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X4 @ ( sup_su370684444chanID @ A @ B ) )
% 2.96/1.56 => ( P @ X4 ) ) )
% 2.96/1.56 = ( ! [X4: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X4 @ A )
% 2.96/1.56 => ( P @ X4 ) )
% 2.96/1.56 & ! [X4: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X4 @ B )
% 2.96/1.56 => ( P @ X4 ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_275_Un__assoc,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 2.96/1.56 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_276_Un__assoc,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 2.96/1.56 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_277_Un__absorb,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ A @ A )
% 2.96/1.56 = A ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_278_Un__absorb,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ A @ A )
% 2.96/1.56 = A ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_279_Un__commute,axiom,
% 2.96/1.56 ( sup_su1301156759ecy_KS
% 2.96/1.56 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_280_Un__commute,axiom,
% 2.96/1.56 ( sup_su370684444chanID
% 2.96/1.56 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_281_Un__left__absorb,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.96/1.56 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_282_Un__left__absorb,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 2.96/1.56 = ( sup_su370684444chanID @ A @ B ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_283_Un__left__commute,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 2.96/1.56 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_284_Un__left__commute,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 2.96/1.56 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_285_Un__empty__left,axiom,
% 2.96/1.56 ! [B: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 2.96/1.56 = B ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_286_Un__empty__left,axiom,
% 2.96/1.56 ! [B: set_Secrecy_specID] :
% 2.96/1.56 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 2.96/1.56 = B ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_287_Un__empty__left,axiom,
% 2.96/1.56 ! [B: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 2.96/1.56 = B ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_288_Un__empty__right,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 2.96/1.56 = A ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_289_Un__empty__right,axiom,
% 2.96/1.56 ! [A: set_Secrecy_specID] :
% 2.96/1.56 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 2.96/1.56 = A ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_290_Un__empty__right,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 2.96/1.56 = A ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_291_singleton__Un__iff,axiom,
% 2.96/1.56 ! [X3: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 2.96/1.56 ( ( ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS )
% 2.96/1.56 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 2.96/1.56 = ( ( ( A = bot_bo1943466239ecy_KS )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 2.96/1.56 & ( B = bot_bo1943466239ecy_KS ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_292_singleton__Un__iff,axiom,
% 2.96/1.56 ! [X3: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.96/1.56 ( ( ( insert1671894227specID @ X3 @ bot_bo1785112429specID )
% 2.96/1.56 = ( sup_su1712599557specID @ A @ B ) )
% 2.96/1.56 = ( ( ( A = bot_bo1785112429specID )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.96/1.56 & ( B = bot_bo1785112429specID ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_293_singleton__Un__iff,axiom,
% 2.96/1.56 ! [X3: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.96/1.56 ( ( ( insert751661162chanID @ X3 @ bot_bo443197316chanID )
% 2.96/1.56 = ( sup_su370684444chanID @ A @ B ) )
% 2.96/1.56 = ( ( ( A = bot_bo443197316chanID )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.96/1.56 & ( B = bot_bo443197316chanID ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_294_Un__singleton__iff,axiom,
% 2.96/1.56 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X3: secrecy_KS] :
% 2.96/1.56 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 2.96/1.56 = ( ( ( A = bot_bo1943466239ecy_KS )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 2.96/1.56 & ( B = bot_bo1943466239ecy_KS ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_295_Un__singleton__iff,axiom,
% 2.96/1.56 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X3: secrecy_specID] :
% 2.96/1.56 ( ( ( sup_su1712599557specID @ A @ B )
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.96/1.56 = ( ( ( A = bot_bo1785112429specID )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.96/1.56 & ( B = bot_bo1785112429specID ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_296_Un__singleton__iff,axiom,
% 2.96/1.56 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X3: secrecy_chanID] :
% 2.96/1.56 ( ( ( sup_su370684444chanID @ A @ B )
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.96/1.56 = ( ( ( A = bot_bo443197316chanID )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.96/1.56 & ( B = bot_bo443197316chanID ) )
% 2.96/1.56 | ( ( A
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.96/1.56 & ( B
% 2.96/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_297_insert__is__Un,axiom,
% 2.96/1.56 ( insert_Secrecy_KS
% 2.96/1.56 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_298_insert__is__Un,axiom,
% 2.96/1.56 ( insert1671894227specID
% 2.96/1.56 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_299_insert__is__Un,axiom,
% 2.96/1.56 ( insert751661162chanID
% 2.96/1.56 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_300_sup__bot_Oright__neutral,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 2.96/1.56 = A2 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_301_sup__bot_Oright__neutral,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_specID] :
% 2.96/1.56 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 2.96/1.56 = A2 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_302_sup__bot_Oright__neutral,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 2.96/1.56 = A2 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_303_sup__bot_Oneutr__eq__iff,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 2.96/1.56 ( ( bot_bo1943466239ecy_KS
% 2.96/1.56 = ( sup_su1301156759ecy_KS @ A2 @ B2 ) )
% 2.96/1.56 = ( ( A2 = bot_bo1943466239ecy_KS )
% 2.96/1.56 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_304_sup__bot_Oneutr__eq__iff,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 2.96/1.56 ( ( bot_bo1785112429specID
% 2.96/1.56 = ( sup_su1712599557specID @ A2 @ B2 ) )
% 2.96/1.56 = ( ( A2 = bot_bo1785112429specID )
% 2.96/1.56 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_305_sup__bot_Oneutr__eq__iff,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.96/1.56 ( ( bot_bo443197316chanID
% 2.96/1.56 = ( sup_su370684444chanID @ A2 @ B2 ) )
% 2.96/1.56 = ( ( A2 = bot_bo443197316chanID )
% 2.96/1.56 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_306_sup__bot_Oleft__neutral,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A2 )
% 2.96/1.56 = A2 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_307_sup__bot_Oleft__neutral,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_specID] :
% 2.96/1.56 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A2 )
% 2.96/1.56 = A2 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_308_sup__bot_Oleft__neutral,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A2 )
% 2.96/1.56 = A2 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_309_sup__bot_Oeq__neutr__iff,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 2.96/1.56 ( ( ( sup_su1301156759ecy_KS @ A2 @ B2 )
% 2.96/1.56 = bot_bo1943466239ecy_KS )
% 2.96/1.56 = ( ( A2 = bot_bo1943466239ecy_KS )
% 2.96/1.56 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_310_sup__bot_Oeq__neutr__iff,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 2.96/1.56 ( ( ( sup_su1712599557specID @ A2 @ B2 )
% 2.96/1.56 = bot_bo1785112429specID )
% 2.96/1.56 = ( ( A2 = bot_bo1785112429specID )
% 2.96/1.56 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_311_sup__bot_Oeq__neutr__iff,axiom,
% 2.96/1.56 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.96/1.56 ( ( ( sup_su370684444chanID @ A2 @ B2 )
% 2.96/1.56 = bot_bo443197316chanID )
% 2.96/1.56 = ( ( A2 = bot_bo443197316chanID )
% 2.96/1.56 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_312_sup__bot__left,axiom,
% 2.96/1.56 ! [X3: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X3 )
% 2.96/1.56 = X3 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_313_sup__bot__left,axiom,
% 2.96/1.56 ! [X3: set_Secrecy_specID] :
% 2.96/1.56 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X3 )
% 2.96/1.56 = X3 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_314_sup__bot__left,axiom,
% 2.96/1.56 ! [X3: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X3 )
% 2.96/1.56 = X3 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_315_sup__bot__right,axiom,
% 2.96/1.56 ! [X3: set_Secrecy_KS] :
% 2.96/1.56 ( ( sup_su1301156759ecy_KS @ X3 @ bot_bo1943466239ecy_KS )
% 2.96/1.56 = X3 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_316_sup__bot__right,axiom,
% 2.96/1.56 ! [X3: set_Secrecy_specID] :
% 2.96/1.56 ( ( sup_su1712599557specID @ X3 @ bot_bo1785112429specID )
% 2.96/1.56 = X3 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_317_sup__bot__right,axiom,
% 2.96/1.56 ! [X3: set_Secrecy_chanID] :
% 2.96/1.56 ( ( sup_su370684444chanID @ X3 @ bot_bo443197316chanID )
% 2.96/1.56 = X3 ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_318_ineM__Un1,axiom,
% 2.96/1.56 ! [P: secrecy_specID,A: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 2.96/1.56 ( ( ineM @ P @ A @ E )
% 2.96/1.56 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_319_TBtheorem5a__empty,axiom,
% 2.96/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.56 ( ( ( eout @ P @ E )
% 2.96/1.56 | ( eout @ Q @ E ) )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( ( loc @ PQ )
% 2.96/1.56 = bot_bo443197316chanID )
% 2.96/1.56 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_320_correctCompositionKS__subcomp1,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Keys] :
% 2.96/1.56 ( ( correctCompositionKS @ C3 )
% 2.96/1.56 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 2.96/1.56 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 2.96/1.56 => ? [X: secrecy_specID] :
% 2.96/1.56 ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.96/1.56 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_321_correctCompositionKS__subcomp2,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Secrets] :
% 2.96/1.56 ( ( correctCompositionKS @ C3 )
% 2.96/1.56 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 2.96/1.56 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 2.96/1.56 => ? [X: secrecy_specID] :
% 2.96/1.56 ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 2.96/1.56 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_322_TBtheorem2a,axiom,
% 2.96/1.56 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.56 ( ( eout @ PQ @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( eout @ P @ E )
% 2.96/1.56 | ( eout @ Q @ E ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_323_correctCompositionKS__subcomp4,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Secrets] :
% 2.96/1.56 ( ( correctCompositionKS @ C3 )
% 2.96/1.56 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 2.96/1.56 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X3 ) )
% 2.96/1.56 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_324_correctCompositionKS__subcomp3,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Keys] :
% 2.96/1.56 ( ( correctCompositionKS @ C3 )
% 2.96/1.56 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 2.96/1.56 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X3 ) )
% 2.96/1.56 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_325_TBtheorem5a__notP1,axiom,
% 2.96/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.56 ( ( eout @ P @ E )
% 2.96/1.56 => ( ~ ( eout @ Q @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.56 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 2.96/1.56 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.56 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_326_TBtheorem5a__notPQ,axiom,
% 2.96/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.96/1.56 ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.96/1.56 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.96/1.56 => ( ! [X: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X @ ChSetP )
% 2.96/1.56 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.56 => ( ! [X: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X @ ChSetQ )
% 2.96/1.56 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.56 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_327_TBtheorem5a__notP2,axiom,
% 2.96/1.56 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.96/1.56 ( ~ ( eout @ Q @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.96/1.56 => ( ! [X: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X @ ChSet )
% 2.96/1.56 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.56 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_328_out__exprChannelSingle__Set,axiom,
% 2.96/1.56 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.56 ( ( out_ex985543062Single @ P @ Ch @ E )
% 2.96/1.56 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_329_out__exprChannelSet__Single,axiom,
% 2.96/1.56 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.56 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 2.96/1.56 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_330_TBtheorem5b__notPQ,axiom,
% 2.96/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M3: set_Secrecy_chanID] :
% 2.96/1.56 ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.96/1.56 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.96/1.56 => ( ( M3
% 2.96/1.56 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 2.96/1.56 => ( ! [X: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X @ ChSetP )
% 2.96/1.56 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.56 => ( ! [X: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X @ ChSetQ )
% 2.96/1.56 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.56 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_331_eout__know__s,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 2.96/1.56 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 2.96/1.56 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 2.96/1.56 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 2.96/1.56 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_332_not__know__s__not__eout,axiom,
% 2.96/1.56 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 2.96/1.56 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 2.96/1.56 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.96/1.56 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 2.96/1.56 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_333_not__eout__eoutM,axiom,
% 2.96/1.56 ! [P: secrecy_specID,E: secrecy_Expression,M3: set_Secrecy_chanID] :
% 2.96/1.56 ( ~ ( eout @ P @ E )
% 2.96/1.56 => ~ ( eoutM @ P @ M3 @ E ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_334_eoutM__eout,axiom,
% 2.96/1.56 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.96/1.56 ( ( eoutM @ P @ M3 @ E )
% 2.96/1.56 => ( eout @ P @ E ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_335_TBtheorem2b,axiom,
% 2.96/1.56 ! [PQ: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.56 ( ( eoutM @ PQ @ M3 @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( eoutM @ P @ M3 @ E )
% 2.96/1.56 | ( eoutM @ Q @ M3 @ E ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_336_TBtheorem5b__notP2,axiom,
% 2.96/1.56 ! [Q: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.96/1.56 ( ~ ( eoutM @ Q @ M3 @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.96/1.56 => ( ! [X: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X @ ChSet )
% 2.96/1.56 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 2.96/1.56 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_337_TBtheorem5b__notP1,axiom,
% 2.96/1.56 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.56 ( ( eoutM @ P @ M3 @ E )
% 2.96/1.56 => ( ~ ( eoutM @ Q @ M3 @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.56 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 2.96/1.56 & ( member1967978193chanID @ Ch2 @ M3 )
% 2.96/1.56 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.56 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_338_eout__know__nonKS__k,axiom,
% 2.96/1.56 ! [M: secrecy_Keys,A: secrecy_specID] :
% 2.96/1.56 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 2.96/1.56 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 2.96/1.56 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 2.96/1.56 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_339_eoutKnowCorrect__L1k,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 2.96/1.56 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 2.96/1.56 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 2.96/1.56 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 2.96/1.56 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_340_not__know__k__not__eout,axiom,
% 2.96/1.56 ! [M: secrecy_Keys,A: secrecy_specID] :
% 2.96/1.56 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 2.96/1.56 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 2.96/1.56 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 2.96/1.56 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_341_eout__know__k,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 2.96/1.56 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 2.96/1.56 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 2.96/1.56 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 2.96/1.56 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_342_eout__know__nonKS__s,axiom,
% 2.96/1.56 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 2.96/1.56 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 2.96/1.56 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 2.96/1.56 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 2.96/1.56 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_343_eoutKnowCorrect__L1s,axiom,
% 2.96/1.56 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 2.96/1.56 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 2.96/1.56 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 2.96/1.56 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 2.96/1.56 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_344_TBtheore54b__P,axiom,
% 2.96/1.56 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.56 ( ( eoutM @ P @ M3 @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 2.96/1.56 & ( exprChannel @ Ch2 @ E )
% 2.96/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.96/1.56 & ( member1967978193chanID @ Ch2 @ M3 ) )
% 2.96/1.56 => ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_345_TBtheorem5b__PQ,axiom,
% 2.96/1.56 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.56 ( ( ( eoutM @ P @ M3 @ E )
% 2.96/1.56 | ( eoutM @ Q @ M3 @ E ) )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.56 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.96/1.56 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.96/1.56 & ( member1967978193chanID @ Ch2 @ M3 )
% 2.96/1.56 & ( exprChannel @ Ch2 @ E )
% 2.96/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.56 => ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_346_TBtheorem45a__P,axiom,
% 2.96/1.56 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.96/1.56 ( ( eout @ P @ E )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.96/1.56 & ( exprChannel @ Ch2 @ E )
% 2.96/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.56 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_347_eout__def,axiom,
% 2.96/1.56 ( eout
% 2.96/1.56 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.96/1.56 ? [Ch3: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.96/1.56 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_348_eoutM__def,axiom,
% 2.96/1.56 ( eoutM
% 2.96/1.56 = ( ^ [SP: secrecy_specID,M4: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.96/1.56 ? [Ch3: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.96/1.56 & ( member1967978193chanID @ Ch3 @ M4 )
% 2.96/1.56 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_349_out__exprChannelSet__def,axiom,
% 2.96/1.56 ( out_exprChannelSet
% 2.96/1.56 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.96/1.56 ( ! [X4: secrecy_chanID] :
% 2.96/1.56 ( ( member1967978193chanID @ X4 @ ChSet2 )
% 2.96/1.56 => ( ( member1967978193chanID @ X4 @ ( out @ SP ) )
% 2.96/1.56 & ( exprChannel @ X4 @ E2 ) ) )
% 2.96/1.56 & ! [X4: secrecy_chanID] :
% 2.96/1.56 ( ( ~ ( member1967978193chanID @ X4 @ ChSet2 )
% 2.96/1.56 & ( member1967978193chanID @ X4 @ ( out @ SP ) ) )
% 2.96/1.56 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_350_out__exprChannelSingle__def,axiom,
% 2.96/1.56 ( out_ex985543062Single
% 2.96/1.56 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 2.96/1.56 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.96/1.56 & ( exprChannel @ Ch3 @ E2 )
% 2.96/1.56 & ! [X4: secrecy_chanID,T: nat] :
% 2.96/1.56 ( ( ( member1967978193chanID @ X4 @ ( out @ SP ) )
% 2.96/1.56 & ( X4 != Ch3 ) )
% 2.96/1.56 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_351_correctCompositionOut__prop1,axiom,
% 2.96/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 2.96/1.56 ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ( member1967978193chanID @ X3 @ ( out @ PQ ) )
% 2.96/1.56 => ( ( member1967978193chanID @ X3 @ ( out @ P ) )
% 2.96/1.56 | ( member1967978193chanID @ X3 @ ( out @ Q ) ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_352_TBtheorem5a__PQ,axiom,
% 2.96/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.96/1.56 ( ( ( eout @ P @ E )
% 2.96/1.56 | ( eout @ Q @ E ) )
% 2.96/1.56 => ( ( ( subcomponents @ PQ )
% 2.96/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.96/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.96/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.96/1.56 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.96/1.56 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.96/1.56 & ( exprChannel @ Ch2 @ E )
% 2.96/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.96/1.56 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_353_outStream__def,axiom,
% 2.96/1.56 ( outStream
% 2.96/1.56 = ( ^ [X4: secrecy_specID] :
% 2.96/1.56 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 2.96/1.56 @ ( out @ X4 ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(fact_354_adv__not__know2,axiom,
% 2.96/1.56 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 2.96/1.56 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 2.96/1.56 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 2.96/1.56 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 2.96/1.56
% 2.96/1.56 thf(conj_0,conjecture,
% 2.96/1.56 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ).
% 2.96/1.56 ------------------------
% 2.96/1.59 % (14310)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/183Mi)
% 2.96/1.59 % (14313)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/2Mi)
% 2.96/1.60 % (14314)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_14089 for (2999ds/2Mi)
% 2.96/1.60 % (14313)Instruction limit reached!
% 2.96/1.60 % (14313)------------------------------
% 2.96/1.60 % (14313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.96/1.60 % (14313)Termination reason: Unknown
% 2.96/1.60 % (14313)Termination phase: shuffling
% 2.96/1.60
% 2.96/1.60 % (14313)Memory used [KB]: 1407
% 2.96/1.60 % (14313)Time elapsed: 0.003 s
% 2.96/1.60 % (14313)Instructions burned: 3 (million)
% 2.96/1.60 % (14313)------------------------------
% 2.96/1.60 % (14313)------------------------------
% 3.02/1.60 % (14314)Instruction limit reached!
% 3.02/1.60 % (14314)------------------------------
% 3.02/1.60 % (14314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (14314)Termination reason: Unknown
% 3.02/1.60 % (14314)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (14314)Memory used [KB]: 1407
% 3.02/1.60 % (14314)Time elapsed: 0.003 s
% 3.02/1.60 % (14314)Instructions burned: 4 (million)
% 3.02/1.60 % (14314)------------------------------
% 3.02/1.60 % (14314)------------------------------
% 3.02/1.60 % (14312)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_14089 for (2999ds/27Mi)
% 3.02/1.60 % (14315)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_14089 for (2999ds/275Mi)
% 3.02/1.60 % (14311)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_14089 for (2999ds/4Mi)
% 3.02/1.60 % (14316)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/18Mi)
% 3.02/1.60 % (14311)Instruction limit reached!
% 3.02/1.60 % (14311)------------------------------
% 3.02/1.60 % (14311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60 % (14311)Termination reason: Unknown
% 3.02/1.60 % (14311)Termination phase: shuffling
% 3.02/1.60
% 3.02/1.60 % (14311)Memory used [KB]: 1407
% 3.02/1.60 % (14311)Time elapsed: 0.004 s
% 3.02/1.60 % (14311)Instructions burned: 4 (million)
% 3.02/1.60 % (14311)------------------------------
% 3.02/1.60 % (14311)------------------------------
% 3.02/1.61 % (14317)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/3Mi)
% 3.02/1.61 % (14317)Instruction limit reached!
% 3.02/1.61 % (14317)------------------------------
% 3.02/1.61 % (14317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (14317)Termination reason: Unknown
% 3.02/1.61 % (14317)Termination phase: shuffling
% 3.02/1.61
% 3.02/1.61 % (14317)Memory used [KB]: 1535
% 3.02/1.61 % (14317)Time elapsed: 0.003 s
% 3.02/1.61 % (14317)Instructions burned: 6 (million)
% 3.02/1.61 % (14317)------------------------------
% 3.02/1.61 % (14317)------------------------------
% 3.02/1.61 % (14318)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_14089 for (2999ds/37Mi)
% 3.02/1.61 % (14316)Instruction limit reached!
% 3.02/1.61 % (14316)------------------------------
% 3.02/1.61 % (14316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61 % (14316)Termination reason: Unknown
% 3.02/1.61 % (14316)Termination phase: shuffling
% 3.02/1.61
% 3.02/1.61 % (14316)Memory used [KB]: 1663
% 3.02/1.61 % (14316)Time elapsed: 0.014 s
% 3.02/1.61 % (14316)Instructions burned: 19 (million)
% 3.02/1.61 % (14316)------------------------------
% 3.02/1.61 % (14316)------------------------------
% 3.02/1.62 % (14320)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_14089 for (2999ds/3Mi)
% 3.02/1.62 % (14320)Instruction limit reached!
% 3.02/1.62 % (14320)------------------------------
% 3.02/1.62 % (14320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (14320)Termination reason: Unknown
% 3.02/1.62 % (14320)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (14320)Memory used [KB]: 1407
% 3.02/1.62 % (14320)Time elapsed: 0.002 s
% 3.02/1.62 % (14320)Instructions burned: 3 (million)
% 3.02/1.62 % (14320)------------------------------
% 3.02/1.62 % (14320)------------------------------
% 3.02/1.62 % (14312)Instruction limit reached!
% 3.02/1.62 % (14312)------------------------------
% 3.02/1.62 % (14312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (14312)Termination reason: Unknown
% 3.02/1.62 % (14312)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (14312)Memory used [KB]: 1918
% 3.02/1.62 % (14312)Time elapsed: 0.018 s
% 3.02/1.62 % (14312)Instructions burned: 27 (million)
% 3.02/1.62 % (14312)------------------------------
% 3.02/1.62 % (14312)------------------------------
% 3.02/1.62 % (14318)Instruction limit reached!
% 3.02/1.62 % (14318)------------------------------
% 3.02/1.62 % (14318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62 % (14318)Termination reason: Unknown
% 3.02/1.62 % (14318)Termination phase: shuffling
% 3.02/1.62
% 3.02/1.62 % (14318)Memory used [KB]: 2174
% 3.02/1.62 % (14318)Time elapsed: 0.013 s
% 3.02/1.62 % (14318)Instructions burned: 37 (million)
% 3.02/1.62 % (14318)------------------------------
% 3.02/1.62 % (14318)------------------------------
% 3.02/1.62 % (14319)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_14089 for (2999ds/15Mi)
% 3.02/1.63 % (14322)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/7Mi)
% 3.02/1.63 % (14324)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_14089 for (2999ds/3Mi)
% 3.02/1.63 % (14322)Instruction limit reached!
% 3.02/1.63 % (14322)------------------------------
% 3.02/1.63 % (14322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63 % (14322)Termination reason: Unknown
% 3.02/1.63 % (14322)Termination phase: shuffling
% 3.02/1.63
% 3.02/1.63 % (14322)Memory used [KB]: 1535
% 3.02/1.63 % (14322)Time elapsed: 0.004 s
% 3.02/1.63 % (14322)Instructions burned: 9 (million)
% 3.02/1.63 % (14322)------------------------------
% 3.02/1.63 % (14322)------------------------------
% 3.02/1.63 % (14324)Instruction limit reached!
% 3.02/1.63 % (14324)------------------------------
% 3.02/1.63 % (14324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63 % (14324)Termination reason: Unknown
% 3.02/1.63 % (14324)Termination phase: shuffling
% 3.02/1.63
% 3.02/1.63 % (14324)Memory used [KB]: 1407
% 3.02/1.63 % (14324)Time elapsed: 0.003 s
% 3.02/1.63 % (14324)Instructions burned: 3 (million)
% 3.02/1.63 % (14324)------------------------------
% 3.02/1.63 % (14324)------------------------------
% 3.02/1.63 % (14319)Instruction limit reached!
% 3.02/1.63 % (14319)------------------------------
% 3.02/1.63 % (14319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63 % (14319)Termination reason: Unknown
% 3.02/1.63 % (14319)Termination phase: shuffling
% 3.02/1.63
% 3.02/1.63 % (14319)Memory used [KB]: 1663
% 3.02/1.63 % (14319)Time elapsed: 0.011 s
% 3.02/1.63 % (14319)Instructions burned: 15 (million)
% 3.02/1.63 % (14319)------------------------------
% 3.02/1.63 % (14319)------------------------------
% 3.02/1.63 % (14321)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_14089 for (2999ds/1041Mi)
% 3.02/1.64 % (14323)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/16Mi)
% 3.02/1.64 % (14315)Refutation not found, incomplete strategy
% 3.02/1.64 % (14315)------------------------------
% 3.02/1.64 % (14315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (14315)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.64
% 3.02/1.64
% 3.02/1.64 % (14315)Memory used [KB]: 6524
% 3.02/1.64 % (14315)Time elapsed: 0.036 s
% 3.02/1.64 % (14315)Instructions burned: 59 (million)
% 3.02/1.64 % (14315)------------------------------
% 3.02/1.64 % (14315)------------------------------
% 3.02/1.64 % (14325)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_14089 for (2999ds/3Mi)
% 3.02/1.64 % (14325)Instruction limit reached!
% 3.02/1.64 % (14325)------------------------------
% 3.02/1.64 % (14325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (14325)Termination reason: Unknown
% 3.02/1.64 % (14325)Termination phase: shuffling
% 3.02/1.64
% 3.02/1.64 % (14325)Memory used [KB]: 1407
% 3.02/1.64 % (14325)Time elapsed: 0.002 s
% 3.02/1.64 % (14325)Instructions burned: 3 (million)
% 3.02/1.64 % (14325)------------------------------
% 3.02/1.64 % (14325)------------------------------
% 3.02/1.64 % (14326)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/7Mi)
% 3.02/1.64 % (14326)Instruction limit reached!
% 3.02/1.64 % (14326)------------------------------
% 3.02/1.64 % (14326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (14326)Termination reason: Unknown
% 3.02/1.64 % (14326)Termination phase: shuffling
% 3.02/1.64
% 3.02/1.64 % (14326)Memory used [KB]: 1535
% 3.02/1.64 % (14326)Time elapsed: 0.005 s
% 3.02/1.64 % (14326)Instructions burned: 9 (million)
% 3.02/1.64 % (14326)------------------------------
% 3.02/1.64 % (14326)------------------------------
% 3.02/1.64 % (14310)Instruction limit reached!
% 3.02/1.64 % (14310)------------------------------
% 3.02/1.64 % (14310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64 % (14310)Termination reason: Unknown
% 3.02/1.64 % (14310)Termination phase: Saturation
% 3.02/1.64
% 3.02/1.64 % (14310)Memory used [KB]: 7291
% 3.02/1.64 % (14310)Time elapsed: 0.052 s
% 3.02/1.64 % (14310)Instructions burned: 184 (million)
% 3.02/1.64 % (14310)------------------------------
% 3.02/1.64 % (14310)------------------------------
% 3.02/1.65 % (14323)Instruction limit reached!
% 3.02/1.65 % (14323)------------------------------
% 3.02/1.65 % (14323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.65 % (14323)Termination reason: Unknown
% 3.02/1.65 % (14323)Termination phase: shuffling
% 3.02/1.65
% 3.02/1.65 % (14323)Memory used [KB]: 1791
% 3.02/1.65 % (14323)Time elapsed: 0.012 s
% 3.02/1.65 % (14323)Instructions burned: 16 (million)
% 3.02/1.65 % (14323)------------------------------
% 3.02/1.65 % (14323)------------------------------
% 3.02/1.65 % (14327)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/3Mi)
% 3.02/1.65 % (14329)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/18Mi)
% 3.02/1.65 % (14327)Instruction limit reached!
% 3.02/1.65 % (14327)------------------------------
% 3.02/1.65 % (14327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.65 % (14327)Termination reason: Unknown
% 3.02/1.65 % (14327)Termination phase: shuffling
% 3.02/1.65
% 3.02/1.65 % (14327)Memory used [KB]: 1535
% 3.02/1.65 % (14327)Time elapsed: 0.004 s
% 3.02/1.65 % (14327)Instructions burned: 5 (million)
% 3.02/1.65 % (14327)------------------------------
% 3.02/1.65 % (14327)------------------------------
% 3.02/1.65 % (14331)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/6Mi)
% 3.02/1.65 % (14330)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/710Mi)
% 3.02/1.66 % (14328)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/4Mi)
% 3.02/1.66 % (14329)Instruction limit reached!
% 3.02/1.66 % (14329)------------------------------
% 3.02/1.66 % (14329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66 % (14329)Termination reason: Unknown
% 3.02/1.66 % (14329)Termination phase: shuffling
% 3.02/1.66
% 3.02/1.66 % (14329)Memory used [KB]: 1791
% 3.02/1.66 % (14329)Time elapsed: 0.007 s
% 3.02/1.66 % (14329)Instructions burned: 18 (million)
% 3.02/1.66 % (14329)------------------------------
% 3.02/1.66 % (14329)------------------------------
% 3.02/1.66 % (14331)Instruction limit reached!
% 3.02/1.66 % (14331)------------------------------
% 3.02/1.66 % (14331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66 % (14331)Termination reason: Unknown
% 3.02/1.66 % (14331)Termination phase: shuffling
% 3.02/1.66
% 3.02/1.66 % (14331)Memory used [KB]: 1535
% 3.02/1.66 % (14331)Time elapsed: 0.003 s
% 3.02/1.66 % (14331)Instructions burned: 6 (million)
% 3.02/1.66 % (14331)------------------------------
% 3.02/1.66 % (14331)------------------------------
% 3.02/1.66 % (14328)Instruction limit reached!
% 3.02/1.66 % (14328)------------------------------
% 3.02/1.66 % (14328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66 % (14328)Termination reason: Unknown
% 3.02/1.66 % (14328)Termination phase: shuffling
% 3.02/1.66
% 3.02/1.66 % (14328)Memory used [KB]: 1535
% 3.02/1.66 % (14328)Time elapsed: 0.005 s
% 3.02/1.66 % (14328)Instructions burned: 5 (million)
% 3.02/1.66 % (14328)------------------------------
% 3.02/1.66 % (14328)------------------------------
% 3.02/1.66 % (14332)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_14089 for (2999ds/902Mi)
% 3.02/1.66 % (14333)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_14089 for (2999ds/21Mi)
% 3.02/1.66 % (14334)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/5Mi)
% 3.02/1.67 % (14335)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_14089 for (2999ds/6Mi)
% 3.02/1.67 % (14334)Instruction limit reached!
% 3.02/1.67 % (14334)------------------------------
% 3.02/1.67 % (14334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67 % (14334)Termination reason: Unknown
% 3.02/1.67 % (14334)Termination phase: shuffling
% 3.02/1.67
% 3.02/1.67 % (14334)Memory used [KB]: 1535
% 3.02/1.67 % (14334)Time elapsed: 0.003 s
% 3.02/1.67 % (14334)Instructions burned: 7 (million)
% 3.02/1.67 % (14334)------------------------------
% 3.02/1.67 % (14334)------------------------------
% 3.02/1.67 % (14335)Instruction limit reached!
% 3.02/1.67 % (14335)------------------------------
% 3.02/1.67 % (14335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67 % (14335)Termination reason: Unknown
% 3.02/1.67 % (14335)Termination phase: shuffling
% 3.02/1.67
% 3.02/1.67 % (14335)Memory used [KB]: 1535
% 3.02/1.67 % (14335)Time elapsed: 0.003 s
% 3.02/1.67 % (14335)Instructions burned: 7 (million)
% 3.02/1.67 % (14335)------------------------------
% 3.02/1.67 % (14335)------------------------------
% 3.02/1.67 % (14333)Instruction limit reached!
% 3.02/1.67 % (14333)------------------------------
% 3.02/1.67 % (14333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67 % (14333)Termination reason: Unknown
% 3.02/1.67 % (14333)Termination phase: shuffling
% 3.02/1.67
% 3.02/1.67 % (14333)Memory used [KB]: 1791
% 3.02/1.67 % (14333)Time elapsed: 0.009 s
% 3.02/1.67 % (14333)Instructions burned: 22 (million)
% 3.02/1.67 % (14333)------------------------------
% 3.02/1.67 % (14333)------------------------------
% 3.02/1.67 % (14330)Refutation not found, incomplete strategy
% 3.02/1.67 % (14330)------------------------------
% 3.02/1.67 % (14330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67 % (14330)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.67
% 3.02/1.67
% 3.02/1.67 % (14330)Memory used [KB]: 6524
% 3.02/1.67 % (14330)Time elapsed: 0.021 s
% 3.02/1.67 % (14330)Instructions burned: 57 (million)
% 3.02/1.67 % (14330)------------------------------
% 3.02/1.67 % (14330)------------------------------
% 3.02/1.68 % (14336)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/377Mi)
% 3.02/1.68 % (14337)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_14089 for (2999ds/779Mi)
% 3.02/1.68 % (14338)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/19Mi)
% 3.02/1.68 % (14339)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14089 for (2999ds/879Mi)
% 3.02/1.68 % (14338)Instruction limit reached!
% 3.02/1.68 % (14338)------------------------------
% 3.02/1.68 % (14338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.68 % (14338)Termination reason: Unknown
% 3.02/1.68 % (14338)Termination phase: shuffling
% 3.02/1.68
% 3.02/1.68 % (14338)Memory used [KB]: 1791
% 3.02/1.68 % (14338)Time elapsed: 0.006 s
% 3.02/1.68 % (14338)Instructions burned: 19 (million)
% 3.02/1.68 % (14338)------------------------------
% 3.02/1.68 % (14338)------------------------------
% 3.02/1.68 % (14340)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/17Mi)
% 3.02/1.69 % (14340)Instruction limit reached!
% 3.02/1.69 % (14340)------------------------------
% 3.02/1.69 % (14340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.69 % (14340)Termination reason: Unknown
% 3.02/1.69 % (14340)Termination phase: shuffling
% 3.02/1.69
% 3.02/1.69 % (14340)Memory used [KB]: 1791
% 3.02/1.69 % (14340)Time elapsed: 0.008 s
% 3.02/1.69 % (14340)Instructions burned: 18 (million)
% 3.02/1.69 % (14340)------------------------------
% 3.02/1.69 % (14340)------------------------------
% 3.02/1.69 % (14341)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/3Mi)
% 3.02/1.69 % (14341)Instruction limit reached!
% 3.02/1.69 % (14341)------------------------------
% 3.02/1.69 % (14341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.69 % (14341)Termination reason: Unknown
% 3.02/1.69 % (14341)Termination phase: shuffling
% 3.02/1.69
% 3.02/1.69 % (14341)Memory used [KB]: 1535
% 3.02/1.69 % (14341)Time elapsed: 0.003 s
% 3.02/1.69 % (14341)Instructions burned: 5 (million)
% 3.02/1.69 % (14341)------------------------------
% 3.02/1.69 % (14341)------------------------------
% 3.02/1.70 % (14342)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/30Mi)
% 3.02/1.70 % (14343)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/127Mi)
% 3.02/1.71 % (14342)Instruction limit reached!
% 3.02/1.71 % (14342)------------------------------
% 3.02/1.71 % (14342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (14342)Termination reason: Unknown
% 3.02/1.71 % (14342)Termination phase: shuffling
% 3.02/1.71
% 3.02/1.71 % (14342)Memory used [KB]: 2046
% 3.02/1.71 % (14342)Time elapsed: 0.012 s
% 3.02/1.71 % (14342)Instructions burned: 30 (million)
% 3.02/1.71 % (14342)------------------------------
% 3.02/1.71 % (14342)------------------------------
% 3.02/1.71 % (14332)Refutation not found, incomplete strategy
% 3.02/1.71 % (14332)------------------------------
% 3.02/1.71 % (14332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (14332)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.71
% 3.02/1.71
% 3.02/1.71 % (14332)Memory used [KB]: 7931
% 3.02/1.71 % (14332)Time elapsed: 0.054 s
% 3.02/1.71 % (14332)Instructions burned: 175 (million)
% 3.02/1.71 % (14332)------------------------------
% 3.02/1.71 % (14332)------------------------------
% 3.02/1.72 % (14344)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/100Mi)
% 3.02/1.72 % (14345)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/3Mi)
% 3.02/1.73 % (14345)Instruction limit reached!
% 3.02/1.73 % (14345)------------------------------
% 3.02/1.73 % (14345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.73 % (14345)Termination reason: Unknown
% 3.02/1.73 % (14345)Termination phase: shuffling
% 3.02/1.73
% 3.02/1.73 % (14345)Memory used [KB]: 1535
% 3.02/1.73 % (14345)Time elapsed: 0.003 s
% 3.02/1.73 % (14345)Instructions burned: 5 (million)
% 3.02/1.73 % (14345)------------------------------
% 3.02/1.73 % (14345)------------------------------
% 3.02/1.74 % (14346)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/20Mi)
% 3.02/1.74 % (14343)Instruction limit reached!
% 3.02/1.74 % (14343)------------------------------
% 3.02/1.74 % (14343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.74 % (14343)Termination reason: Unknown
% 3.02/1.74 % (14343)Termination phase: Property scanning
% 3.02/1.74
% 3.02/1.74 % (14343)Memory used [KB]: 2558
% 3.02/1.74 % (14343)Time elapsed: 0.037 s
% 3.02/1.74 % (14343)Instructions burned: 129 (million)
% 3.02/1.74 % (14343)------------------------------
% 3.02/1.74 % (14343)------------------------------
% 3.02/1.74 % (14346)Instruction limit reached!
% 3.02/1.74 % (14346)------------------------------
% 3.02/1.74 % (14346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.74 % (14346)Termination reason: Unknown
% 3.02/1.74 % (14346)Termination phase: shuffling
% 3.02/1.74
% 3.02/1.74 % (14346)Memory used [KB]: 1791
% 3.02/1.74 % (14346)Time elapsed: 0.008 s
% 3.02/1.74 % (14346)Instructions burned: 22 (million)
% 3.02/1.74 % (14346)------------------------------
% 3.02/1.74 % (14346)------------------------------
% 3.02/1.75 % (14344)Instruction limit reached!
% 3.02/1.75 % (14344)------------------------------
% 3.02/1.75 % (14344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.75 % (14344)Termination reason: Unknown
% 3.02/1.75 % (14344)Termination phase: Property scanning
% 3.02/1.75
% 3.02/1.75 % (14344)Memory used [KB]: 2430
% 3.02/1.75 % (14344)Time elapsed: 0.028 s
% 3.02/1.75 % (14344)Instructions burned: 100 (million)
% 3.02/1.75 % (14344)------------------------------
% 3.02/1.75 % (14344)------------------------------
% 3.02/1.75 % (14347)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/86Mi)
% 3.02/1.75 % (14348)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/107Mi)
% 3.02/1.76 % (14349)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/39Mi)
% 3.02/1.77 % (14349)Instruction limit reached!
% 3.02/1.77 % (14349)------------------------------
% 3.02/1.77 % (14349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.77 % (14349)Termination reason: Unknown
% 3.02/1.77 % (14349)Termination phase: shuffling
% 3.02/1.77
% 3.02/1.77 % (14349)Memory used [KB]: 2174
% 3.02/1.77 % (14349)Time elapsed: 0.012 s
% 3.02/1.77 % (14349)Instructions burned: 39 (million)
% 3.02/1.77 % (14349)------------------------------
% 3.02/1.77 % (14349)------------------------------
% 3.02/1.77 % (14347)Instruction limit reached!
% 3.02/1.77 % (14347)------------------------------
% 3.02/1.77 % (14347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.77 % (14347)Termination reason: Unknown
% 3.02/1.77 % (14347)Termination phase: Property scanning
% 3.02/1.77
% 3.02/1.77 % (14347)Memory used [KB]: 2430
% 3.02/1.77 % (14347)Time elapsed: 0.026 s
% 3.02/1.77 % (14347)Instructions burned: 86 (million)
% 3.02/1.77 % (14347)------------------------------
% 3.02/1.77 % (14347)------------------------------
% 3.02/1.78 % (14350)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/448Mi)
% 3.02/1.78 % (14351)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_14089 for (2998ds/46Mi)
% 3.02/1.78 % (14348)Instruction limit reached!
% 3.02/1.78 % (14348)------------------------------
% 3.02/1.78 % (14348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.78 % (14348)Termination reason: Unknown
% 3.02/1.78 % (14348)Termination phase: Property scanning
% 3.02/1.78
% 3.02/1.78 % (14348)Memory used [KB]: 2430
% 3.02/1.78 % (14348)Time elapsed: 0.032 s
% 3.02/1.78 % (14348)Instructions burned: 108 (million)
% 3.02/1.78 % (14348)------------------------------
% 3.02/1.78 % (14348)------------------------------
% 3.02/1.79 % (14352)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_14089 for (2997ds/98Mi)
% 3.02/1.80 % (14351)Instruction limit reached!
% 3.02/1.80 % (14351)------------------------------
% 3.02/1.80 % (14351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.80 % (14351)Termination reason: Unknown
% 3.02/1.80 % (14351)Termination phase: Property scanning
% 3.02/1.80
% 3.02/1.80 % (14351)Memory used [KB]: 2046
% 3.02/1.80 % (14351)Time elapsed: 0.015 s
% 3.02/1.80 % (14351)Instructions burned: 46 (million)
% 3.02/1.80 % (14351)------------------------------
% 3.02/1.80 % (14351)------------------------------
% 3.02/1.81 % (14353)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_14089 for (2997ds/507Mi)
% 3.02/1.81 % (14336)Instruction limit reached!
% 3.02/1.81 % (14336)------------------------------
% 3.02/1.81 % (14336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.81 % (14336)Termination reason: Unknown
% 3.02/1.81 % (14336)Termination phase: Saturation
% 3.02/1.81
% 3.02/1.81 % (14336)Memory used [KB]: 8315
% 3.02/1.81 % (14336)Time elapsed: 0.134 s
% 3.02/1.81 % (14336)Instructions burned: 380 (million)
% 3.02/1.81 % (14336)------------------------------
% 3.02/1.81 % (14336)------------------------------
% 3.02/1.82 % (14354)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_14089 for (2997ds/149Mi)
% 3.02/1.82 % (14352)Instruction limit reached!
% 3.02/1.82 % (14352)------------------------------
% 3.02/1.82 % (14352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.82 % (14352)Termination reason: Unknown
% 3.02/1.82 % (14352)Termination phase: Property scanning
% 3.02/1.82
% 3.02/1.82 % (14352)Memory used [KB]: 2430
% 3.02/1.82 % (14352)Time elapsed: 0.028 s
% 3.02/1.82 % (14352)Instructions burned: 99 (million)
% 3.02/1.82 % (14352)------------------------------
% 3.02/1.82 % (14352)------------------------------
% 3.02/1.83 % (14355)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14089 for (2997ds/39Mi)
% 3.02/1.84 % (14355)Instruction limit reached!
% 3.02/1.84 % (14355)------------------------------
% 3.02/1.84 % (14355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.84 % (14355)Termination reason: Unknown
% 3.02/1.84 % (14355)Termination phase: Property scanning
% 3.02/1.84
% 3.02/1.84 % (14355)Memory used [KB]: 2046
% 3.02/1.84 % (14355)Time elapsed: 0.013 s
% 3.02/1.84 % (14355)Instructions burned: 40 (million)
% 3.02/1.84 % (14355)------------------------------
% 3.02/1.84 % (14355)------------------------------
% 3.02/1.85 % (14356)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14089 for (2997ds/6Mi)
% 3.02/1.85 % (14356)Instruction limit reached!
% 3.02/1.85 % (14356)------------------------------
% 3.02/1.85 % (14356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.85 % (14356)Termination reason: Unknown
% 3.02/1.85 % (14356)Termination phase: shuffling
% 3.02/1.85
% 3.02/1.85 % (14356)Memory used [KB]: 1535
% 3.02/1.85 % (14356)Time elapsed: 0.003 s
% 3.02/1.85 % (14356)Instructions burned: 6 (million)
% 3.02/1.85 % (14356)------------------------------
% 3.02/1.85 % (14356)------------------------------
% 3.02/1.86 % (14357)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_14089 for (2997ds/1087Mi)
% 3.02/1.86 % (14354)Instruction limit reached!
% 3.02/1.86 % (14354)------------------------------
% 3.02/1.86 % (14354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.86 % (14354)Termination reason: Unknown
% 3.02/1.86 % (14354)Termination phase: Saturation
% 3.02/1.86
% 3.02/1.86 % (14354)Memory used [KB]: 7164
% 3.02/1.86 % (14354)Time elapsed: 0.046 s
% 3.02/1.86 % (14354)Instructions burned: 151 (million)
% 3.02/1.86 % (14354)------------------------------
% 3.02/1.86 % (14354)------------------------------
% 3.02/1.87 % (14358)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14089 for (2996ds/47Mi)
% 3.02/1.88 % (14353)First to succeed.
% 3.02/1.88 % (14353)Refutation found. Thanks to Tanya!
% 3.02/1.88 % SZS status Theorem for DTF2THF_14089
% 3.02/1.88 % SZS output start Proof for DTF2THF_14089
% 3.02/1.88 thf(type_def_5, type, secrecy_specID: $tType).
% 3.02/1.88 thf(type_def_6, type, set_Secrecy_KS: $tType).
% 3.02/1.88 thf(type_def_8, type, secrecy_KS: $tType).
% 3.02/1.88 thf(type_def_9, type, set_Secrecy_Keys: $tType).
% 3.02/1.88 thf(type_def_10, type, set_Secrecy_Secrets: $tType).
% 3.02/1.88 thf(type_def_11, type, set_Secrecy_chanID: $tType).
% 3.02/1.88 thf(type_def_12, type, set_Secrecy_specID: $tType).
% 3.02/1.88 thf(type_def_13, type, secrecy_Expression: $tType).
% 3.02/1.88 thf(type_def_14, type, list_S529945141ession: $tType).
% 3.02/1.88 thf(type_def_15, type, secrecy_Keys: $tType).
% 3.02/1.88 thf(type_def_16, type, secrecy_Secrets: $tType).
% 3.02/1.88 thf(type_def_17, type, secrecy_chanID: $tType).
% 3.02/1.88 thf(type_def_18, type, nat: $tType).
% 3.02/1.88 thf(func_def_0, type, list_S529945141ession: $tType).
% 3.02/1.88 thf(func_def_1, type, set_Secrecy_Secrets: $tType).
% 3.02/1.88 thf(func_def_2, type, set_Secrecy_specID: $tType).
% 3.02/1.88 thf(func_def_3, type, set_Secrecy_chanID: $tType).
% 3.02/1.88 thf(func_def_4, type, set_Secrecy_Keys: $tType).
% 3.02/1.88 thf(func_def_5, type, set_Secrecy_KS: $tType).
% 3.02/1.88 thf(func_def_6, type, secrecy_Expression: $tType).
% 3.02/1.88 thf(func_def_7, type, secrecy_Secrets: $tType).
% 3.02/1.88 thf(func_def_8, type, secrecy_specID: $tType).
% 3.02/1.88 thf(func_def_9, type, secrecy_chanID: $tType).
% 3.02/1.88 thf(func_def_10, type, secrecy_Keys: $tType).
% 3.02/1.88 thf(func_def_11, type, secrecy_KS: $tType).
% 3.02/1.88 thf(func_def_12, type, nat: $tType).
% 3.02/1.88 thf(func_def_13, type, localSecrets: secrecy_specID > set_Secrecy_KS).
% 3.02/1.88 thf(func_def_14, type, knowle233900195orrect: secrecy_specID > secrecy_KS > $o).
% 3.02/1.88 thf(func_def_15, type, knowle945212990e_know: secrecy_specID > secrecy_KS > $o).
% 3.02/1.88 thf(func_def_16, type, sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 3.02/1.88 thf(func_def_17, type, sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 3.02/1.88 thf(func_def_18, type, sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 3.02/1.88 thf(func_def_19, type, sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_20, type, sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 3.02/1.88 thf(func_def_21, type, mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o).
% 3.02/1.88 thf(func_def_22, type, bot_bot_Secrecy_KS_o: secrecy_KS > $o).
% 3.02/1.88 thf(func_def_23, type, bot_bo2072920570Keys_o: secrecy_Keys > $o).
% 3.02/1.88 thf(func_def_24, type, bot_bo1909946299rets_o: secrecy_Secrets > $o).
% 3.02/1.88 thf(func_def_25, type, bot_bo1012329985anID_o: secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_26, type, bot_bo1767780696ecID_o: secrecy_specID > $o).
% 3.02/1.88 thf(func_def_27, type, bot_bo1943466239ecy_KS: set_Secrecy_KS).
% 3.02/1.88 thf(func_def_28, type, bot_bo701486667y_Keys: set_Secrecy_Keys).
% 3.02/1.88 thf(func_def_29, type, bot_bo1124690338ecrets: set_Secrecy_Secrets).
% 3.02/1.88 thf(func_def_30, type, bot_bo443197316chanID: set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_31, type, bot_bo1785112429specID: set_Secrecy_specID).
% 3.02/1.88 thf(func_def_32, type, ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_33, type, correctCompositionKS: secrecy_specID > $o).
% 3.02/1.88 thf(func_def_34, type, eout: secrecy_specID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_35, type, eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_36, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_37, type, ine: secrecy_specID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_38, type, ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_39, type, ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_40, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_41, type, notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o).
% 3.02/1.88 thf(func_def_42, type, out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_43, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 3.02/1.88 thf(func_def_44, type, specKeys: secrecy_specID > set_Secrecy_Keys).
% 3.02/1.88 thf(func_def_45, type, specKeysSecrets: secrecy_specID > set_Secrecy_KS).
% 3.02/1.88 thf(func_def_46, type, specSecrets: secrecy_specID > set_Secrecy_Secrets).
% 3.02/1.88 thf(func_def_47, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 3.02/1.88 thf(func_def_48, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 3.02/1.88 thf(func_def_49, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 3.02/1.88 thf(func_def_50, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 3.02/1.88 thf(func_def_51, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 3.02/1.88 thf(func_def_52, type, collect_Secrecy_KS: (secrecy_KS > $o) > set_Secrecy_KS).
% 3.02/1.88 thf(func_def_53, type, collect_Secrecy_Keys: (secrecy_Keys > $o) > set_Secrecy_Keys).
% 3.02/1.88 thf(func_def_54, type, collec836099393ecrets: (secrecy_Secrets > $o) > set_Secrecy_Secrets).
% 3.02/1.88 thf(func_def_55, type, collec625564175chanID: (secrecy_chanID > $o) > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_56, type, collec1545797240specID: (secrecy_specID > $o) > set_Secrecy_specID).
% 3.02/1.88 thf(func_def_57, type, insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 3.02/1.88 thf(func_def_58, type, insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 3.02/1.88 thf(func_def_59, type, insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 3.02/1.88 thf(func_def_60, type, insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_61, type, insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 3.02/1.88 thf(func_def_62, type, is_emp928984296chanID: set_Secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_63, type, is_emp1849217361specID: set_Secrecy_specID > $o).
% 3.02/1.88 thf(func_def_64, type, is_sin1442426433ecy_KS: set_Secrecy_KS > $o).
% 3.02/1.88 thf(func_def_65, type, is_sin1096471309y_Keys: set_Secrecy_Keys > $o).
% 3.02/1.88 thf(func_def_66, type, is_sin1002224330ecrets: set_Secrecy_Secrets > $o).
% 3.02/1.88 thf(func_def_67, type, is_sin581274182chanID: set_Secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_68, type, is_sin1501507247specID: set_Secrecy_specID > $o).
% 3.02/1.88 thf(func_def_69, type, the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_70, type, the_el827131246specID: set_Secrecy_specID > secrecy_specID).
% 3.02/1.88 thf(func_def_71, type, correctCompositionIn: secrecy_specID > $o).
% 3.02/1.88 thf(func_def_72, type, correc965049635ionLoc: secrecy_specID > $o).
% 3.02/1.88 thf(func_def_73, type, correc990227761ionOut: secrecy_specID > $o).
% 3.02/1.88 thf(func_def_74, type, inStream: secrecy_specID > set_Secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_75, type, ins: secrecy_specID > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_76, type, loc: secrecy_specID > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_77, type, locStream: secrecy_specID > set_Secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_78, type, out: secrecy_specID > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_79, type, outStream: secrecy_specID > set_Secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_80, type, subcomponents: secrecy_specID > set_Secrecy_specID).
% 3.02/1.88 thf(func_def_81, type, member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o).
% 3.02/1.88 thf(func_def_82, type, member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o).
% 3.02/1.88 thf(func_def_83, type, member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o).
% 3.02/1.88 thf(func_def_84, type, member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o).
% 3.02/1.88 thf(func_def_85, type, member740727610specID: secrecy_specID > set_Secrecy_specID > $o).
% 3.02/1.88 thf(func_def_86, type, p: secrecy_specID).
% 3.02/1.88 thf(func_def_87, type, pq: secrecy_specID).
% 3.02/1.88 thf(func_def_88, type, q: secrecy_specID).
% 3.02/1.88 thf(func_def_89, type, m: secrecy_KS).
% 3.02/1.88 thf(func_def_90, type, secret: secrecy_Secrets).
% 3.02/1.88 thf(func_def_106, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.02/1.88 thf(func_def_107, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.02/1.88 thf(func_def_108, type, sK2: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 3.02/1.88 thf(func_def_109, type, sK3: set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_110, type, sK4: set_Secrecy_specID > secrecy_specID).
% 3.02/1.88 thf(func_def_111, type, sK5: set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_112, type, sK6: secrecy_specID > secrecy_Keys > secrecy_specID).
% 3.02/1.88 thf(func_def_113, type, sK7: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_114, type, sK8: set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_115, type, sK9: set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_116, type, sK10: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_117, type, sK11: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_118, type, sK12: secrecy_specID > secrecy_Secrets > secrecy_chanID).
% 3.02/1.88 thf(func_def_119, type, sK13: set_Secrecy_Secrets > secrecy_Secrets).
% 3.02/1.88 thf(func_def_120, type, sK14: set_Secrecy_Secrets > secrecy_Secrets).
% 3.02/1.88 thf(func_def_121, type, sK15: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_122, type, sK16: set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_123, type, sK17: set_Secrecy_chanID > secrecy_chanID > set_Secrecy_chanID).
% 3.02/1.88 thf(func_def_124, type, sK18: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_125, type, sK19: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_126, type, sK20: (secrecy_KS > $o) > secrecy_Secrets).
% 3.02/1.88 thf(func_def_127, type, sK21: (secrecy_KS > $o) > secrecy_Keys).
% 3.02/1.88 thf(func_def_128, type, sK22: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_129, type, sK23: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_130, type, sK24: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS).
% 3.02/1.88 thf(func_def_131, type, sK25: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets).
% 3.02/1.88 thf(func_def_132, type, sK26: set_Secrecy_specID > secrecy_specID > set_Secrecy_specID).
% 3.02/1.88 thf(func_def_133, type, sK27: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 3.02/1.88 thf(func_def_134, type, sK28: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_135, type, sK29: set_Secrecy_Secrets > secrecy_Secrets).
% 3.02/1.88 thf(func_def_136, type, sK30: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_137, type, sK31: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_138, type, sK32: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys).
% 3.02/1.88 thf(func_def_139, type, sK33: secrecy_specID > secrecy_Keys > secrecy_chanID).
% 3.02/1.88 thf(func_def_140, type, sK34: secrecy_specID > secrecy_Secrets > secrecy_specID).
% 3.02/1.88 thf(func_def_141, type, sK35: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_142, type, sK36: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_143, type, sK37: set_Secrecy_KS > secrecy_KS > set_Secrecy_KS).
% 3.02/1.88 thf(func_def_144, type, sK38: set_Secrecy_Keys > secrecy_Keys).
% 3.02/1.88 thf(func_def_145, type, sK39: set_Secrecy_Keys > secrecy_Keys).
% 3.02/1.88 thf(func_def_146, type, sK40: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets).
% 3.02/1.88 thf(func_def_147, type, sK41: secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys).
% 3.02/1.88 thf(func_def_148, type, sK42: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 3.02/1.88 thf(func_def_149, type, sK43: set_Secrecy_specID > secrecy_specID).
% 3.02/1.88 thf(func_def_150, type, sK44: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys).
% 3.02/1.88 thf(func_def_151, type, sK45: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets).
% 3.02/1.88 thf(func_def_152, type, sK46: set_Secrecy_specID > secrecy_specID).
% 3.02/1.88 thf(func_def_153, type, sK47: set_Secrecy_specID > secrecy_specID).
% 3.02/1.88 thf(func_def_154, type, sK48: set_Secrecy_Keys > secrecy_Keys).
% 3.02/1.88 thf(func_def_155, type, sK49: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 3.02/1.88 thf(func_def_156, type, sK50: secrecy_KS > secrecy_Keys).
% 3.02/1.88 thf(func_def_157, type, sK51: secrecy_KS > secrecy_Secrets).
% 3.02/1.88 thf(func_def_158, type, sK52: set_Secrecy_KS > secrecy_KS).
% 3.02/1.88 thf(func_def_159, type, sK53: set_Secrecy_KS > secrecy_KS).
% 3.02/1.88 thf(func_def_160, type, sK54: set_Secrecy_KS > secrecy_KS).
% 3.02/1.88 thf(func_def_161, type, sK55: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 3.02/1.88 thf(func_def_163, type, ph57: !>[X0: $tType]:(X0)).
% 3.02/1.88 thf(f2536,plain,(
% 3.02/1.88 $false),
% 3.02/1.88 inference(subsumption_resolution,[status(thm)],[f2522,f2175])).
% 3.02/1.88 thf(f2175,plain,(
% 3.02/1.88 ($true != (knowle945212990e_know @ q @ (secrecy_sKS @ secret)))),
% 3.02/1.88 inference(definition_unfolding,[status(thm)],[f1893,f1609])).
% 3.02/1.88 thf(f1609,plain,(
% 3.02/1.88 (m = (secrecy_sKS @ secret))),
% 3.02/1.88 inference(cnf_transformation,[status(thm)],[f975])).
% 3.02/1.88 thf(f975,plain,(
% 3.02/1.88 (m = (secrecy_sKS @ secret))),
% 3.02/1.88 inference(fool_elimination,[status(thm)],[f2])).
% 3.02/1.88 thf(f2,axiom,(
% 3.02/1.88 (m = (secrecy_sKS @ secret))),
% 3.02/1.88 file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_1_a2)).
% 3.02/1.88 thf(f1893,plain,(
% 3.02/1.88 ((knowle945212990e_know @ q @ m) != $true)),
% 3.02/1.88 inference(cnf_transformation,[status(thm)],[f1170])).
% 3.02/1.88 thf(f1170,plain,(
% 3.02/1.88 ((knowle945212990e_know @ q @ m) != $true)),
% 3.02/1.88 inference(flattening,[status(thm)],[f913])).
% 3.02/1.88 thf(f913,plain,(
% 3.02/1.88 ~((knowle945212990e_know @ q @ m) = $true)),
% 3.02/1.88 inference(fool_elimination,[status(thm)],[f912])).
% 3.02/1.88 thf(f912,plain,(
% 3.02/1.88 ~(knowle945212990e_know @ q @ m)),
% 3.02/1.88 inference(rectify,[status(thm)],[f1])).
% 3.02/1.88 thf(f1,axiom,(
% 3.02/1.88 ~(knowle945212990e_know @ q @ m)),
% 3.02/1.88 file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_0_not__knowQm)).
% 3.02/1.88 thf(f2522,plain,(
% 3.02/1.88 ($true = (knowle945212990e_know @ q @ (secrecy_sKS @ secret)))),
% 3.02/1.88 inference(trivial_inequality_removal,[status(thm)],[f2516])).
% 3.02/1.88 thf(f2516,plain,(
% 3.02/1.88 ($false = $true) | ($true = (knowle945212990e_know @ q @ (secrecy_sKS @ secret)))),
% 3.02/1.88 inference(superposition,[status(thm)],[f2377,f1081])).
% 3.02/1.88 thf(f1081,plain,(
% 3.02/1.88 ( ! [X2 : $o,X1 : $o] : (((X1 | X2) = $true) | ($false = X2)) )),
% 3.02/1.88 introduced(definition,[],[logical_or_proxy_axiom])).
% 3.02/1.88 thf(f2377,plain,(
% 3.02/1.88 (((?? @ secrecy_chanID @ (^[Y0 : secrecy_chanID]: ((member1967978193chanID @ Y0 @ (ins @ q)) & (exprChannel @ Y0 @ (secrecy_sE @ secret))))) | $true) = (knowle945212990e_know @ q @ (secrecy_sKS @ secret)))),
% 3.02/1.88 inference(superposition,[status(thm)],[f2318,f1930])).
% 3.02/1.88 thf(f1930,plain,(
% 3.02/1.88 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 3.02/1.88 inference(cnf_transformation,[status(thm)],[f1162])).
% 3.02/1.88 thf(f1162,plain,(
% 3.02/1.88 ((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 3.02/1.88 inference(flattening,[status(thm)],[f876])).
% 3.02/1.88 thf(f876,plain,(
% 3.02/1.88 ~~((member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 3.02/1.88 inference(fool_elimination,[status(thm)],[f875])).
% 3.02/1.88 thf(f875,plain,(
% 3.02/1.88 ~~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q))),
% 3.02/1.88 inference(rectify,[status(thm)],[f357])).
% 3.02/1.88 thf(f357,negated_conjecture,(
% 3.02/1.88 ~~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q))),
% 3.02/1.88 inference(negated_conjecture,[status(cth)],[f356])).
% 3.02/1.88 thf(f356,conjecture,(
% 3.02/1.88 ~(member_Secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q))),
% 3.02/1.88 file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',conj_0)).
% 3.02/1.88 thf(f2318,plain,(
% 3.02/1.88 ( ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : ((((?? @ secrecy_chanID @ (^[Y0 : secrecy_chanID]: ((member1967978193chanID @ Y0 @ (ins @ X1)) & (exprChannel @ Y0 @ (secrecy_sE @ X0))))) | (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))) = (knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)))) )),
% 3.02/1.88 inference(beta_eta_normalization,[status(thm)],[f2166])).
% 3.02/1.88 thf(f2166,plain,(
% 3.02/1.88 ( ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : (((knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)) = (((^[Y0 : secrecy_specID]: ((^[Y1 : secrecy_Expression]: (?? @ secrecy_chanID @ (^[Y2 : secrecy_chanID]: ((member1967978193chanID @ Y2 @ (ins @ Y0)) & (exprChannel @ Y2 @ Y1))))))) @ X1 @ (secrecy_sE @ X0)) | (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))))) )),
% 3.02/1.88 inference(definition_unfolding,[status(thm)],[f1875,f1794])).
% 3.02/1.88 thf(f1794,plain,(
% 3.02/1.88 (ine = (^[Y0 : secrecy_specID]: ((^[Y1 : secrecy_Expression]: (?? @ secrecy_chanID @ (^[Y2 : secrecy_chanID]: ((member1967978193chanID @ Y2 @ (ins @ Y0)) & (exprChannel @ Y2 @ Y1))))))))),
% 3.02/1.88 inference(cnf_transformation,[status(thm)],[f396])).
% 3.02/1.88 thf(f396,plain,(
% 3.02/1.88 (ine = (^[Y0 : secrecy_specID]: ((^[Y1 : secrecy_Expression]: (?? @ secrecy_chanID @ (^[Y2 : secrecy_chanID]: ((member1967978193chanID @ Y2 @ (ins @ Y0)) & (exprChannel @ Y2 @ Y1))))))))),
% 3.02/1.88 inference(fool_elimination,[status(thm)],[f395])).
% 3.02/1.88 thf(f395,plain,(
% 3.02/1.88 (ine = (^[X0 : secrecy_specID, X1 : secrecy_Expression] : (? [X2 : secrecy_chanID] : ((exprChannel @ X2 @ X1) & (member1967978193chanID @ X2 @ (ins @ X0))))))),
% 3.02/1.88 inference(rectify,[status(thm)],[f192])).
% 3.02/1.88 thf(f192,axiom,(
% 3.02/1.88 (ine = (^[X40 : secrecy_specID, X42 : secrecy_Expression] : (? [X43 : secrecy_chanID] : ((exprChannel @ X43 @ X42) & (member1967978193chanID @ X43 @ (ins @ X40))))))),
% 3.02/1.88 file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_191_ine__def)).
% 3.02/1.88 thf(f1875,plain,(
% 3.02/1.88 ( ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : ((((ine @ X1 @ (secrecy_sE @ X0)) | (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))) = (knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)))) )),
% 3.02/1.88 inference(cnf_transformation,[status(thm)],[f426])).
% 3.02/1.88 thf(f426,plain,(
% 3.02/1.88 ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : (((ine @ X1 @ (secrecy_sE @ X0)) | (member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1))) = (knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)))),
% 3.02/1.88 inference(fool_elimination,[status(thm)],[f425])).
% 3.02/1.88 thf(f425,plain,(
% 3.02/1.88 ! [X0 : secrecy_Secrets,X1 : secrecy_specID] : ((member_Secrecy_KS @ (secrecy_sKS @ X0) @ (localSecrets @ X1)) | (ine @ X1 @ (secrecy_sE @ X0)) = (knowle945212990e_know @ X1 @ (secrecy_sKS @ X0)))),
% 3.02/1.88 inference(rectify,[status(thm)],[f9])).
% 3.02/1.88 thf(f9,axiom,(
% 3.02/1.88 ! [X3 : secrecy_Secrets,X2 : secrecy_specID] : ((member_Secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X2)) | (ine @ X2 @ (secrecy_sE @ X3)) = (knowle945212990e_know @ X2 @ (secrecy_sKS @ X3)))),
% 3.02/1.88 file('/export/starexec/sandbox2/tmp/tmp.NxyseVupxa/DTF2THF_14089.p',fact_8_know_Osimps_I2_J)).
% 3.02/1.88 % SZS output end Proof for DTF2THF_14089
% 3.02/1.88 % (14353)------------------------------
% 3.02/1.88 % (14353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.88 % (14353)Termination reason: Refutation
% 3.02/1.88
% 3.02/1.88 % (14353)Memory used [KB]: 8315
% 3.02/1.88 % (14353)Time elapsed: 0.074 s
% 3.02/1.88 % (14353)Instructions burned: 248 (million)
% 3.02/1.88 % (14353)------------------------------
% 3.02/1.88 % (14353)------------------------------
% 3.02/1.88 % (14309)Success in time 0.321 s
%------------------------------------------------------------------------------