%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP086^1 : 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 08:55:26 AM UTC 2026
% Result : Theorem 2.92s 1.73s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 205 ( 69 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 324 ( 38 ~; 29 |; 0 &; 237 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 9 con; 0-3 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Secrecy_chanID: $tType ).
thf(type_def_7,type,
set_Secrecy_specID: $tType ).
thf(type_def_8,type,
secrecy_chanID: $tType ).
thf(type_def_9,type,
secrecy_specID: $tType ).
thf(type_def_10,type,
secrecy_Expression: $tType ).
thf(type_def_11,type,
nat: $tType ).
thf(func_def_0,type,
set_Secrecy_specID: $tType ).
thf(func_def_1,type,
set_Secrecy_chanID: $tType ).
thf(func_def_2,type,
secrecy_Expression: $tType ).
thf(func_def_3,type,
secrecy_specID: $tType ).
thf(func_def_4,type,
secrecy_chanID: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
uminus1044094777chanID: set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_7,type,
uminus238526242specID: set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_8,type,
inf_in1474033538chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_9,type,
inf_in668465003specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_10,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_11,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_12,type,
bot_bo1012329985anID_o: secrecy_chanID > $o ).
thf(func_def_13,type,
bot_bo1767780696ecID_o: secrecy_specID > $o ).
thf(func_def_15,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(func_def_16,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(func_def_17,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_18,type,
ord_le996703545specID: set_Secrecy_specID > set_Secrecy_specID > $o ).
thf(func_def_19,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_20,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_21,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_22,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(func_def_23,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_24,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_25,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_26,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_27,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(func_def_28,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(func_def_29,type,
collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
thf(func_def_30,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(func_def_31,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(func_def_32,type,
is_emp928984296chanID: set_Secrecy_chanID > $o ).
thf(func_def_33,type,
is_emp1849217361specID: set_Secrecy_specID > $o ).
thf(func_def_34,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(func_def_35,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(func_def_36,type,
pairwi1741995279chanID: ( secrecy_chanID > secrecy_chanID > $o ) > set_Secrecy_chanID > $o ).
thf(func_def_37,type,
pairwi514744696specID: ( secrecy_specID > secrecy_specID > $o ) > set_Secrecy_specID > $o ).
thf(func_def_38,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_39,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(func_def_40,type,
correctCompositionIn: secrecy_specID > $o ).
thf(func_def_41,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(func_def_42,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(func_def_43,type,
correctInOutLoc: secrecy_specID > $o ).
thf(func_def_44,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_45,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_46,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_47,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_48,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(func_def_49,type,
outStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(func_def_50,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(func_def_51,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(func_def_52,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(func_def_53,type,
p: secrecy_specID ).
thf(func_def_54,type,
pq: secrecy_specID ).
thf(func_def_55,type,
q: secrecy_specID ).
thf(func_def_56,type,
ch: secrecy_chanID ).
thf(func_def_57,type,
m: secrecy_Expression ).
thf(func_def_73,type,
sK0: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_74,type,
sK1: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_75,type,
sK2: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_76,type,
sK3: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_77,type,
sK4: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_78,type,
sK5: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_79,type,
sK6: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_80,type,
sK7: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_81,type,
sK8: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_82,type,
sK9: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(func_def_83,type,
sK10: secrecy_specID > set_Secrecy_chanID > secrecy_chanID ).
thf(func_def_84,type,
sK11: set_Secrecy_chanID > secrecy_specID > secrecy_chanID ).
thf(f1158,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1157,f1100]) ).
thf(f1100,plain,
( ( exprChannel @ ch @ m )
= $true ),
inference(cnf_transformation,[status(thm)],[f686]) ).
thf(f686,plain,
( ( exprChannel @ ch @ m )
= $true ),
inference(fool_elimination,[status(thm)],[f685]) ).
thf(f685,plain,
exprChannel @ ch @ m,
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
exprChannel @ ch @ m,
file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_1_assms_I4_J) ).
thf(f1157,plain,
( ( exprChannel @ ch @ m )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1156]) ).
thf(f1156,plain,
( ( $true != $true )
| ( ( exprChannel @ ch @ m )
!= $true ) ),
inference(superposition,[status(thm)],[f1120,f1154]) ).
thf(f1154,plain,
( $true
= ( member1967978193chanID @ ch @ ( ins @ pq ) ) ),
inference(subsumption_resolution,[status(thm)],[f1153,f1109]) ).
thf(f1109,plain,
( ( member1967978193chanID @ ch @ ( loc @ pq ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f983]) ).
thf(f983,plain,
( ( member1967978193chanID @ ch @ ( loc @ pq ) )
!= $true ),
inference(flattening,[status(thm)],[f576]) ).
thf(f576,plain,
( ( member1967978193chanID @ ch @ ( loc @ pq ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f575]) ).
thf(f575,plain,
~ ( member1967978193chanID @ ch @ ( loc @ pq ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ( member1967978193chanID @ ch @ ( loc @ pq ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
member1967978193chanID @ ch @ ( loc @ pq ),
file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',conj_0) ).
thf(f1153,plain,
( ( ( member1967978193chanID @ ch @ ( loc @ pq ) )
= $true )
| ( $true
= ( member1967978193chanID @ ch @ ( ins @ pq ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f1152,f1084]) ).
thf(f1084,plain,
( ( correctCompositionIn @ pq )
= $true ),
inference(cnf_transformation,[status(thm)],[f540]) ).
thf(f540,plain,
( ( correctCompositionIn @ pq )
= $true ),
inference(fool_elimination,[status(thm)],[f539]) ).
thf(f539,plain,
correctCompositionIn @ pq,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
correctCompositionIn @ pq,
file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_0_assms_I2_J) ).
thf(f1152,plain,
( ( ( correctCompositionIn @ pq )
!= $true )
| ( ( member1967978193chanID @ ch @ ( loc @ pq ) )
= $true )
| ( $true
= ( member1967978193chanID @ ch @ ( ins @ pq ) ) ) ),
inference(equality_resolution,[status(thm)],[f1150]) ).
thf(f1150,plain,
! [X0: secrecy_specID] :
( ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
= ( member1967978193chanID @ ch @ ( ins @ X0 ) ) )
| ( $true
= ( member1967978193chanID @ ch @ ( loc @ X0 ) ) )
| ( $true
!= ( correctCompositionIn @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1149]) ).
thf(f1149,plain,
! [X0: secrecy_specID] :
( ( $true
= ( member1967978193chanID @ ch @ ( ins @ X0 ) ) )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
= ( member1967978193chanID @ ch @ ( loc @ X0 ) ) )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1148,f1121]) ).
thf(f1121,plain,
( ( member1967978193chanID @ ch @ ( ins @ p ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f800]) ).
thf(f800,plain,
( ( member1967978193chanID @ ch @ ( ins @ p ) )
= $true ),
inference(fool_elimination,[status(thm)],[f799]) ).
thf(f799,plain,
member1967978193chanID @ ch @ ( ins @ p ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
member1967978193chanID @ ch @ ( ins @ p ),
file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_2_assms_I3_J) ).
thf(f1148,plain,
! [X0: secrecy_specID,X1: secrecy_chanID] :
( ( $true
!= ( member1967978193chanID @ X1 @ ( ins @ p ) ) )
| ( $true
= ( member1967978193chanID @ X1 @ ( loc @ X0 ) ) )
| ( ( member1967978193chanID @ X1 @ ( ins @ X0 ) )
= $true )
| ( ( subcomponents @ pq )
!= ( subcomponents @ X0 ) )
| ( $true
!= ( correctCompositionIn @ X0 ) ) ),
inference(superposition,[status(thm)],[f1082,f1110]) ).
thf(f1110,plain,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_4_assms_I1_J) ).
thf(f1082,plain,
! [X2: secrecy_specID,X3: secrecy_specID,X0: secrecy_specID,X1: secrecy_chanID] :
( ( ( subcomponents @ X0 )
!= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
| ( $true
= ( member1967978193chanID @ X1 @ ( loc @ X0 ) ) )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( ( member1967978193chanID @ X1 @ ( ins @ X0 ) )
= $true )
| ( ( member1967978193chanID @ X1 @ ( ins @ X2 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1052]) ).
thf(f1052,plain,
! [X0: secrecy_specID,X1: secrecy_chanID,X2: secrecy_specID,X3: secrecy_specID] :
( ( $true
= ( member1967978193chanID @ X1 @ ( loc @ X0 ) ) )
| ( ( subcomponents @ X0 )
!= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
| ( ( member1967978193chanID @ X1 @ ( ins @ X2 ) )
!= $true )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( ( member1967978193chanID @ X1 @ ( ins @ X0 ) )
= $true ) ),
inference(flattening,[status(thm)],[f1051]) ).
thf(f1051,plain,
! [X0: secrecy_specID,X1: secrecy_chanID,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( member1967978193chanID @ X1 @ ( ins @ X0 ) )
= $true )
| ( ( member1967978193chanID @ X1 @ ( ins @ X2 ) )
!= $true )
| ( $true
= ( member1967978193chanID @ X1 @ ( loc @ X0 ) ) )
| ( $true
!= ( correctCompositionIn @ X0 ) )
| ( ( subcomponents @ X0 )
!= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ),
inference(ennf_transformation,[status(thm)],[f989]) ).
thf(f989,plain,
! [X0: secrecy_specID,X1: secrecy_chanID,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( subcomponents @ X0 )
= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( $true
= ( correctCompositionIn @ X0 ) )
=> ( ( $true
!= ( member1967978193chanID @ X1 @ ( loc @ X0 ) ) )
=> ( ( ( member1967978193chanID @ X1 @ ( ins @ X2 ) )
= $true )
=> ( ( member1967978193chanID @ X1 @ ( ins @ X0 ) )
= $true ) ) ) ) ),
inference(flattening,[status(thm)],[f862]) ).
thf(f862,plain,
! [X0: secrecy_specID,X1: secrecy_chanID,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( subcomponents @ X0 )
= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( $true
= ( correctCompositionIn @ X0 ) )
=> ( ( $true
!= ( member1967978193chanID @ X1 @ ( loc @ X0 ) ) )
=> ( ( ( member1967978193chanID @ X1 @ ( ins @ X2 ) )
= $true )
=> ( ( member1967978193chanID @ X1 @ ( ins @ X0 ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f861]) ).
thf(f861,plain,
! [X0: secrecy_specID,X1: secrecy_chanID,X2: secrecy_specID,X3: secrecy_specID] :
( ( ( subcomponents @ X0 )
= ( insert1671894227specID @ X2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ X0 )
=> ( ~ ( member1967978193chanID @ X1 @ ( loc @ X0 ) )
=> ( ( member1967978193chanID @ X1 @ ( ins @ X2 ) )
=> ( member1967978193chanID @ X1 @ ( ins @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X4: secrecy_specID,X7: secrecy_chanID,X5: secrecy_specID,X6: secrecy_specID] :
( ( ( subcomponents @ X4 )
= ( insert1671894227specID @ X5 @ ( insert1671894227specID @ X6 @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ X4 )
=> ( ~ ( member1967978193chanID @ X7 @ ( loc @ X4 ) )
=> ( ( member1967978193chanID @ X7 @ ( ins @ X5 ) )
=> ( member1967978193chanID @ X7 @ ( ins @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_6_correctCompositionIn__L1) ).
thf(f1120,plain,
! [X0: secrecy_chanID] :
( ( ( member1967978193chanID @ X0 @ ( ins @ pq ) )
!= $true )
| ( ( exprChannel @ X0 @ m )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1022]) ).
thf(f1022,plain,
! [X0: secrecy_chanID] :
( ( ( member1967978193chanID @ X0 @ ( ins @ pq ) )
!= $true )
| ( ( exprChannel @ X0 @ m )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f1005]) ).
thf(f1005,plain,
! [X0: secrecy_chanID] :
( ( ( member1967978193chanID @ X0 @ ( ins @ pq ) )
= $true )
=> ( ( exprChannel @ X0 @ m )
!= $true ) ),
inference(flattening,[status(thm)],[f426]) ).
thf(f426,plain,
! [X0: secrecy_chanID] :
( ( ( member1967978193chanID @ X0 @ ( ins @ pq ) )
= $true )
=> ( ( exprChannel @ X0 @ m )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f425]) ).
thf(f425,plain,
! [X0: secrecy_chanID] :
( ( member1967978193chanID @ X0 @ ( ins @ pq ) )
=> ~ ( exprChannel @ X0 @ m ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: secrecy_chanID] :
( ( member1967978193chanID @ X0 @ ( ins @ pq ) )
=> ~ ( exprChannel @ X0 @ m ) ),
file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_3_assms_I5_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP086^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.12 % 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 08:25:38 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
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : ITP086^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.45 % Domain : Interactive Theorem Proving
% 0.28/0.45 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_194__3293238_1
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English :
% 0.28/0.45
% 0.28/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [Des21]
% 0.28/0.45 % Names : KnowledgeKeysSecrets/prob_194__3293238_1 [Des21]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.28/0.45 % Syntax : Number of formulae : 414 ( 177 unt; 58 typ; 0 def)
% 0.28/0.45 % Number of atoms : 1148 ( 411 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 10 ( 3 avg)
% 0.28/0.45 % Number of connectives : 3132 ( 131 ~; 36 |; 110 &;2409 @)
% 0.28/0.45 % ( 0 <=>; 446 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 19 ( 6 avg)
% 0.28/0.45 % Number of types : 7 ( 6 usr)
% 0.28/0.45 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 53 ( 52 usr; 8 con; 0-3 aty)
% 0.28/0.45 % Number of variables : 1013 ( 84 ^; 902 !; 27 ?;1013 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:07.612
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % Could-be-implicit typings (6)
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.45 set_Secrecy_specID: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.45 set_Secrecy_chanID: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.28/0.45 secrecy_Expression: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.28/0.45 secrecy_specID: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Secrecy____types__OchanID,type,
% 0.28/0.45 secrecy_chanID: $tType ).
% 0.28/0.45
% 0.28/0.45 thf(ty_n_t__Nat__Onat,type,
% 0.28/0.45 nat: $tType ).
% 0.28/0.45
% 0.28/0.45 % Explicit typings (52)
% 0.28/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.45 uminus1044094777chanID: set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.45 uminus238526242specID: set_Secrecy_specID > set_Secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.45 inf_in1474033538chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.45 inf_in668465003specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.45 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.45 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 0.28/0.45 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 0.28/0.45 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.28/0.45 bot_bot_o: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.45 bot_bo443197316chanID: set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.45 bot_bo1785112429specID: set_Secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.45 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.45 ord_le996703545specID: set_Secrecy_specID > set_Secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_Oeout,type,
% 0.28/0.45 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_OeoutM,type,
% 0.28/0.45 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_OexprChannel,type,
% 0.28/0.45 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_Oine,type,
% 0.28/0.45 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_OineM,type,
% 0.28/0.45 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.28/0.45 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.28/0.45 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.28/0.45 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.28/0.45 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 0.28/0.45 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 0.28/0.45 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 0.28/0.45 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 0.28/0.45 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 0.28/0.45 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 0.28/0.45 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 0.28/0.45 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 0.28/0.45 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Opairwise_001t__Secrecy____types__OchanID,type,
% 0.28/0.45 pairwi1741995279chanID: ( secrecy_chanID > secrecy_chanID > $o ) > set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Opairwise_001t__Secrecy____types__OspecID,type,
% 0.28/0.45 pairwi514744696specID: ( secrecy_specID > secrecy_specID > $o ) > set_Secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 0.28/0.45 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 0.28/0.45 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.28/0.45 correctCompositionIn: secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.28/0.45 correc965049635ionLoc: secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.28/0.45 correc990227761ionOut: secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_OcorrectInOutLoc,type,
% 0.28/0.45 correctInOutLoc: secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_OinStream,type,
% 0.28/0.45 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_Oins,type,
% 0.28/0.45 ins: secrecy_specID > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_Oloc,type,
% 0.28/0.45 loc: secrecy_specID > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_OlocStream,type,
% 0.28/0.45 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_Oout,type,
% 0.28/0.45 out: secrecy_specID > set_Secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_OoutStream,type,
% 0.28/0.45 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_inout_Osubcomponents,type,
% 0.28/0.45 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 0.28/0.45 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 0.28/0.45 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_P,type,
% 0.28/0.45 p: secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_PQ,type,
% 0.28/0.45 pq: secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_Q,type,
% 0.28/0.45 q: secrecy_specID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_ch,type,
% 0.28/0.45 ch: secrecy_chanID ).
% 0.28/0.45
% 0.28/0.45 thf(sy_v_m,type,
% 0.28/0.45 m: secrecy_Expression ).
% 0.28/0.45
% 0.28/0.45 % Relevant facts (355)
% 0.28/0.45 thf(fact_0_assms_I2_J,axiom,
% 0.28/0.45 correctCompositionIn @ pq ).
% 0.28/0.45
% 0.28/0.45 % assms(2)
% 0.28/0.45 thf(fact_1_assms_I4_J,axiom,
% 0.28/0.45 exprChannel @ ch @ m ).
% 0.28/0.45
% 0.28/0.45 % assms(4)
% 0.28/0.45 thf(fact_2_assms_I3_J,axiom,
% 0.28/0.45 member1967978193chanID @ ch @ ( ins @ p ) ).
% 0.28/0.45
% 0.28/0.45 % assms(3)
% 0.28/0.45 thf(fact_3_assms_I5_J,axiom,
% 0.28/0.45 ! [X: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ X @ ( ins @ pq ) )
% 0.28/0.45 => ~ ( exprChannel @ X @ m ) ) ).
% 0.28/0.45
% 0.28/0.45 % assms(5)
% 0.28/0.45 thf(fact_4_assms_I1_J,axiom,
% 0.28/0.45 ( ( subcomponents @ pq )
% 0.28/0.45 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % assms(1)
% 0.28/0.45 thf(fact_5_locStream__def,axiom,
% 0.28/0.45 ( locStream
% 0.28/0.45 = ( ^ [X2: secrecy_specID] :
% 0.28/0.45 ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z )
% 0.28/0.45 @ ( loc @ X2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % locStream_def
% 0.28/0.45 thf(fact_6_correctCompositionIn__L1,axiom,
% 0.28/0.45 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.45 ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 0.28/0.45 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.45 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % correctCompositionIn_L1
% 0.28/0.45 thf(fact_7_correctCompositionIn__L2,axiom,
% 0.28/0.45 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.45 ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.45 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.45 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % correctCompositionIn_L2
% 0.28/0.45 thf(fact_8_correctCompositionIn__prop1,axiom,
% 0.28/0.45 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.28/0.45 ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 0.28/0.45 => ( ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 0.28/0.45 | ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % correctCompositionIn_prop1
% 0.28/0.45 thf(fact_9_singletonI,axiom,
% 0.28/0.45 ! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ).
% 0.28/0.45
% 0.28/0.45 % singletonI
% 0.28/0.45 thf(fact_10_singletonI,axiom,
% 0.28/0.45 ! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ).
% 0.28/0.45
% 0.28/0.45 % singletonI
% 0.28/0.45 thf(fact_11_TBtheorem4b__P,axiom,
% 0.28/0.45 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.45 ( ( ineM @ P @ M @ E )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 0.28/0.45 & ( exprChannel @ Ch2 @ E )
% 0.28/0.45 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.28/0.45 & ( member1967978193chanID @ Ch2 @ M ) )
% 0.28/0.45 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4b_P
% 0.28/0.45 thf(fact_12_TBtheorem4b__PQ,axiom,
% 0.28/0.45 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.45 ( ( ( ineM @ P @ M @ E )
% 0.28/0.45 | ( ineM @ Q @ M @ E ) )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.45 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.28/0.45 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.28/0.45 & ( member1967978193chanID @ Ch2 @ M )
% 0.28/0.45 & ( exprChannel @ Ch2 @ E )
% 0.28/0.45 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.45 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4b_PQ
% 0.28/0.45 thf(fact_13_TBlemma3b,axiom,
% 0.28/0.45 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.45 ( ~ ( ineM @ P @ M @ E )
% 0.28/0.45 => ( ~ ( ineM @ Q @ M @ E )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ( member1967978193chanID @ Ch @ M )
% 0.28/0.45 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.45 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBlemma3b
% 0.28/0.45 thf(fact_14_inStream__def,axiom,
% 0.28/0.45 ( inStream
% 0.28/0.45 = ( ^ [X2: secrecy_specID] :
% 0.28/0.45 ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z )
% 0.28/0.45 @ ( ins @ X2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inStream_def
% 0.28/0.45 thf(fact_15_insertCI,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.45 ( ( ~ ( member1967978193chanID @ A @ B )
% 0.28/0.45 => ( A = B2 ) )
% 0.28/0.45 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertCI
% 0.28/0.45 thf(fact_16_insertCI,axiom,
% 0.28/0.45 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.28/0.45 ( ( ~ ( member740727610specID @ A @ B )
% 0.28/0.45 => ( A = B2 ) )
% 0.28/0.45 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertCI
% 0.28/0.45 thf(fact_17_insert__iff,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 0.28/0.45 = ( ( A = B2 )
% 0.28/0.45 | ( member1967978193chanID @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_iff
% 0.28/0.45 thf(fact_18_insert__iff,axiom,
% 0.28/0.45 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 0.28/0.45 = ( ( A = B2 )
% 0.28/0.45 | ( member740727610specID @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_iff
% 0.28/0.45 thf(fact_19_insert__absorb2,axiom,
% 0.28/0.45 ! [X3: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X3 @ A2 ) )
% 0.28/0.45 = ( insert1671894227specID @ X3 @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_absorb2
% 0.28/0.45 thf(fact_20_insert__absorb2,axiom,
% 0.28/0.45 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ X3 @ A2 ) )
% 0.28/0.45 = ( insert751661162chanID @ X3 @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_absorb2
% 0.28/0.45 thf(fact_21_empty__iff,axiom,
% 0.28/0.45 ! [C: secrecy_specID] :
% 0.28/0.45 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 0.28/0.45
% 0.28/0.45 % empty_iff
% 0.28/0.45 thf(fact_22_empty__iff,axiom,
% 0.28/0.45 ! [C: secrecy_chanID] :
% 0.28/0.45 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 0.28/0.45
% 0.28/0.45 % empty_iff
% 0.28/0.45 thf(fact_23_all__not__in__conv,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( ! [X2: secrecy_specID] :
% 0.28/0.45 ~ ( member740727610specID @ X2 @ A2 ) )
% 0.28/0.45 = ( A2 = bot_bo1785112429specID ) ) ).
% 0.28/0.45
% 0.28/0.45 % all_not_in_conv
% 0.28/0.45 thf(fact_24_all__not__in__conv,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( ! [X2: secrecy_chanID] :
% 0.28/0.45 ~ ( member1967978193chanID @ X2 @ A2 ) )
% 0.28/0.45 = ( A2 = bot_bo443197316chanID ) ) ).
% 0.28/0.45
% 0.28/0.45 % all_not_in_conv
% 0.28/0.45 thf(fact_25_Collect__empty__eq,axiom,
% 0.28/0.45 ! [P: secrecy_specID > $o] :
% 0.28/0.45 ( ( ( collec1545797240specID @ P )
% 0.28/0.45 = bot_bo1785112429specID )
% 0.28/0.45 = ( ! [X2: secrecy_specID] :
% 0.28/0.45 ~ ( P @ X2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_empty_eq
% 0.28/0.45 thf(fact_26_Collect__empty__eq,axiom,
% 0.28/0.45 ! [P: secrecy_chanID > $o] :
% 0.28/0.45 ( ( ( collec625564175chanID @ P )
% 0.28/0.45 = bot_bo443197316chanID )
% 0.28/0.45 = ( ! [X2: secrecy_chanID] :
% 0.28/0.45 ~ ( P @ X2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_empty_eq
% 0.28/0.45 thf(fact_27_empty__Collect__eq,axiom,
% 0.28/0.45 ! [P: secrecy_specID > $o] :
% 0.28/0.45 ( ( bot_bo1785112429specID
% 0.28/0.45 = ( collec1545797240specID @ P ) )
% 0.28/0.45 = ( ! [X2: secrecy_specID] :
% 0.28/0.45 ~ ( P @ X2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % empty_Collect_eq
% 0.28/0.45 thf(fact_28_empty__Collect__eq,axiom,
% 0.28/0.45 ! [P: secrecy_chanID > $o] :
% 0.28/0.45 ( ( bot_bo443197316chanID
% 0.28/0.45 = ( collec625564175chanID @ P ) )
% 0.28/0.45 = ( ! [X2: secrecy_chanID] :
% 0.28/0.45 ~ ( P @ X2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % empty_Collect_eq
% 0.28/0.45 thf(fact_29_ineM__def,axiom,
% 0.28/0.45 ( ineM
% 0.28/0.45 = ( ^ [SP: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.45 ? [Ch3: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.28/0.45 & ( member1967978193chanID @ Ch3 @ M2 )
% 0.28/0.45 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ineM_def
% 0.28/0.45 thf(fact_30_ineM__L1,axiom,
% 0.28/0.45 ! [Ch: secrecy_chanID,M: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.28/0.45 ( ( member1967978193chanID @ Ch @ M )
% 0.28/0.45 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.45 => ( ( exprChannel @ Ch @ E )
% 0.28/0.45 => ( ineM @ P @ M @ E ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ineM_L1
% 0.28/0.45 thf(fact_31_ex__in__conv,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( ? [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 0.28/0.45 = ( A2 != bot_bo1785112429specID ) ) ).
% 0.28/0.45
% 0.28/0.45 % ex_in_conv
% 0.28/0.45 thf(fact_32_ex__in__conv,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( ? [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 0.28/0.45 = ( A2 != bot_bo443197316chanID ) ) ).
% 0.28/0.45
% 0.28/0.45 % ex_in_conv
% 0.28/0.45 thf(fact_33_equals0I,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_specID] :
% 0.28/0.45 ( ! [Y2: secrecy_specID] :
% 0.28/0.45 ~ ( member740727610specID @ Y2 @ A2 )
% 0.28/0.45 => ( A2 = bot_bo1785112429specID ) ) ).
% 0.28/0.45
% 0.28/0.45 % equals0I
% 0.28/0.45 thf(fact_34_equals0I,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ! [Y2: secrecy_chanID] :
% 0.28/0.45 ~ ( member1967978193chanID @ Y2 @ A2 )
% 0.28/0.45 => ( A2 = bot_bo443197316chanID ) ) ).
% 0.28/0.45
% 0.28/0.45 % equals0I
% 0.28/0.45 thf(fact_35_equals0D,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_specID,A: secrecy_specID] :
% 0.28/0.45 ( ( A2 = bot_bo1785112429specID )
% 0.28/0.45 => ~ ( member740727610specID @ A @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % equals0D
% 0.28/0.45 thf(fact_36_equals0D,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_chanID,A: secrecy_chanID] :
% 0.28/0.45 ( ( A2 = bot_bo443197316chanID )
% 0.28/0.45 => ~ ( member1967978193chanID @ A @ A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % equals0D
% 0.28/0.45 thf(fact_37_emptyE,axiom,
% 0.28/0.45 ! [A: secrecy_specID] :
% 0.28/0.45 ~ ( member740727610specID @ A @ bot_bo1785112429specID ) ).
% 0.28/0.45
% 0.28/0.45 % emptyE
% 0.28/0.45 thf(fact_38_emptyE,axiom,
% 0.28/0.45 ! [A: secrecy_chanID] :
% 0.28/0.45 ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ) ).
% 0.28/0.45
% 0.28/0.45 % emptyE
% 0.28/0.45 thf(fact_39_mk__disjoint__insert,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ A @ A2 )
% 0.28/0.45 => ? [B3: set_Secrecy_chanID] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( insert751661162chanID @ A @ B3 ) )
% 0.28/0.45 & ~ ( member1967978193chanID @ A @ B3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % mk_disjoint_insert
% 0.28/0.45 thf(fact_40_mk__disjoint__insert,axiom,
% 0.28/0.45 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ A @ A2 )
% 0.28/0.45 => ? [B3: set_Secrecy_specID] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( insert1671894227specID @ A @ B3 ) )
% 0.28/0.45 & ~ ( member740727610specID @ A @ B3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % mk_disjoint_insert
% 0.28/0.45 thf(fact_41_insert__commute,axiom,
% 0.28/0.45 ! [X3: secrecy_specID,Y3: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ Y3 @ A2 ) )
% 0.28/0.45 = ( insert1671894227specID @ Y3 @ ( insert1671894227specID @ X3 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_commute
% 0.28/0.45 thf(fact_42_insert__commute,axiom,
% 0.28/0.45 ! [X3: secrecy_chanID,Y3: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ Y3 @ A2 ) )
% 0.28/0.45 = ( insert751661162chanID @ Y3 @ ( insert751661162chanID @ X3 @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_commute
% 0.28/0.45 thf(fact_43_insert__eq__iff,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.45 ( ~ ( member1967978193chanID @ A @ A2 )
% 0.28/0.45 => ( ~ ( member1967978193chanID @ B2 @ B )
% 0.28/0.45 => ( ( ( insert751661162chanID @ A @ A2 )
% 0.28/0.45 = ( insert751661162chanID @ B2 @ B ) )
% 0.28/0.45 = ( ( ( A = B2 )
% 0.28/0.45 => ( A2 = B ) )
% 0.28/0.45 & ( ( A != B2 )
% 0.28/0.45 => ? [C2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( insert751661162chanID @ B2 @ C2 ) )
% 0.28/0.45 & ~ ( member1967978193chanID @ B2 @ C2 )
% 0.28/0.45 & ( B
% 0.28/0.45 = ( insert751661162chanID @ A @ C2 ) )
% 0.28/0.45 & ~ ( member1967978193chanID @ A @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_eq_iff
% 0.28/0.45 thf(fact_44_insert__eq__iff,axiom,
% 0.28/0.45 ! [A: secrecy_specID,A2: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.45 ( ~ ( member740727610specID @ A @ A2 )
% 0.28/0.45 => ( ~ ( member740727610specID @ B2 @ B )
% 0.28/0.45 => ( ( ( insert1671894227specID @ A @ A2 )
% 0.28/0.45 = ( insert1671894227specID @ B2 @ B ) )
% 0.28/0.45 = ( ( ( A = B2 )
% 0.28/0.45 => ( A2 = B ) )
% 0.28/0.45 & ( ( A != B2 )
% 0.28/0.45 => ? [C2: set_Secrecy_specID] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( insert1671894227specID @ B2 @ C2 ) )
% 0.28/0.45 & ~ ( member740727610specID @ B2 @ C2 )
% 0.28/0.45 & ( B
% 0.28/0.45 = ( insert1671894227specID @ A @ C2 ) )
% 0.28/0.45 & ~ ( member740727610specID @ A @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_eq_iff
% 0.28/0.45 thf(fact_45_insert__absorb,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ A @ A2 )
% 0.28/0.45 => ( ( insert751661162chanID @ A @ A2 )
% 0.28/0.45 = A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_absorb
% 0.28/0.45 thf(fact_46_insert__absorb,axiom,
% 0.28/0.45 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ A @ A2 )
% 0.28/0.45 => ( ( insert1671894227specID @ A @ A2 )
% 0.28/0.45 = A2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_absorb
% 0.28/0.45 thf(fact_47_insert__ident,axiom,
% 0.28/0.45 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.45 ( ~ ( member1967978193chanID @ X3 @ A2 )
% 0.28/0.45 => ( ~ ( member1967978193chanID @ X3 @ B )
% 0.28/0.45 => ( ( ( insert751661162chanID @ X3 @ A2 )
% 0.28/0.45 = ( insert751661162chanID @ X3 @ B ) )
% 0.28/0.45 = ( A2 = B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_ident
% 0.28/0.45 thf(fact_48_insert__ident,axiom,
% 0.28/0.45 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.45 ( ~ ( member740727610specID @ X3 @ A2 )
% 0.28/0.45 => ( ~ ( member740727610specID @ X3 @ B )
% 0.28/0.45 => ( ( ( insert1671894227specID @ X3 @ A2 )
% 0.28/0.45 = ( insert1671894227specID @ X3 @ B ) )
% 0.28/0.45 = ( A2 = B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_ident
% 0.28/0.45 thf(fact_49_Set_Oset__insert,axiom,
% 0.28/0.45 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ X3 @ A2 )
% 0.28/0.45 => ~ ! [B3: set_Secrecy_chanID] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( insert751661162chanID @ X3 @ B3 ) )
% 0.28/0.45 => ( member1967978193chanID @ X3 @ B3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Set.set_insert
% 0.28/0.45 thf(fact_50_Set_Oset__insert,axiom,
% 0.28/0.45 ! [X3: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ X3 @ A2 )
% 0.28/0.45 => ~ ! [B3: set_Secrecy_specID] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( insert1671894227specID @ X3 @ B3 ) )
% 0.28/0.45 => ( member740727610specID @ X3 @ B3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Set.set_insert
% 0.28/0.45 thf(fact_51_insertI2,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ A @ B )
% 0.28/0.45 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertI2
% 0.28/0.45 thf(fact_52_insertI2,axiom,
% 0.28/0.45 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ A @ B )
% 0.28/0.45 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertI2
% 0.28/0.45 thf(fact_53_insertI1,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertI1
% 0.28/0.45 thf(fact_54_insertI1,axiom,
% 0.28/0.45 ! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertI1
% 0.28/0.45 thf(fact_55_insertE,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 0.28/0.45 => ( ( A != B2 )
% 0.28/0.45 => ( member1967978193chanID @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertE
% 0.28/0.45 thf(fact_56_insertE,axiom,
% 0.28/0.45 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 0.28/0.45 => ( ( A != B2 )
% 0.28/0.45 => ( member740727610specID @ A @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insertE
% 0.28/0.45 thf(fact_57_TBtheorem3b,axiom,
% 0.28/0.45 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.45 ( ~ ( ineM @ P @ M @ E )
% 0.28/0.45 => ( ~ ( ineM @ Q @ M @ E )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem3b
% 0.28/0.45 thf(fact_58_TBtheorem1b,axiom,
% 0.28/0.45 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.45 ( ( ineM @ PQ @ M @ E )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ( ineM @ P @ M @ E )
% 0.28/0.45 | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem1b
% 0.28/0.45 thf(fact_59_singleton__inject,axiom,
% 0.28/0.45 ! [A: secrecy_specID,B2: secrecy_specID] :
% 0.28/0.45 ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
% 0.28/0.45 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.28/0.45 => ( A = B2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % singleton_inject
% 0.28/0.45 thf(fact_60_singleton__inject,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.45 ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
% 0.28/0.45 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.28/0.45 => ( A = B2 ) ) ).
% 0.28/0.45
% 0.28/0.45 % singleton_inject
% 0.28/0.45 thf(fact_61_insert__not__empty,axiom,
% 0.28/0.45 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( insert1671894227specID @ A @ A2 )
% 0.28/0.45 != bot_bo1785112429specID ) ).
% 0.28/0.45
% 0.28/0.45 % insert_not_empty
% 0.28/0.45 thf(fact_62_insert__not__empty,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( insert751661162chanID @ A @ A2 )
% 0.28/0.45 != bot_bo443197316chanID ) ).
% 0.28/0.45
% 0.28/0.45 % insert_not_empty
% 0.28/0.45 thf(fact_63_doubleton__eq__iff,axiom,
% 0.28/0.45 ! [A: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 0.28/0.45 ( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.28/0.45 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 0.28/0.45 = ( ( ( A = C )
% 0.28/0.45 & ( B2 = D ) )
% 0.28/0.45 | ( ( A = D )
% 0.28/0.45 & ( B2 = C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % doubleton_eq_iff
% 0.28/0.45 thf(fact_64_doubleton__eq__iff,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 0.28/0.45 ( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.28/0.45 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 0.28/0.45 = ( ( ( A = C )
% 0.28/0.45 & ( B2 = D ) )
% 0.28/0.45 | ( ( A = D )
% 0.28/0.45 & ( B2 = C ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % doubleton_eq_iff
% 0.28/0.45 thf(fact_65_singleton__iff,axiom,
% 0.28/0.45 ! [B2: secrecy_specID,A: secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 0.28/0.45 = ( B2 = A ) ) ).
% 0.28/0.45
% 0.28/0.45 % singleton_iff
% 0.28/0.45 thf(fact_66_singleton__iff,axiom,
% 0.28/0.45 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 0.28/0.45 = ( B2 = A ) ) ).
% 0.28/0.45
% 0.28/0.45 % singleton_iff
% 0.28/0.45 thf(fact_67_singletonD,axiom,
% 0.28/0.45 ! [B2: secrecy_specID,A: secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 0.28/0.45 => ( B2 = A ) ) ).
% 0.28/0.45
% 0.28/0.45 % singletonD
% 0.28/0.45 thf(fact_68_singletonD,axiom,
% 0.28/0.45 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 0.28/0.45 => ( B2 = A ) ) ).
% 0.28/0.45
% 0.28/0.45 % singletonD
% 0.28/0.45 thf(fact_69_TBtheorem4b__notP1,axiom,
% 0.28/0.45 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.45 ( ( ineM @ P @ M @ E )
% 0.28/0.45 => ( ~ ( ineM @ Q @ M @ E )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.45 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.28/0.45 & ( member1967978193chanID @ Ch2 @ M )
% 0.28/0.45 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.45 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4b_notP1
% 0.28/0.45 thf(fact_70_TBtheorem4b__notPQ,axiom,
% 0.28/0.45 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 0.28/0.45 ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.45 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.45 => ( ! [X4: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.28/0.45 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.45 => ( ! [X4: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.28/0.45 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.45 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4b_notPQ
% 0.28/0.45 thf(fact_71_mem__Collect__eq,axiom,
% 0.28/0.45 ! [A: secrecy_chanID,P: secrecy_chanID > $o] :
% 0.28/0.45 ( ( member1967978193chanID @ A @ ( collec625564175chanID @ P ) )
% 0.28/0.45 = ( P @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % mem_Collect_eq
% 0.28/0.45 thf(fact_72_mem__Collect__eq,axiom,
% 0.28/0.45 ! [A: secrecy_specID,P: secrecy_specID > $o] :
% 0.28/0.45 ( ( member740727610specID @ A @ ( collec1545797240specID @ P ) )
% 0.28/0.45 = ( P @ A ) ) ).
% 0.28/0.45
% 0.28/0.45 % mem_Collect_eq
% 0.28/0.45 thf(fact_73_Collect__mem__eq,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( collec625564175chanID
% 0.28/0.45 @ ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 0.28/0.45 = A2 ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_mem_eq
% 0.28/0.45 thf(fact_74_Collect__mem__eq,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( collec1545797240specID
% 0.28/0.45 @ ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 0.28/0.45 = A2 ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_mem_eq
% 0.28/0.45 thf(fact_75_Collect__cong,axiom,
% 0.28/0.45 ! [P: secrecy_chanID > $o,Q: secrecy_chanID > $o] :
% 0.28/0.45 ( ! [X4: secrecy_chanID] :
% 0.28/0.45 ( ( P @ X4 )
% 0.28/0.45 = ( Q @ X4 ) )
% 0.28/0.45 => ( ( collec625564175chanID @ P )
% 0.28/0.45 = ( collec625564175chanID @ Q ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_cong
% 0.28/0.45 thf(fact_76_Collect__cong,axiom,
% 0.28/0.45 ! [P: secrecy_specID > $o,Q: secrecy_specID > $o] :
% 0.28/0.45 ( ! [X4: secrecy_specID] :
% 0.28/0.45 ( ( P @ X4 )
% 0.28/0.45 = ( Q @ X4 ) )
% 0.28/0.45 => ( ( collec1545797240specID @ P )
% 0.28/0.45 = ( collec1545797240specID @ Q ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_cong
% 0.28/0.45 thf(fact_77_TBtheorem4b__notP2,axiom,
% 0.28/0.45 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.45 ( ~ ( ineM @ Q @ M @ E )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.45 => ( ! [X4: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.28/0.45 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.45 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4b_notP2
% 0.28/0.45 thf(fact_78_the__elem__eq,axiom,
% 0.28/0.45 ! [X3: secrecy_specID] :
% 0.28/0.45 ( ( the_el827131246specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % the_elem_eq
% 0.28/0.45 thf(fact_79_the__elem__eq,axiom,
% 0.28/0.45 ! [X3: secrecy_chanID] :
% 0.28/0.45 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % the_elem_eq
% 0.28/0.45 thf(fact_80_bot__apply,axiom,
% 0.28/0.45 ( bot_bo1012329985anID_o
% 0.28/0.45 = ( ^ [X2: secrecy_chanID] : bot_bot_o ) ) ).
% 0.28/0.45
% 0.28/0.45 % bot_apply
% 0.28/0.45 thf(fact_81_bot__apply,axiom,
% 0.28/0.45 ( bot_bo1767780696ecID_o
% 0.28/0.45 = ( ^ [X2: secrecy_specID] : bot_bot_o ) ) ).
% 0.28/0.45
% 0.28/0.45 % bot_apply
% 0.28/0.45 thf(fact_82_TBtheorem4a__PQ,axiom,
% 0.28/0.45 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.45 ( ( ( ine @ P @ E )
% 0.28/0.45 | ( ine @ Q @ E ) )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.45 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.28/0.45 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.28/0.45 & ( exprChannel @ Ch2 @ E )
% 0.28/0.45 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.45 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4a_PQ
% 0.28/0.45 thf(fact_83_TBtheorem4a__P,axiom,
% 0.28/0.45 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.45 ( ( ine @ P @ E )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.28/0.45 & ( exprChannel @ Ch2 @ E )
% 0.28/0.45 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.45 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4a_P
% 0.28/0.45 thf(fact_84_is__singletonI,axiom,
% 0.28/0.45 ! [X3: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singletonI
% 0.28/0.45 thf(fact_85_is__singletonI,axiom,
% 0.28/0.45 ! [X3: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singletonI
% 0.28/0.45 thf(fact_86_TBtheorem4a__empty,axiom,
% 0.28/0.45 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.45 ( ( ( ine @ P @ E )
% 0.28/0.45 | ( ine @ Q @ E ) )
% 0.28/0.45 => ( ( ( subcomponents @ PQ )
% 0.28/0.45 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.45 => ( ( correctCompositionIn @ PQ )
% 0.28/0.45 => ( ( ( loc @ PQ )
% 0.28/0.45 = bot_bo443197316chanID )
% 0.28/0.45 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % TBtheorem4a_empty
% 0.28/0.45 thf(fact_87_ine__exprChannelSingle__def,axiom,
% 0.28/0.45 ( ine_ex1303305700Single
% 0.28/0.45 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.45 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.28/0.45 & ( exprChannel @ Ch3 @ E2 )
% 0.28/0.45 & ! [X2: secrecy_chanID,T: nat] :
% 0.28/0.45 ( ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 0.28/0.45 & ( X2 != Ch3 ) )
% 0.28/0.45 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ine_exprChannelSingle_def
% 0.28/0.45 thf(fact_88_ine__empty__exprChannelSet,axiom,
% 0.28/0.45 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.45 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.45 => ( ( ChSet = bot_bo443197316chanID )
% 0.28/0.45 => ~ ( ine @ P @ E ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ine_empty_exprChannelSet
% 0.28/0.45 thf(fact_89_ine__exprChannelSet__Single,axiom,
% 0.28/0.45 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.45 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.28/0.45 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.28/0.45
% 0.28/0.45 % ine_exprChannelSet_Single
% 0.28/0.45 thf(fact_90_ine__exprChannelSingle__Set,axiom,
% 0.28/0.45 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.45 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.28/0.45 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.28/0.45
% 0.28/0.45 % ine_exprChannelSingle_Set
% 0.28/0.45 thf(fact_91_ine__nonempty__exprChannelSet,axiom,
% 0.28/0.45 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.45 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.45 => ( ( ChSet != bot_bo443197316chanID )
% 0.28/0.45 => ( ine @ P @ E ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ine_nonempty_exprChannelSet
% 0.28/0.45 thf(fact_92_bot__set__def,axiom,
% 0.28/0.45 ( bot_bo1785112429specID
% 0.28/0.45 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 0.28/0.45
% 0.28/0.45 % bot_set_def
% 0.28/0.45 thf(fact_93_bot__set__def,axiom,
% 0.28/0.45 ( bot_bo443197316chanID
% 0.28/0.45 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 0.28/0.45
% 0.28/0.45 % bot_set_def
% 0.28/0.45 thf(fact_94_not__ine__ineM,axiom,
% 0.28/0.45 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 0.28/0.45 ( ~ ( ine @ P @ E )
% 0.28/0.45 => ~ ( ineM @ P @ M @ E ) ) ).
% 0.28/0.45
% 0.28/0.45 % not_ine_ineM
% 0.28/0.45 thf(fact_95_ineM__ine,axiom,
% 0.28/0.45 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.45 ( ( ineM @ P @ M @ E )
% 0.28/0.45 => ( ine @ P @ E ) ) ).
% 0.28/0.45
% 0.28/0.45 % ineM_ine
% 0.28/0.45 thf(fact_96_is__singleton__the__elem,axiom,
% 0.28/0.45 ( is_sin1501507247specID
% 0.28/0.45 = ( ^ [A3: set_Secrecy_specID] :
% 0.28/0.45 ( A3
% 0.28/0.45 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singleton_the_elem
% 0.28/0.45 thf(fact_97_is__singleton__the__elem,axiom,
% 0.28/0.45 ( is_sin581274182chanID
% 0.28/0.45 = ( ^ [A3: set_Secrecy_chanID] :
% 0.28/0.45 ( A3
% 0.28/0.45 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singleton_the_elem
% 0.28/0.45 thf(fact_98_ine__def,axiom,
% 0.28/0.45 ( ine
% 0.28/0.45 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.28/0.45 ? [Ch3: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.28/0.45 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ine_def
% 0.28/0.45 thf(fact_99_ine__ins__neg1,axiom,
% 0.28/0.45 ! [P: secrecy_specID,M3: secrecy_Expression,X3: secrecy_chanID] :
% 0.28/0.45 ( ~ ( ine @ P @ M3 )
% 0.28/0.45 => ( ( exprChannel @ X3 @ M3 )
% 0.28/0.45 => ~ ( member1967978193chanID @ X3 @ ( ins @ P ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % ine_ins_neg1
% 0.28/0.45 thf(fact_100_is__singletonI_H,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_specID] :
% 0.28/0.45 ( ( A2 != bot_bo1785112429specID )
% 0.28/0.45 => ( ! [X4: secrecy_specID,Y2: secrecy_specID] :
% 0.28/0.45 ( ( member740727610specID @ X4 @ A2 )
% 0.28/0.45 => ( ( member740727610specID @ Y2 @ A2 )
% 0.28/0.45 => ( X4 = Y2 ) ) )
% 0.28/0.45 => ( is_sin1501507247specID @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singletonI'
% 0.28/0.45 thf(fact_101_is__singletonI_H,axiom,
% 0.28/0.45 ! [A2: set_Secrecy_chanID] :
% 0.28/0.45 ( ( A2 != bot_bo443197316chanID )
% 0.28/0.45 => ( ! [X4: secrecy_chanID,Y2: secrecy_chanID] :
% 0.28/0.45 ( ( member1967978193chanID @ X4 @ A2 )
% 0.28/0.46 => ( ( member1967978193chanID @ Y2 @ A2 )
% 0.28/0.46 => ( X4 = Y2 ) ) )
% 0.28/0.46 => ( is_sin581274182chanID @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % is_singletonI'
% 0.28/0.46 thf(fact_102_bot__fun__def,axiom,
% 0.28/0.46 ( bot_bo1012329985anID_o
% 0.28/0.46 = ( ^ [X2: secrecy_chanID] : bot_bot_o ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_fun_def
% 0.28/0.46 thf(fact_103_bot__fun__def,axiom,
% 0.28/0.46 ( bot_bo1767780696ecID_o
% 0.28/0.46 = ( ^ [X2: secrecy_specID] : bot_bot_o ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_fun_def
% 0.28/0.46 thf(fact_104_TBtheorem4a__notP2,axiom,
% 0.28/0.46 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( ine @ Q @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correctCompositionIn @ PQ )
% 0.28/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem4a_notP2
% 0.28/0.46 thf(fact_105_TBtheorem4a__notPQ,axiom,
% 0.28/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correctCompositionIn @ PQ )
% 0.28/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem4a_notPQ
% 0.28/0.46 thf(fact_106_TBtheorem4a__notP1,axiom,
% 0.28/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.46 ( ( ine @ P @ E )
% 0.28/0.46 => ( ~ ( ine @ Q @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correctCompositionIn @ PQ )
% 0.28/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.46 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.28/0.46 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem4a_notP1
% 0.28/0.46 thf(fact_107_ine__exprChannelSet__def,axiom,
% 0.28/0.46 ( ine_exprChannelSet
% 0.28/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.46 ( ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 0.28/0.46 => ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 0.28/0.46 & ( exprChannel @ X2 @ E2 ) ) )
% 0.28/0.46 & ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 0.28/0.46 & ( member1967978193chanID @ X2 @ ( ins @ SP ) ) )
% 0.28/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ine_exprChannelSet_def
% 0.28/0.46 thf(fact_108_is__singletonE,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID] :
% 0.28/0.46 ( ( is_sin1501507247specID @ A2 )
% 0.28/0.46 => ~ ! [X4: secrecy_specID] :
% 0.28/0.46 ( A2
% 0.28/0.46 != ( insert1671894227specID @ X4 @ bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % is_singletonE
% 0.28/0.46 thf(fact_109_is__singletonE,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( is_sin581274182chanID @ A2 )
% 0.28/0.46 => ~ ! [X4: secrecy_chanID] :
% 0.28/0.46 ( A2
% 0.28/0.46 != ( insert751661162chanID @ X4 @ bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % is_singletonE
% 0.28/0.46 thf(fact_110_is__singleton__def,axiom,
% 0.28/0.46 ( is_sin1501507247specID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_specID] :
% 0.28/0.46 ? [X2: secrecy_specID] :
% 0.28/0.46 ( A3
% 0.28/0.46 = ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % is_singleton_def
% 0.28/0.46 thf(fact_111_is__singleton__def,axiom,
% 0.28/0.46 ( is_sin581274182chanID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_chanID] :
% 0.28/0.46 ? [X2: secrecy_chanID] :
% 0.28/0.46 ( A3
% 0.28/0.46 = ( insert751661162chanID @ X2 @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % is_singleton_def
% 0.28/0.46 thf(fact_112_TBtheorem1a,axiom,
% 0.28/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.46 ( ( ine @ PQ @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correctCompositionIn @ PQ )
% 0.28/0.46 => ( ( ine @ P @ E )
% 0.28/0.46 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem1a
% 0.28/0.46 thf(fact_113_TBtheorem3a,axiom,
% 0.28/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.46 ( ~ ( ine @ P @ E )
% 0.28/0.46 => ( ~ ( ine @ Q @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correctCompositionIn @ PQ )
% 0.28/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem3a
% 0.28/0.46 thf(fact_114_subcomponents__loc,axiom,
% 0.28/0.46 ! [X3: secrecy_specID] :
% 0.28/0.46 ( ( correc965049635ionLoc @ X3 )
% 0.28/0.46 => ( ( ( subcomponents @ X3 )
% 0.28/0.46 = bot_bo1785112429specID )
% 0.28/0.46 => ( ( loc @ X3 )
% 0.28/0.46 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subcomponents_loc
% 0.28/0.46 thf(fact_115_Set_Ois__empty__def,axiom,
% 0.28/0.46 ( is_emp1849217361specID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Set.is_empty_def
% 0.28/0.46 thf(fact_116_Set_Ois__empty__def,axiom,
% 0.28/0.46 ( is_emp928984296chanID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Set.is_empty_def
% 0.28/0.46 thf(fact_117_TBtheorem5a__empty,axiom,
% 0.28/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.46 ( ( ( eout @ P @ E )
% 0.28/0.46 | ( eout @ Q @ E ) )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( ( loc @ PQ )
% 0.28/0.46 = bot_bo443197316chanID )
% 0.28/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5a_empty
% 0.28/0.46 thf(fact_118_bot__empty__eq,axiom,
% 0.28/0.46 ( bot_bo1767780696ecID_o
% 0.28/0.46 = ( ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_empty_eq
% 0.28/0.46 thf(fact_119_bot__empty__eq,axiom,
% 0.28/0.46 ( bot_bo1012329985anID_o
% 0.28/0.46 = ( ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_empty_eq
% 0.28/0.46 thf(fact_120_Collect__empty__eq__bot,axiom,
% 0.28/0.46 ! [P: secrecy_specID > $o] :
% 0.28/0.46 ( ( ( collec1545797240specID @ P )
% 0.28/0.46 = bot_bo1785112429specID )
% 0.28/0.46 = ( P = bot_bo1767780696ecID_o ) ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_empty_eq_bot
% 0.28/0.46 thf(fact_121_Collect__empty__eq__bot,axiom,
% 0.28/0.46 ! [P: secrecy_chanID > $o] :
% 0.28/0.46 ( ( ( collec625564175chanID @ P )
% 0.28/0.46 = bot_bo443197316chanID )
% 0.28/0.46 = ( P = bot_bo1012329985anID_o ) ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_empty_eq_bot
% 0.28/0.46 thf(fact_122_pairwise__singleton,axiom,
% 0.28/0.46 ! [P: secrecy_specID > secrecy_specID > $o,A2: secrecy_specID] : ( pairwi514744696specID @ P @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwise_singleton
% 0.28/0.46 thf(fact_123_pairwise__singleton,axiom,
% 0.28/0.46 ! [P: secrecy_chanID > secrecy_chanID > $o,A2: secrecy_chanID] : ( pairwi1741995279chanID @ P @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwise_singleton
% 0.28/0.46 thf(fact_124_singleton__insert__inj__eq,axiom,
% 0.28/0.46 ! [B2: secrecy_specID,A: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ( insert1671894227specID @ B2 @ bot_bo1785112429specID )
% 0.28/0.46 = ( insert1671894227specID @ A @ A2 ) )
% 0.28/0.46 = ( ( A = B2 )
% 0.28/0.46 & ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % singleton_insert_inj_eq
% 0.28/0.46 thf(fact_125_singleton__insert__inj__eq,axiom,
% 0.28/0.46 ! [B2: secrecy_chanID,A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( insert751661162chanID @ B2 @ bot_bo443197316chanID )
% 0.28/0.46 = ( insert751661162chanID @ A @ A2 ) )
% 0.28/0.46 = ( ( A = B2 )
% 0.28/0.46 & ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % singleton_insert_inj_eq
% 0.28/0.46 thf(fact_126_order__refl,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X3 @ X3 ) ).
% 0.28/0.46
% 0.28/0.46 % order_refl
% 0.28/0.46 thf(fact_127_order__refl,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID] : ( ord_le996703545specID @ X3 @ X3 ) ).
% 0.28/0.46
% 0.28/0.46 % order_refl
% 0.28/0.46 thf(fact_128_subsetI,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ A2 )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ B ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ A2 @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % subsetI
% 0.28/0.46 thf(fact_129_subsetI,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ! [X4: secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ X4 @ A2 )
% 0.28/0.46 => ( member740727610specID @ X4 @ B ) )
% 0.28/0.46 => ( ord_le996703545specID @ A2 @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % subsetI
% 0.28/0.46 thf(fact_130_subset__antisym,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ B )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B @ A2 )
% 0.28/0.46 => ( A2 = B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_antisym
% 0.28/0.46 thf(fact_131_subset__antisym,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A2 @ B )
% 0.28/0.46 => ( ( ord_le996703545specID @ B @ A2 )
% 0.28/0.46 => ( A2 = B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_antisym
% 0.28/0.46 thf(fact_132_empty__subsetI,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID] : ( ord_le996703545specID @ bot_bo1785112429specID @ A2 ) ).
% 0.28/0.46
% 0.28/0.46 % empty_subsetI
% 0.28/0.46 thf(fact_133_empty__subsetI,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ bot_bo443197316chanID @ A2 ) ).
% 0.28/0.46
% 0.28/0.46 % empty_subsetI
% 0.28/0.46 thf(fact_134_subset__empty,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A2 @ bot_bo1785112429specID )
% 0.28/0.46 = ( A2 = bot_bo1785112429specID ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_empty
% 0.28/0.46 thf(fact_135_subset__empty,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ bot_bo443197316chanID )
% 0.28/0.46 = ( A2 = bot_bo443197316chanID ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_empty
% 0.28/0.46 thf(fact_136_insert__subset,axiom,
% 0.28/0.46 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ ( insert751661162chanID @ X3 @ A2 ) @ B )
% 0.28/0.46 = ( ( member1967978193chanID @ X3 @ B )
% 0.28/0.46 & ( ord_le1802272080chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_subset
% 0.28/0.46 thf(fact_137_insert__subset,axiom,
% 0.28/0.46 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ ( insert1671894227specID @ X3 @ A2 ) @ B )
% 0.28/0.46 = ( ( member740727610specID @ X3 @ B )
% 0.28/0.46 & ( ord_le996703545specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_subset
% 0.28/0.46 thf(fact_138_singleton__insert__inj__eq_H,axiom,
% 0.28/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID,B2: secrecy_specID] :
% 0.28/0.46 ( ( ( insert1671894227specID @ A @ A2 )
% 0.28/0.46 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.28/0.46 = ( ( A = B2 )
% 0.28/0.46 & ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % singleton_insert_inj_eq'
% 0.28/0.46 thf(fact_139_singleton__insert__inj__eq_H,axiom,
% 0.28/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.46 ( ( ( insert751661162chanID @ A @ A2 )
% 0.28/0.46 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.28/0.46 = ( ( A = B2 )
% 0.28/0.46 & ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % singleton_insert_inj_eq'
% 0.28/0.46 thf(fact_140_order__subst1,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_141_order__subst1,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,F: set_Secrecy_specID > set_Secrecy_chanID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le996703545specID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_142_order__subst1,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,F: set_Secrecy_chanID > set_Secrecy_specID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_143_order__subst1,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le996703545specID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst1
% 0.28/0.46 thf(fact_144_order__subst2,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ ( F @ B2 ) @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_145_order__subst2,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le996703545specID @ ( F @ B2 ) @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_146_order__subst2,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ ( F @ B2 ) @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_147_order__subst2,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le996703545specID @ ( F @ B2 ) @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_subst2
% 0.28/0.46 thf(fact_148_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( A
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_149_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,F: set_Secrecy_chanID > set_Secrecy_specID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( A
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_150_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,F: set_Secrecy_specID > set_Secrecy_chanID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( A
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le996703545specID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_151_ord__eq__le__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( A
% 0.28/0.46 = ( F @ B2 ) )
% 0.28/0.46 => ( ( ord_le996703545specID @ B2 @ C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_subst
% 0.28/0.46 thf(fact_152_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_153_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_154_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_155_ord__le__eq__subst,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ B2 )
% 0.28/0.46 => ( ( ( F @ B2 )
% 0.28/0.46 = C )
% 0.28/0.46 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X4 @ Y2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 0.28/0.46 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_subst
% 0.28/0.46 thf(fact_156_eq__iff,axiom,
% 0.28/0.46 ( ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [X2: set_Secrecy_chanID,Y4: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X2 @ Y4 )
% 0.28/0.46 & ( ord_le1802272080chanID @ Y4 @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_iff
% 0.28/0.46 thf(fact_157_eq__iff,axiom,
% 0.28/0.46 ( ( ^ [Y: set_Secrecy_specID,Z: set_Secrecy_specID] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [X2: set_Secrecy_specID,Y4: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X2 @ Y4 )
% 0.28/0.46 & ( ord_le996703545specID @ Y4 @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_iff
% 0.28/0.46 thf(fact_158_antisym,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 0.28/0.46 => ( X3 = Y3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % antisym
% 0.28/0.46 thf(fact_159_antisym,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X3 @ Y3 )
% 0.28/0.46 => ( ( ord_le996703545specID @ Y3 @ X3 )
% 0.28/0.46 => ( X3 = Y3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % antisym
% 0.28/0.46 thf(fact_160_eq__refl,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( X3 = Y3 )
% 0.28/0.46 => ( ord_le1802272080chanID @ X3 @ Y3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_refl
% 0.28/0.46 thf(fact_161_eq__refl,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 0.28/0.46 ( ( X3 = Y3 )
% 0.28/0.46 => ( ord_le996703545specID @ X3 @ Y3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_refl
% 0.28/0.46 thf(fact_162_order_Otrans,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ C )
% 0.28/0.46 => ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order.trans
% 0.28/0.46 thf(fact_163_order_Otrans,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le996703545specID @ B2 @ C )
% 0.28/0.46 => ( ord_le996703545specID @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order.trans
% 0.28/0.46 thf(fact_164_antisym__conv,axiom,
% 0.28/0.46 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 0.28/0.46 = ( X3 = Y3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % antisym_conv
% 0.28/0.46 thf(fact_165_antisym__conv,axiom,
% 0.28/0.46 ! [Y3: set_Secrecy_specID,X3: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ Y3 @ X3 )
% 0.28/0.46 => ( ( ord_le996703545specID @ X3 @ Y3 )
% 0.28/0.46 = ( X3 = Y3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % antisym_conv
% 0.28/0.46 thf(fact_166_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.46 ( ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [A4: set_Secrecy_chanID,B4: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A4 @ B4 )
% 0.28/0.46 & ( ord_le1802272080chanID @ B4 @ A4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_class.order.eq_iff
% 0.28/0.46 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.46 ( ( ^ [Y: set_Secrecy_specID,Z: set_Secrecy_specID] : ( Y = Z ) )
% 0.28/0.46 = ( ^ [A4: set_Secrecy_specID,B4: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A4 @ B4 )
% 0.28/0.46 & ( ord_le996703545specID @ B4 @ A4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_class.order.eq_iff
% 0.28/0.46 thf(fact_168_ord__eq__le__trans,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( A = B2 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ C )
% 0.28/0.46 => ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_trans
% 0.28/0.46 thf(fact_169_ord__eq__le__trans,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( A = B2 )
% 0.28/0.46 => ( ( ord_le996703545specID @ B2 @ C )
% 0.28/0.46 => ( ord_le996703545specID @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_eq_le_trans
% 0.28/0.46 thf(fact_170_ord__le__eq__trans,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( B2 = C )
% 0.28/0.46 => ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_trans
% 0.28/0.46 thf(fact_171_ord__le__eq__trans,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ B2 )
% 0.28/0.46 => ( ( B2 = C )
% 0.28/0.46 => ( ord_le996703545specID @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ord_le_eq_trans
% 0.28/0.46 thf(fact_172_order__class_Oorder_Oantisym,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ A )
% 0.28/0.46 => ( A = B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_class.order.antisym
% 0.28/0.46 thf(fact_173_order__class_Oorder_Oantisym,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ B2 )
% 0.28/0.46 => ( ( ord_le996703545specID @ B2 @ A )
% 0.28/0.46 => ( A = B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_class.order.antisym
% 0.28/0.46 thf(fact_174_order__trans,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ Y3 @ Z2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ X3 @ Z2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_trans
% 0.28/0.46 thf(fact_175_order__trans,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID,Z2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X3 @ Y3 )
% 0.28/0.46 => ( ( ord_le996703545specID @ Y3 @ Z2 )
% 0.28/0.46 => ( ord_le996703545specID @ X3 @ Z2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % order_trans
% 0.28/0.46 thf(fact_176_dual__order_Orefl,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID] : ( ord_le996703545specID @ A @ A ) ).
% 0.28/0.46
% 0.28/0.46 % dual_order.refl
% 0.28/0.46 thf(fact_177_in__mono,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,X3: secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ B )
% 0.28/0.46 => ( ( member1967978193chanID @ X3 @ A2 )
% 0.28/0.46 => ( member1967978193chanID @ X3 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % in_mono
% 0.28/0.46 thf(fact_178_in__mono,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,X3: secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A2 @ B )
% 0.28/0.46 => ( ( member740727610specID @ X3 @ A2 )
% 0.28/0.46 => ( member740727610specID @ X3 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % in_mono
% 0.28/0.46 thf(fact_179_subsetD,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ B )
% 0.28/0.46 => ( ( member1967978193chanID @ C @ A2 )
% 0.28/0.46 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subsetD
% 0.28/0.46 thf(fact_180_subsetD,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A2 @ B )
% 0.28/0.46 => ( ( member740727610specID @ C @ A2 )
% 0.28/0.46 => ( member740727610specID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subsetD
% 0.28/0.46 thf(fact_181_pairwiseD,axiom,
% 0.28/0.46 ! [R: secrecy_chanID > secrecy_chanID > $o,S: set_Secrecy_chanID,X3: secrecy_chanID,Y3: secrecy_chanID] :
% 0.28/0.46 ( ( pairwi1741995279chanID @ R @ S )
% 0.28/0.46 => ( ( member1967978193chanID @ X3 @ S )
% 0.28/0.46 => ( ( member1967978193chanID @ Y3 @ S )
% 0.28/0.46 => ( ( X3 != Y3 )
% 0.28/0.46 => ( R @ X3 @ Y3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwiseD
% 0.28/0.46 thf(fact_182_pairwiseD,axiom,
% 0.28/0.46 ! [R: secrecy_specID > secrecy_specID > $o,S: set_Secrecy_specID,X3: secrecy_specID,Y3: secrecy_specID] :
% 0.28/0.46 ( ( pairwi514744696specID @ R @ S )
% 0.28/0.46 => ( ( member740727610specID @ X3 @ S )
% 0.28/0.46 => ( ( member740727610specID @ Y3 @ S )
% 0.28/0.46 => ( ( X3 != Y3 )
% 0.28/0.46 => ( R @ X3 @ Y3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwiseD
% 0.28/0.46 thf(fact_183_pairwiseI,axiom,
% 0.28/0.46 ! [S: set_Secrecy_chanID,R: secrecy_chanID > secrecy_chanID > $o] :
% 0.28/0.46 ( ! [X4: secrecy_chanID,Y2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ S )
% 0.28/0.46 => ( ( member1967978193chanID @ Y2 @ S )
% 0.28/0.46 => ( ( X4 != Y2 )
% 0.28/0.46 => ( R @ X4 @ Y2 ) ) ) )
% 0.28/0.46 => ( pairwi1741995279chanID @ R @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwiseI
% 0.28/0.46 thf(fact_184_pairwiseI,axiom,
% 0.28/0.46 ! [S: set_Secrecy_specID,R: secrecy_specID > secrecy_specID > $o] :
% 0.28/0.46 ( ! [X4: secrecy_specID,Y2: secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ X4 @ S )
% 0.28/0.46 => ( ( member740727610specID @ Y2 @ S )
% 0.28/0.46 => ( ( X4 != Y2 )
% 0.28/0.46 => ( R @ X4 @ Y2 ) ) ) )
% 0.28/0.46 => ( pairwi514744696specID @ R @ S ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwiseI
% 0.28/0.46 thf(fact_185_subset__eq,axiom,
% 0.28/0.46 ( ord_le1802272080chanID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] :
% 0.28/0.46 ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ A3 )
% 0.28/0.46 => ( member1967978193chanID @ X2 @ B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_eq
% 0.28/0.46 thf(fact_186_subset__eq,axiom,
% 0.28/0.46 ( ord_le996703545specID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_specID,B5: set_Secrecy_specID] :
% 0.28/0.46 ! [X2: secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ X2 @ A3 )
% 0.28/0.46 => ( member740727610specID @ X2 @ B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_eq
% 0.28/0.46 thf(fact_187_subset__iff,axiom,
% 0.28/0.46 ( ord_le1802272080chanID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] :
% 0.28/0.46 ! [T: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ T @ A3 )
% 0.28/0.46 => ( member1967978193chanID @ T @ B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_iff
% 0.28/0.46 thf(fact_188_subset__iff,axiom,
% 0.28/0.46 ( ord_le996703545specID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_specID,B5: set_Secrecy_specID] :
% 0.28/0.46 ! [T: secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ T @ A3 )
% 0.28/0.46 => ( member740727610specID @ T @ B5 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_iff
% 0.28/0.46 thf(fact_189_bot_Oextremum__uniqueI,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ bot_bo1785112429specID )
% 0.28/0.46 => ( A = bot_bo1785112429specID ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot.extremum_uniqueI
% 0.28/0.46 thf(fact_190_bot_Oextremum__uniqueI,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ bot_bo443197316chanID )
% 0.28/0.46 => ( A = bot_bo443197316chanID ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot.extremum_uniqueI
% 0.28/0.46 thf(fact_191_bot_Oextremum__unique,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A @ bot_bo1785112429specID )
% 0.28/0.46 = ( A = bot_bo1785112429specID ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot.extremum_unique
% 0.28/0.46 thf(fact_192_bot_Oextremum__unique,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ bot_bo443197316chanID )
% 0.28/0.46 = ( A = bot_bo443197316chanID ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot.extremum_unique
% 0.28/0.46 thf(fact_193_bot_Oextremum,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID] : ( ord_le996703545specID @ bot_bo1785112429specID @ A ) ).
% 0.28/0.46
% 0.28/0.46 % bot.extremum
% 0.28/0.46 thf(fact_194_bot_Oextremum,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID] : ( ord_le1802272080chanID @ bot_bo443197316chanID @ A ) ).
% 0.28/0.46
% 0.28/0.46 % bot.extremum
% 0.28/0.46 thf(fact_195_subset__insertI2,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A2 @ B )
% 0.28/0.46 => ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_insertI2
% 0.28/0.46 thf(fact_196_subset__insertI2,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ B )
% 0.28/0.46 => ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_insertI2
% 0.28/0.46 thf(fact_197_subset__insertI,axiom,
% 0.28/0.46 ! [B: set_Secrecy_specID,A: secrecy_specID] : ( ord_le996703545specID @ B @ ( insert1671894227specID @ A @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_insertI
% 0.28/0.46 thf(fact_198_subset__insertI,axiom,
% 0.28/0.46 ! [B: set_Secrecy_chanID,A: secrecy_chanID] : ( ord_le1802272080chanID @ B @ ( insert751661162chanID @ A @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_insertI
% 0.28/0.46 thf(fact_199_subset__insert,axiom,
% 0.28/0.46 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( member1967978193chanID @ X3 @ A2 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ X3 @ B ) )
% 0.28/0.46 = ( ord_le1802272080chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_insert
% 0.28/0.46 thf(fact_200_subset__insert,axiom,
% 0.28/0.46 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ~ ( member740727610specID @ X3 @ A2 )
% 0.28/0.46 => ( ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ X3 @ B ) )
% 0.28/0.46 = ( ord_le996703545specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_insert
% 0.28/0.46 thf(fact_201_insert__mono,axiom,
% 0.28/0.46 ! [C3: set_Secrecy_specID,D2: set_Secrecy_specID,A: secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ C3 @ D2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( insert1671894227specID @ A @ C3 ) @ ( insert1671894227specID @ A @ D2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_mono
% 0.28/0.46 thf(fact_202_insert__mono,axiom,
% 0.28/0.46 ! [C3: set_Secrecy_chanID,D2: set_Secrecy_chanID,A: secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ C3 @ D2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( insert751661162chanID @ A @ C3 ) @ ( insert751661162chanID @ A @ D2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_mono
% 0.28/0.46 thf(fact_203_pairwise__empty,axiom,
% 0.28/0.46 ! [P: secrecy_specID > secrecy_specID > $o] : ( pairwi514744696specID @ P @ bot_bo1785112429specID ) ).
% 0.28/0.46
% 0.28/0.46 % pairwise_empty
% 0.28/0.46 thf(fact_204_pairwise__empty,axiom,
% 0.28/0.46 ! [P: secrecy_chanID > secrecy_chanID > $o] : ( pairwi1741995279chanID @ P @ bot_bo443197316chanID ) ).
% 0.28/0.46
% 0.28/0.46 % pairwise_empty
% 0.28/0.46 thf(fact_205_pairwise__insert,axiom,
% 0.28/0.46 ! [R2: secrecy_chanID > secrecy_chanID > $o,X3: secrecy_chanID,S2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( pairwi1741995279chanID @ R2 @ ( insert751661162chanID @ X3 @ S2 ) )
% 0.28/0.46 = ( ! [Y4: secrecy_chanID] :
% 0.28/0.46 ( ( ( member1967978193chanID @ Y4 @ S2 )
% 0.28/0.46 & ( Y4 != X3 ) )
% 0.28/0.46 => ( ( R2 @ X3 @ Y4 )
% 0.28/0.46 & ( R2 @ Y4 @ X3 ) ) )
% 0.28/0.46 & ( pairwi1741995279chanID @ R2 @ S2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwise_insert
% 0.28/0.46 thf(fact_206_pairwise__insert,axiom,
% 0.28/0.46 ! [R2: secrecy_specID > secrecy_specID > $o,X3: secrecy_specID,S2: set_Secrecy_specID] :
% 0.28/0.46 ( ( pairwi514744696specID @ R2 @ ( insert1671894227specID @ X3 @ S2 ) )
% 0.28/0.46 = ( ! [Y4: secrecy_specID] :
% 0.28/0.46 ( ( ( member740727610specID @ Y4 @ S2 )
% 0.28/0.46 & ( Y4 != X3 ) )
% 0.28/0.46 => ( ( R2 @ X3 @ Y4 )
% 0.28/0.46 & ( R2 @ Y4 @ X3 ) ) )
% 0.28/0.46 & ( pairwi514744696specID @ R2 @ S2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pairwise_insert
% 0.28/0.46 thf(fact_207_subset__singleton__iff,axiom,
% 0.28/0.46 ! [X5: set_Secrecy_specID,A: secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ X5 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 0.28/0.46 = ( ( X5 = bot_bo1785112429specID )
% 0.28/0.46 | ( X5
% 0.28/0.46 = ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_singleton_iff
% 0.28/0.46 thf(fact_208_subset__singleton__iff,axiom,
% 0.28/0.46 ! [X5: set_Secrecy_chanID,A: secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X5 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 0.28/0.46 = ( ( X5 = bot_bo443197316chanID )
% 0.28/0.46 | ( X5
% 0.28/0.46 = ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_singleton_iff
% 0.28/0.46 thf(fact_209_subset__singletonD,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,X3: secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.46 => ( ( A2 = bot_bo1785112429specID )
% 0.28/0.46 | ( A2
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_singletonD
% 0.28/0.46 thf(fact_210_subset__singletonD,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,X3: secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.46 => ( ( A2 = bot_bo443197316chanID )
% 0.28/0.46 | ( A2
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_singletonD
% 0.28/0.46 thf(fact_211_TBtheorem2a,axiom,
% 0.28/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.46 ( ( eout @ PQ @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( eout @ P @ E )
% 0.28/0.46 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem2a
% 0.28/0.46 thf(fact_212_TBtheorem5a__notP1,axiom,
% 0.28/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.46 ( ( eout @ P @ E )
% 0.28/0.46 => ( ~ ( eout @ Q @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.46 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.28/0.46 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5a_notP1
% 0.28/0.46 thf(fact_213_TBtheorem5a__notPQ,axiom,
% 0.28/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5a_notPQ
% 0.28/0.46 thf(fact_214_TBtheorem5a__notP2,axiom,
% 0.28/0.46 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( eout @ Q @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5a_notP2
% 0.28/0.46 thf(fact_215_TBtheorem5a__PQ,axiom,
% 0.28/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.46 ( ( ( eout @ P @ E )
% 0.28/0.46 | ( eout @ Q @ E ) )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.46 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.28/0.46 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.28/0.46 & ( exprChannel @ Ch2 @ E )
% 0.28/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5a_PQ
% 0.28/0.46 thf(fact_216_TBtheorem45a__P,axiom,
% 0.28/0.46 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.46 ( ( eout @ P @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.28/0.46 & ( exprChannel @ Ch2 @ E )
% 0.28/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem45a_P
% 0.28/0.46 thf(fact_217_TBtheorem2b,axiom,
% 0.28/0.46 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.46 ( ( eoutM @ PQ @ M @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( eoutM @ P @ M @ E )
% 0.28/0.46 | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem2b
% 0.28/0.46 thf(fact_218_eoutM__def,axiom,
% 0.28/0.46 ( eoutM
% 0.28/0.46 = ( ^ [SP: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.46 ? [Ch3: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.28/0.46 & ( member1967978193chanID @ Ch3 @ M2 )
% 0.28/0.46 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eoutM_def
% 0.28/0.46 thf(fact_219_out__exprChannelSet__def,axiom,
% 0.28/0.46 ( out_exprChannelSet
% 0.28/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.46 ( ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 0.28/0.46 => ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 0.28/0.46 & ( exprChannel @ X2 @ E2 ) ) )
% 0.28/0.46 & ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 0.28/0.46 & ( member1967978193chanID @ X2 @ ( out @ SP ) ) )
% 0.28/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % out_exprChannelSet_def
% 0.28/0.46 thf(fact_220_out__exprChannelSingle__def,axiom,
% 0.28/0.46 ( out_ex985543062Single
% 0.28/0.46 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.46 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.28/0.46 & ( exprChannel @ Ch3 @ E2 )
% 0.28/0.46 & ! [X2: secrecy_chanID,T: nat] :
% 0.28/0.46 ( ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 0.28/0.46 & ( X2 != Ch3 ) )
% 0.28/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % out_exprChannelSingle_def
% 0.28/0.46 thf(fact_221_not__eout__eoutM,axiom,
% 0.28/0.46 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( eout @ P @ E )
% 0.28/0.46 => ~ ( eoutM @ P @ M @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % not_eout_eoutM
% 0.28/0.46 thf(fact_222_eoutM__eout,axiom,
% 0.28/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.46 ( ( eoutM @ P @ M @ E )
% 0.28/0.46 => ( eout @ P @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % eoutM_eout
% 0.28/0.46 thf(fact_223_out__exprChannelSet__Single,axiom,
% 0.28/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.46 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.28/0.46 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % out_exprChannelSet_Single
% 0.28/0.46 thf(fact_224_out__exprChannelSingle__Set,axiom,
% 0.28/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.46 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.28/0.46 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % out_exprChannelSingle_Set
% 0.28/0.46 thf(fact_225_eout__def,axiom,
% 0.28/0.46 ( eout
% 0.28/0.46 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.28/0.46 ? [Ch3: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.28/0.46 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eout_def
% 0.28/0.46 thf(fact_226_TBtheorem5b__notP2,axiom,
% 0.28/0.46 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( eoutM @ Q @ M @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSet )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5b_notP2
% 0.28/0.46 thf(fact_227_TBtheore54b__P,axiom,
% 0.28/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.46 ( ( eoutM @ P @ M @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 0.28/0.46 & ( exprChannel @ Ch2 @ E )
% 0.28/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.28/0.46 & ( member1967978193chanID @ Ch2 @ M ) )
% 0.28/0.46 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheore54b_P
% 0.28/0.46 thf(fact_228_TBtheorem5b__PQ,axiom,
% 0.28/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.46 ( ( ( eoutM @ P @ M @ E )
% 0.28/0.46 | ( eoutM @ Q @ M @ E ) )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.46 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.28/0.46 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.28/0.46 & ( member1967978193chanID @ Ch2 @ M )
% 0.28/0.46 & ( exprChannel @ Ch2 @ E )
% 0.28/0.46 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5b_PQ
% 0.28/0.46 thf(fact_229_TBtheorem5b__notP1,axiom,
% 0.28/0.46 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.46 ( ( eoutM @ P @ M @ E )
% 0.28/0.46 => ( ~ ( eoutM @ Q @ M @ E )
% 0.28/0.46 => ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.46 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.28/0.46 & ( member1967978193chanID @ Ch2 @ M )
% 0.28/0.46 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5b_notP1
% 0.28/0.46 thf(fact_230_correctCompositionOut__prop1,axiom,
% 0.28/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.28/0.46 ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( member1967978193chanID @ X3 @ ( out @ PQ ) )
% 0.28/0.46 => ( ( member1967978193chanID @ X3 @ ( out @ P ) )
% 0.28/0.46 | ( member1967978193chanID @ X3 @ ( out @ Q ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % correctCompositionOut_prop1
% 0.28/0.46 thf(fact_231_outStream__def,axiom,
% 0.28/0.46 ( outStream
% 0.28/0.46 = ( ^ [X2: secrecy_specID] :
% 0.28/0.46 ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z )
% 0.28/0.46 @ ( out @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % outStream_def
% 0.28/0.46 thf(fact_232_TBtheorem5b__notPQ,axiom,
% 0.28/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( subcomponents @ PQ )
% 0.28/0.46 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.46 => ( ( M
% 0.28/0.46 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSetP )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 0.28/0.46 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 0.28/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % TBtheorem5b_notPQ
% 0.28/0.46 thf(fact_233_insert__subsetI,axiom,
% 0.28/0.46 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,X5: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X3 @ A2 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ X5 @ A2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( insert751661162chanID @ X3 @ X5 ) @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_subsetI
% 0.28/0.46 thf(fact_234_insert__subsetI,axiom,
% 0.28/0.46 ! [X3: secrecy_specID,A2: set_Secrecy_specID,X5: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ X3 @ A2 )
% 0.28/0.46 => ( ( ord_le996703545specID @ X5 @ A2 )
% 0.28/0.46 => ( ord_le996703545specID @ ( insert1671894227specID @ X3 @ X5 ) @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_subsetI
% 0.28/0.46 thf(fact_235_UnCI,axiom,
% 0.28/0.46 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ~ ( member740727610specID @ C @ B )
% 0.28/0.46 => ( member740727610specID @ C @ A2 ) )
% 0.28/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnCI
% 0.28/0.46 thf(fact_236_UnCI,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ~ ( member1967978193chanID @ C @ B )
% 0.28/0.46 => ( member1967978193chanID @ C @ A2 ) )
% 0.28/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnCI
% 0.28/0.46 thf(fact_237_Un__iff,axiom,
% 0.28/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 0.28/0.46 = ( ( member740727610specID @ C @ A2 )
% 0.28/0.46 | ( member740727610specID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_iff
% 0.28/0.46 thf(fact_238_Un__iff,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.28/0.46 = ( ( member1967978193chanID @ C @ A2 )
% 0.28/0.46 | ( member1967978193chanID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_iff
% 0.28/0.46 thf(fact_239_Un__empty,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( ( sup_su1712599557specID @ A2 @ B )
% 0.28/0.46 = bot_bo1785112429specID )
% 0.28/0.46 = ( ( A2 = bot_bo1785112429specID )
% 0.28/0.46 & ( B = bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_empty
% 0.28/0.46 thf(fact_240_Un__empty,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( sup_su370684444chanID @ A2 @ B )
% 0.28/0.46 = bot_bo443197316chanID )
% 0.28/0.46 = ( ( A2 = bot_bo443197316chanID )
% 0.28/0.46 & ( B = bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_empty
% 0.28/0.46 thf(fact_241_Un__insert__left,axiom,
% 0.28/0.46 ! [A: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 0.28/0.46 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_insert_left
% 0.28/0.46 thf(fact_242_Un__insert__left,axiom,
% 0.28/0.46 ! [A: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 0.28/0.46 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_insert_left
% 0.28/0.46 thf(fact_243_Un__insert__right,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,A: secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 0.28/0.46 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_insert_right
% 0.28/0.46 thf(fact_244_Un__insert__right,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,A: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 0.28/0.46 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_insert_right
% 0.28/0.46 thf(fact_245_Un__subset__iff,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 )
% 0.28/0.46 = ( ( ord_le1802272080chanID @ A2 @ C3 )
% 0.28/0.46 & ( ord_le1802272080chanID @ B @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_subset_iff
% 0.28/0.46 thf(fact_246_Un__empty__left,axiom,
% 0.28/0.46 ! [B: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 0.28/0.46 = B ) ).
% 0.28/0.46
% 0.28/0.46 % Un_empty_left
% 0.28/0.46 thf(fact_247_Un__empty__left,axiom,
% 0.28/0.46 ! [B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 0.28/0.46 = B ) ).
% 0.28/0.46
% 0.28/0.46 % Un_empty_left
% 0.28/0.46 thf(fact_248_Un__empty__right,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 0.28/0.46 = A2 ) ).
% 0.28/0.46
% 0.28/0.46 % Un_empty_right
% 0.28/0.46 thf(fact_249_Un__empty__right,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 0.28/0.46 = A2 ) ).
% 0.28/0.46
% 0.28/0.46 % Un_empty_right
% 0.28/0.46 thf(fact_250_subset__Un__eq,axiom,
% 0.28/0.46 ( ord_le1802272080chanID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A3 @ B5 )
% 0.28/0.46 = B5 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_Un_eq
% 0.28/0.46 thf(fact_251_subset__UnE,axiom,
% 0.28/0.46 ! [C3: set_Secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ C3 @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.28/0.46 => ~ ! [A5: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A5 @ A2 )
% 0.28/0.46 => ! [B6: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ B6 @ B )
% 0.28/0.46 => ( C3
% 0.28/0.46 != ( sup_su370684444chanID @ A5 @ B6 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_UnE
% 0.28/0.46 thf(fact_252_Un__absorb2,axiom,
% 0.28/0.46 ! [B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ B @ A2 )
% 0.28/0.46 => ( ( sup_su370684444chanID @ A2 @ B )
% 0.28/0.46 = A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_absorb2
% 0.28/0.46 thf(fact_253_Un__absorb1,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ B )
% 0.28/0.46 => ( ( sup_su370684444chanID @ A2 @ B )
% 0.28/0.46 = B ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_absorb1
% 0.28/0.46 thf(fact_254_Un__upper2,axiom,
% 0.28/0.46 ! [B: set_Secrecy_chanID,A2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ B @ ( sup_su370684444chanID @ A2 @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_upper2
% 0.28/0.46 thf(fact_255_Un__upper1,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( ord_le1802272080chanID @ A2 @ ( sup_su370684444chanID @ A2 @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_upper1
% 0.28/0.46 thf(fact_256_Un__least,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ C3 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B @ C3 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_least
% 0.28/0.46 thf(fact_257_Un__mono,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID,D2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ C3 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B @ D2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A2 @ B ) @ ( sup_su370684444chanID @ C3 @ D2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_mono
% 0.28/0.46 thf(fact_258_ineM__Un1,axiom,
% 0.28/0.46 ! [P: secrecy_specID,A2: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ineM @ P @ A2 @ E )
% 0.28/0.46 => ( ineM @ P @ ( sup_su370684444chanID @ A2 @ B ) @ E ) ) ).
% 0.28/0.46
% 0.28/0.46 % ineM_Un1
% 0.28/0.46 thf(fact_259_UnE,axiom,
% 0.28/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 0.28/0.46 => ( ~ ( member740727610specID @ C @ A2 )
% 0.28/0.46 => ( member740727610specID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnE
% 0.28/0.46 thf(fact_260_UnE,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.28/0.46 => ( ~ ( member1967978193chanID @ C @ A2 )
% 0.28/0.46 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnE
% 0.28/0.46 thf(fact_261_UnI1,axiom,
% 0.28/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ C @ A2 )
% 0.28/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnI1
% 0.28/0.46 thf(fact_262_UnI1,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ C @ A2 )
% 0.28/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnI1
% 0.28/0.46 thf(fact_263_UnI2,axiom,
% 0.28/0.46 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ C @ B )
% 0.28/0.46 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnI2
% 0.28/0.46 thf(fact_264_UnI2,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ C @ B )
% 0.28/0.46 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UnI2
% 0.28/0.46 thf(fact_265_bex__Un,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.28/0.46 ( ( ? [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.28/0.46 & ( P @ X2 ) ) )
% 0.28/0.46 = ( ? [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ A2 )
% 0.28/0.46 & ( P @ X2 ) )
% 0.28/0.46 | ? [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ B )
% 0.28/0.46 & ( P @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bex_Un
% 0.28/0.46 thf(fact_266_ball__Un,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.28/0.46 ( ( ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.28/0.46 => ( P @ X2 ) ) )
% 0.28/0.46 = ( ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ A2 )
% 0.28/0.46 => ( P @ X2 ) )
% 0.28/0.46 & ! [X2: secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ X2 @ B )
% 0.28/0.46 => ( P @ X2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ball_Un
% 0.28/0.46 thf(fact_267_Un__assoc,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 )
% 0.28/0.46 = ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_assoc
% 0.28/0.46 thf(fact_268_Un__absorb,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A2 @ A2 )
% 0.28/0.46 = A2 ) ).
% 0.28/0.46
% 0.28/0.46 % Un_absorb
% 0.28/0.46 thf(fact_269_Un__commute,axiom,
% 0.28/0.46 ( sup_su370684444chanID
% 0.28/0.46 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] : ( sup_su370684444chanID @ B5 @ A3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_commute
% 0.28/0.46 thf(fact_270_Un__left__absorb,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 0.28/0.46 = ( sup_su370684444chanID @ A2 @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_left_absorb
% 0.28/0.46 thf(fact_271_Un__left__commute,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) )
% 0.28/0.46 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A2 @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_left_commute
% 0.28/0.46 thf(fact_272_singleton__Un__iff,axiom,
% 0.28/0.46 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( ( insert1671894227specID @ X3 @ bot_bo1785112429specID )
% 0.28/0.46 = ( sup_su1712599557specID @ A2 @ B ) )
% 0.28/0.46 = ( ( ( A2 = bot_bo1785112429specID )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.46 & ( B = bot_bo1785112429specID ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % singleton_Un_iff
% 0.28/0.46 thf(fact_273_singleton__Un__iff,axiom,
% 0.28/0.46 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( insert751661162chanID @ X3 @ bot_bo443197316chanID )
% 0.28/0.46 = ( sup_su370684444chanID @ A2 @ B ) )
% 0.28/0.46 = ( ( ( A2 = bot_bo443197316chanID )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.46 & ( B = bot_bo443197316chanID ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % singleton_Un_iff
% 0.28/0.46 thf(fact_274_Un__singleton__iff,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,X3: secrecy_specID] :
% 0.28/0.46 ( ( ( sup_su1712599557specID @ A2 @ B )
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.46 = ( ( ( A2 = bot_bo1785112429specID )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.46 & ( B = bot_bo1785112429specID ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_singleton_iff
% 0.28/0.46 thf(fact_275_Un__singleton__iff,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,X3: secrecy_chanID] :
% 0.28/0.46 ( ( ( sup_su370684444chanID @ A2 @ B )
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.46 = ( ( ( A2 = bot_bo443197316chanID )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.46 & ( B = bot_bo443197316chanID ) )
% 0.28/0.46 | ( ( A2
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.46 & ( B
% 0.28/0.46 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Un_singleton_iff
% 0.28/0.46 thf(fact_276_insert__is__Un,axiom,
% 0.28/0.46 ( insert1671894227specID
% 0.28/0.46 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_is_Un
% 0.28/0.46 thf(fact_277_insert__is__Un,axiom,
% 0.28/0.46 ( insert751661162chanID
% 0.28/0.46 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_is_Un
% 0.28/0.46 thf(fact_278_subset__emptyI,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID] :
% 0.28/0.46 ( ! [X4: secrecy_specID] :
% 0.28/0.46 ~ ( member740727610specID @ X4 @ A2 )
% 0.28/0.46 => ( ord_le996703545specID @ A2 @ bot_bo1785112429specID ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_emptyI
% 0.28/0.46 thf(fact_279_subset__emptyI,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ! [X4: secrecy_chanID] :
% 0.28/0.46 ~ ( member1967978193chanID @ X4 @ A2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_emptyI
% 0.28/0.46 thf(fact_280_sup__bot_Oright__neutral,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 0.28/0.46 = A ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.right_neutral
% 0.28/0.46 thf(fact_281_sup__bot_Oright__neutral,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 0.28/0.46 = A ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.right_neutral
% 0.28/0.46 thf(fact_282_sup__bot_Oneutr__eq__iff,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.28/0.46 ( ( bot_bo1785112429specID
% 0.28/0.46 = ( sup_su1712599557specID @ A @ B2 ) )
% 0.28/0.46 = ( ( A = bot_bo1785112429specID )
% 0.28/0.46 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.neutr_eq_iff
% 0.28/0.46 thf(fact_283_sup__bot_Oneutr__eq__iff,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( bot_bo443197316chanID
% 0.28/0.46 = ( sup_su370684444chanID @ A @ B2 ) )
% 0.28/0.46 = ( ( A = bot_bo443197316chanID )
% 0.28/0.46 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.neutr_eq_iff
% 0.28/0.46 thf(fact_284_sup__bot_Oleft__neutral,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
% 0.28/0.46 = A ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.left_neutral
% 0.28/0.46 thf(fact_285_sup__bot_Oleft__neutral,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
% 0.28/0.46 = A ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.left_neutral
% 0.28/0.46 thf(fact_286_le__sup__iff,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ X3 @ Y3 ) @ Z2 )
% 0.28/0.46 = ( ( ord_le1802272080chanID @ X3 @ Z2 )
% 0.28/0.46 & ( ord_le1802272080chanID @ Y3 @ Z2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_sup_iff
% 0.28/0.46 thf(fact_287_sup_Obounded__iff,axiom,
% 0.28/0.46 ! [B2: set_Secrecy_chanID,C: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ B2 @ C ) @ A )
% 0.28/0.46 = ( ( ord_le1802272080chanID @ B2 @ A )
% 0.28/0.46 & ( ord_le1802272080chanID @ C @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.bounded_iff
% 0.28/0.46 thf(fact_288_sup__bot__left,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X3 )
% 0.28/0.46 = X3 ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot_left
% 0.28/0.46 thf(fact_289_sup__bot__left,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X3 )
% 0.28/0.46 = X3 ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot_left
% 0.28/0.46 thf(fact_290_sup__bot__right,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID] :
% 0.28/0.46 ( ( sup_su1712599557specID @ X3 @ bot_bo1785112429specID )
% 0.28/0.46 = X3 ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot_right
% 0.28/0.46 thf(fact_291_sup__bot__right,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ X3 @ bot_bo443197316chanID )
% 0.28/0.46 = X3 ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot_right
% 0.28/0.46 thf(fact_292_bot__eq__sup__iff,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 0.28/0.46 ( ( bot_bo1785112429specID
% 0.28/0.46 = ( sup_su1712599557specID @ X3 @ Y3 ) )
% 0.28/0.46 = ( ( X3 = bot_bo1785112429specID )
% 0.28/0.46 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_eq_sup_iff
% 0.28/0.46 thf(fact_293_bot__eq__sup__iff,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( bot_bo443197316chanID
% 0.28/0.46 = ( sup_su370684444chanID @ X3 @ Y3 ) )
% 0.28/0.46 = ( ( X3 = bot_bo443197316chanID )
% 0.28/0.46 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % bot_eq_sup_iff
% 0.28/0.46 thf(fact_294_sup__eq__bot__iff,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 0.28/0.46 ( ( ( sup_su1712599557specID @ X3 @ Y3 )
% 0.28/0.46 = bot_bo1785112429specID )
% 0.28/0.46 = ( ( X3 = bot_bo1785112429specID )
% 0.28/0.46 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_eq_bot_iff
% 0.28/0.46 thf(fact_295_sup__eq__bot__iff,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( sup_su370684444chanID @ X3 @ Y3 )
% 0.28/0.46 = bot_bo443197316chanID )
% 0.28/0.46 = ( ( X3 = bot_bo443197316chanID )
% 0.28/0.46 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_eq_bot_iff
% 0.28/0.46 thf(fact_296_sup__bot_Oeq__neutr__iff,axiom,
% 0.28/0.46 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.28/0.46 ( ( ( sup_su1712599557specID @ A @ B2 )
% 0.28/0.46 = bot_bo1785112429specID )
% 0.28/0.46 = ( ( A = bot_bo1785112429specID )
% 0.28/0.46 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.eq_neutr_iff
% 0.28/0.46 thf(fact_297_sup__bot_Oeq__neutr__iff,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ( sup_su370684444chanID @ A @ B2 )
% 0.28/0.46 = bot_bo443197316chanID )
% 0.28/0.46 = ( ( A = bot_bo443197316chanID )
% 0.28/0.46 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_bot.eq_neutr_iff
% 0.28/0.46 thf(fact_298_inf__sup__ord_I4_J,axiom,
% 0.28/0.46 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ Y3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % inf_sup_ord(4)
% 0.28/0.46 thf(fact_299_inf__sup__ord_I3_J,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % inf_sup_ord(3)
% 0.28/0.46 thf(fact_300_le__supE,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,X3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A @ B2 ) @ X3 )
% 0.28/0.46 => ~ ( ( ord_le1802272080chanID @ A @ X3 )
% 0.28/0.46 => ~ ( ord_le1802272080chanID @ B2 @ X3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_supE
% 0.28/0.46 thf(fact_301_le__supI,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,X3: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ X3 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ X3 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A @ B2 ) @ X3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_supI
% 0.28/0.46 thf(fact_302_sup__ge1,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_ge1
% 0.28/0.46 thf(fact_303_sup__ge2,axiom,
% 0.28/0.46 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ Y3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_ge2
% 0.28/0.46 thf(fact_304_le__supI1,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X3 @ A )
% 0.28/0.46 => ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_supI1
% 0.28/0.46 thf(fact_305_le__supI2,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X3 @ B2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_supI2
% 0.28/0.46 thf(fact_306_sup_Omono,axiom,
% 0.28/0.46 ! [C: set_Secrecy_chanID,A: set_Secrecy_chanID,D: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ C @ A )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ D @ B2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ C @ D ) @ ( sup_su370684444chanID @ A @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.mono
% 0.28/0.46 thf(fact_307_sup__mono,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,C: set_Secrecy_chanID,B2: set_Secrecy_chanID,D: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ C )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ B2 @ D )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A @ B2 ) @ ( sup_su370684444chanID @ C @ D ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_mono
% 0.28/0.46 thf(fact_308_sup__least,axiom,
% 0.28/0.46 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ Z2 @ X3 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ Y3 @ Z2 ) @ X3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_least
% 0.28/0.46 thf(fact_309_le__iff__sup,axiom,
% 0.28/0.46 ( ord_le1802272080chanID
% 0.28/0.46 = ( ^ [X2: set_Secrecy_chanID,Y4: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ X2 @ Y4 )
% 0.28/0.46 = Y4 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_iff_sup
% 0.28/0.46 thf(fact_310_sup_OorderE,axiom,
% 0.28/0.46 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ B2 @ A )
% 0.28/0.46 => ( A
% 0.28/0.46 = ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.orderE
% 0.28/0.46 thf(fact_311_sup_OorderI,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( A
% 0.28/0.46 = ( sup_su370684444chanID @ A @ B2 ) )
% 0.28/0.46 => ( ord_le1802272080chanID @ B2 @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.orderI
% 0.28/0.46 thf(fact_312_sup__unique,axiom,
% 0.28/0.46 ! [F: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID,X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.28/0.46 ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X4 @ ( F @ X4 @ Y2 ) )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ Y2 @ ( F @ X4 @ Y2 ) )
% 0.28/0.46 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID,Z3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ Y2 @ X4 )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ Z3 @ X4 )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( F @ Y2 @ Z3 ) @ X4 ) ) )
% 0.28/0.46 => ( ( sup_su370684444chanID @ X3 @ Y3 )
% 0.28/0.46 = ( F @ X3 @ Y3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_unique
% 0.28/0.46 thf(fact_313_sup_Oabsorb1,axiom,
% 0.28/0.46 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ B2 @ A )
% 0.28/0.46 => ( ( sup_su370684444chanID @ A @ B2 )
% 0.28/0.46 = A ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.absorb1
% 0.28/0.46 thf(fact_314_sup_Oabsorb2,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 => ( ( sup_su370684444chanID @ A @ B2 )
% 0.28/0.46 = B2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.absorb2
% 0.28/0.46 thf(fact_315_sup__absorb1,axiom,
% 0.28/0.46 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 0.28/0.46 => ( ( sup_su370684444chanID @ X3 @ Y3 )
% 0.28/0.46 = X3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_absorb1
% 0.28/0.46 thf(fact_316_sup__absorb2,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 0.28/0.46 => ( ( sup_su370684444chanID @ X3 @ Y3 )
% 0.28/0.46 = Y3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup_absorb2
% 0.28/0.46 thf(fact_317_sup_OboundedE,axiom,
% 0.28/0.46 ! [B2: set_Secrecy_chanID,C: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ B2 @ C ) @ A )
% 0.28/0.46 => ~ ( ( ord_le1802272080chanID @ B2 @ A )
% 0.28/0.46 => ~ ( ord_le1802272080chanID @ C @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.boundedE
% 0.28/0.46 thf(fact_318_sup_OboundedI,axiom,
% 0.28/0.46 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ B2 @ A )
% 0.28/0.46 => ( ( ord_le1802272080chanID @ C @ A )
% 0.28/0.46 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ B2 @ C ) @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.boundedI
% 0.28/0.46 thf(fact_319_sup_Oorder__iff,axiom,
% 0.28/0.46 ( ord_le1802272080chanID
% 0.28/0.46 = ( ^ [B4: set_Secrecy_chanID,A4: set_Secrecy_chanID] :
% 0.28/0.46 ( A4
% 0.28/0.46 = ( sup_su370684444chanID @ A4 @ B4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.order_iff
% 0.28/0.46 thf(fact_320_sup_Ocobounded1,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ A @ ( sup_su370684444chanID @ A @ B2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.cobounded1
% 0.28/0.46 thf(fact_321_sup_Ocobounded2,axiom,
% 0.28/0.46 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID] : ( ord_le1802272080chanID @ B2 @ ( sup_su370684444chanID @ A @ B2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.cobounded2
% 0.28/0.46 thf(fact_322_sup_Oabsorb__iff1,axiom,
% 0.28/0.46 ( ord_le1802272080chanID
% 0.28/0.46 = ( ^ [B4: set_Secrecy_chanID,A4: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A4 @ B4 )
% 0.28/0.46 = A4 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.absorb_iff1
% 0.28/0.46 thf(fact_323_sup_Oabsorb__iff2,axiom,
% 0.28/0.46 ( ord_le1802272080chanID
% 0.28/0.46 = ( ^ [A4: set_Secrecy_chanID,B4: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ A4 @ B4 )
% 0.28/0.46 = B4 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.absorb_iff2
% 0.28/0.46 thf(fact_324_sup_OcoboundedI1,axiom,
% 0.28/0.46 ! [C: set_Secrecy_chanID,A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ C @ A )
% 0.28/0.46 => ( ord_le1802272080chanID @ C @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.coboundedI1
% 0.28/0.46 thf(fact_325_sup_OcoboundedI2,axiom,
% 0.28/0.46 ! [C: set_Secrecy_chanID,B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ C @ B2 )
% 0.28/0.46 => ( ord_le1802272080chanID @ C @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % sup.coboundedI2
% 0.28/0.46 thf(fact_326_correctInOutLoc__def,axiom,
% 0.28/0.46 ( correctInOutLoc
% 0.28/0.46 = ( ^ [X2: secrecy_specID] :
% 0.28/0.46 ( ( ( inf_in1474033538chanID @ ( ins @ X2 ) @ ( out @ X2 ) )
% 0.28/0.46 = bot_bo443197316chanID )
% 0.28/0.46 & ( ( inf_in1474033538chanID @ ( ins @ X2 ) @ ( loc @ X2 ) )
% 0.28/0.46 = bot_bo443197316chanID )
% 0.28/0.46 & ( ( inf_in1474033538chanID @ ( loc @ X2 ) @ ( out @ X2 ) )
% 0.28/0.46 = bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % correctInOutLoc_def
% 0.28/0.46 thf(fact_327_subset__Compl__singleton,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_specID,B2: secrecy_specID] :
% 0.28/0.46 ( ( ord_le996703545specID @ A2 @ ( uminus238526242specID @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) ) )
% 0.28/0.46 = ( ~ ( member740727610specID @ B2 @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_Compl_singleton
% 0.28/0.46 thf(fact_328_subset__Compl__singleton,axiom,
% 0.28/0.46 ! [A2: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A2 @ ( uminus1044094777chanID @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) ) )
% 0.28/0.46 = ( ~ ( member1967978193chanID @ B2 @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % subset_Compl_singleton
% 0.28/0.46 thf(fact_329_IntI,axiom,
% 0.28/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ C @ A2 )
% 0.28/0.46 => ( ( member740727610specID @ C @ B )
% 0.28/0.46 => ( member740727610specID @ C @ ( inf_in668465003specID @ A2 @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % IntI
% 0.28/0.46 thf(fact_330_IntI,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ C @ A2 )
% 0.28/0.46 => ( ( member1967978193chanID @ C @ B )
% 0.28/0.46 => ( member1967978193chanID @ C @ ( inf_in1474033538chanID @ A2 @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % IntI
% 0.28/0.46 thf(fact_331_Int__iff,axiom,
% 0.28/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ C @ ( inf_in668465003specID @ A2 @ B ) )
% 0.28/0.46 = ( ( member740727610specID @ C @ A2 )
% 0.28/0.46 & ( member740727610specID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_iff
% 0.28/0.46 thf(fact_332_Int__iff,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ C @ ( inf_in1474033538chanID @ A2 @ B ) )
% 0.28/0.46 = ( ( member1967978193chanID @ C @ A2 )
% 0.28/0.46 & ( member1967978193chanID @ C @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_iff
% 0.28/0.46 thf(fact_333_ComplI,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( member1967978193chanID @ C @ A2 )
% 0.28/0.46 => ( member1967978193chanID @ C @ ( uminus1044094777chanID @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ComplI
% 0.28/0.46 thf(fact_334_ComplI,axiom,
% 0.28/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.46 ( ~ ( member740727610specID @ C @ A2 )
% 0.28/0.46 => ( member740727610specID @ C @ ( uminus238526242specID @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ComplI
% 0.28/0.46 thf(fact_335_Compl__iff,axiom,
% 0.28/0.46 ! [C: secrecy_chanID,A2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ C @ ( uminus1044094777chanID @ A2 ) )
% 0.28/0.46 = ( ~ ( member1967978193chanID @ C @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Compl_iff
% 0.28/0.46 thf(fact_336_Compl__iff,axiom,
% 0.28/0.46 ! [C: secrecy_specID,A2: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ C @ ( uminus238526242specID @ A2 ) )
% 0.28/0.46 = ( ~ ( member740727610specID @ C @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Compl_iff
% 0.28/0.46 thf(fact_337_le__inf__iff,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ X3 @ ( inf_in1474033538chanID @ Y3 @ Z2 ) )
% 0.28/0.46 = ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 0.28/0.46 & ( ord_le1802272080chanID @ X3 @ Z2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_inf_iff
% 0.28/0.46 thf(fact_338_inf_Obounded__iff,axiom,
% 0.28/0.46 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ A @ ( inf_in1474033538chanID @ B2 @ C ) )
% 0.28/0.46 = ( ( ord_le1802272080chanID @ A @ B2 )
% 0.28/0.46 & ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inf.bounded_iff
% 0.28/0.46 thf(fact_339_inf__bot__left,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID] :
% 0.28/0.46 ( ( inf_in668465003specID @ bot_bo1785112429specID @ X3 )
% 0.28/0.46 = bot_bo1785112429specID ) ).
% 0.28/0.46
% 0.28/0.46 % inf_bot_left
% 0.28/0.46 thf(fact_340_inf__bot__left,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( inf_in1474033538chanID @ bot_bo443197316chanID @ X3 )
% 0.28/0.46 = bot_bo443197316chanID ) ).
% 0.28/0.46
% 0.28/0.46 % inf_bot_left
% 0.28/0.46 thf(fact_341_inf__bot__right,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_specID] :
% 0.28/0.46 ( ( inf_in668465003specID @ X3 @ bot_bo1785112429specID )
% 0.28/0.46 = bot_bo1785112429specID ) ).
% 0.28/0.46
% 0.28/0.46 % inf_bot_right
% 0.28/0.46 thf(fact_342_inf__bot__right,axiom,
% 0.28/0.46 ! [X3: set_Secrecy_chanID] :
% 0.28/0.46 ( ( inf_in1474033538chanID @ X3 @ bot_bo443197316chanID )
% 0.28/0.46 = bot_bo443197316chanID ) ).
% 0.28/0.46
% 0.28/0.46 % inf_bot_right
% 0.28/0.46 thf(fact_343_Int__insert__left__if0,axiom,
% 0.28/0.46 ! [A: secrecy_specID,C3: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ~ ( member740727610specID @ A @ C3 )
% 0.28/0.46 => ( ( inf_in668465003specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 0.28/0.46 = ( inf_in668465003specID @ B @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_left_if0
% 0.28/0.46 thf(fact_344_Int__insert__left__if0,axiom,
% 0.28/0.46 ! [A: secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( member1967978193chanID @ A @ C3 )
% 0.28/0.46 => ( ( inf_in1474033538chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 0.28/0.46 = ( inf_in1474033538chanID @ B @ C3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_left_if0
% 0.28/0.46 thf(fact_345_Int__insert__left__if1,axiom,
% 0.28/0.46 ! [A: secrecy_specID,C3: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ A @ C3 )
% 0.28/0.46 => ( ( inf_in668465003specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 0.28/0.46 = ( insert1671894227specID @ A @ ( inf_in668465003specID @ B @ C3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_left_if1
% 0.28/0.46 thf(fact_346_Int__insert__left__if1,axiom,
% 0.28/0.46 ! [A: secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ A @ C3 )
% 0.28/0.46 => ( ( inf_in1474033538chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 0.28/0.46 = ( insert751661162chanID @ A @ ( inf_in1474033538chanID @ B @ C3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_left_if1
% 0.28/0.46 thf(fact_347_insert__inter__insert,axiom,
% 0.28/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( inf_in668465003specID @ ( insert1671894227specID @ A @ A2 ) @ ( insert1671894227specID @ A @ B ) )
% 0.28/0.46 = ( insert1671894227specID @ A @ ( inf_in668465003specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_inter_insert
% 0.28/0.46 thf(fact_348_insert__inter__insert,axiom,
% 0.28/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( inf_in1474033538chanID @ ( insert751661162chanID @ A @ A2 ) @ ( insert751661162chanID @ A @ B ) )
% 0.28/0.46 = ( insert751661162chanID @ A @ ( inf_in1474033538chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % insert_inter_insert
% 0.28/0.46 thf(fact_349_Int__insert__right__if0,axiom,
% 0.28/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ~ ( member740727610specID @ A @ A2 )
% 0.28/0.46 => ( ( inf_in668465003specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 0.28/0.46 = ( inf_in668465003specID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_right_if0
% 0.28/0.46 thf(fact_350_Int__insert__right__if0,axiom,
% 0.28/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ~ ( member1967978193chanID @ A @ A2 )
% 0.28/0.46 => ( ( inf_in1474033538chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 0.28/0.46 = ( inf_in1474033538chanID @ A2 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_right_if0
% 0.28/0.46 thf(fact_351_Int__insert__right__if1,axiom,
% 0.28/0.46 ! [A: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.46 ( ( member740727610specID @ A @ A2 )
% 0.28/0.46 => ( ( inf_in668465003specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 0.28/0.46 = ( insert1671894227specID @ A @ ( inf_in668465003specID @ A2 @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_right_if1
% 0.28/0.46 thf(fact_352_Int__insert__right__if1,axiom,
% 0.28/0.46 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( member1967978193chanID @ A @ A2 )
% 0.28/0.46 => ( ( inf_in1474033538chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 0.28/0.46 = ( insert751661162chanID @ A @ ( inf_in1474033538chanID @ A2 @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_insert_right_if1
% 0.28/0.46 thf(fact_353_Int__subset__iff,axiom,
% 0.28/0.46 ! [C3: set_Secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.46 ( ( ord_le1802272080chanID @ C3 @ ( inf_in1474033538chanID @ A2 @ B ) )
% 0.28/0.46 = ( ( ord_le1802272080chanID @ C3 @ A2 )
% 0.28/0.46 & ( ord_le1802272080chanID @ C3 @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Int_subset_iff
% 0.28/0.46 thf(fact_354_Int__Un__eq_I4_J,axiom,
% 0.28/0.46 ! [T2: set_Secrecy_chanID,S: set_Secrecy_chanID] :
% 0.28/0.46 ( ( sup_su370684444chanID @ T2 @ ( inf_in1474033538chanID @ S @ T2 ) )
% 0.28/0.46 = T2 ) ).
% 0.28/0.46
% 0.28/0.46 % Int_Un_eq(4)
% 0.28/0.46
% 0.28/0.46 % Conjectures (1)
% 0.28/0.46 thf(conj_0,conjecture,
% 0.28/0.46 member1967978193chanID @ ch @ ( loc @ pq ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 2.85/1.52 ---- Embedded in THF ---
% 2.85/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.85/1.52 %%% Generated on Tue Feb 24 08:25:39 EST 2026
% 2.85/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.85/1.52 %%% Logic specification used:
% 2.85/1.52 %%% thf(spec, logic, $$dhol).
% 2.85/1.52
% 2.85/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2DTF12739.p
% See solution above
% 2.85/1.53 ------------------------
% 2.85/1.56 ---- Cleaned THF ---
% 2.85/1.56 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.85/1.56 set_Secrecy_specID: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.85/1.56 set_Secrecy_chanID: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_n_t__Secrecy____types__OExpression,type,
% 2.85/1.56 secrecy_Expression: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_n_t__Secrecy____types__OspecID,type,
% 2.85/1.56 secrecy_specID: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_n_t__Secrecy____types__OchanID,type,
% 2.85/1.56 secrecy_chanID: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(ty_n_t__Nat__Onat,type,
% 2.85/1.56 nat: $tType ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.85/1.56 uminus1044094777chanID: set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.85/1.56 uminus238526242specID: set_Secrecy_specID > set_Secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.85/1.56 inf_in1474033538chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.85/1.56 inf_in668465003specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.85/1.56 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.85/1.56 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 2.85/1.56 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 2.85/1.56 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 2.85/1.56 bot_bot_o: $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.85/1.56 bot_bo443197316chanID: set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.85/1.56 bot_bo1785112429specID: set_Secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 2.85/1.56 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 2.85/1.56 ord_le996703545specID: set_Secrecy_specID > set_Secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_Oeout,type,
% 2.85/1.56 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_OeoutM,type,
% 2.85/1.56 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_OexprChannel,type,
% 2.85/1.56 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_Oine,type,
% 2.85/1.56 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_OineM,type,
% 2.85/1.56 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 2.85/1.56 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 2.85/1.56 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 2.85/1.56 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 2.85/1.56 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 2.85/1.56 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 2.85/1.56 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 2.85/1.56 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 2.85/1.56 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 2.85/1.56 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 2.85/1.56 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 2.85/1.56 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 2.85/1.56 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Opairwise_001t__Secrecy____types__OchanID,type,
% 2.85/1.56 pairwi1741995279chanID: ( secrecy_chanID > secrecy_chanID > $o ) > set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Opairwise_001t__Secrecy____types__OspecID,type,
% 2.85/1.56 pairwi514744696specID: ( secrecy_specID > secrecy_specID > $o ) > set_Secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 2.85/1.56 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 2.85/1.56 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_OcorrectCompositionIn,type,
% 2.85/1.56 correctCompositionIn: secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 2.85/1.56 correc965049635ionLoc: secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_OcorrectCompositionOut,type,
% 2.85/1.56 correc990227761ionOut: secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_OcorrectInOutLoc,type,
% 2.85/1.56 correctInOutLoc: secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_OinStream,type,
% 2.85/1.56 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_Oins,type,
% 2.85/1.56 ins: secrecy_specID > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_Oloc,type,
% 2.85/1.56 loc: secrecy_specID > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_OlocStream,type,
% 2.85/1.56 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_Oout,type,
% 2.85/1.56 out: secrecy_specID > set_Secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_OoutStream,type,
% 2.85/1.56 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_inout_Osubcomponents,type,
% 2.85/1.56 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 2.85/1.56 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 2.85/1.56 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 2.85/1.56
% 2.85/1.56 thf(sy_v_P,type,
% 2.85/1.56 p: secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_v_PQ,type,
% 2.85/1.56 pq: secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_v_Q,type,
% 2.85/1.56 q: secrecy_specID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_v_ch,type,
% 2.85/1.56 ch: secrecy_chanID ).
% 2.85/1.56
% 2.85/1.56 thf(sy_v_m,type,
% 2.85/1.56 m: secrecy_Expression ).
% 2.85/1.56
% 2.85/1.56 thf(fact_0_assms_I2_J,axiom,
% 2.85/1.56 correctCompositionIn @ pq ).
% 2.85/1.56
% 2.85/1.56 thf(fact_1_assms_I4_J,axiom,
% 2.85/1.56 exprChannel @ ch @ m ).
% 2.85/1.56
% 2.85/1.56 thf(fact_2_assms_I3_J,axiom,
% 2.85/1.56 member1967978193chanID @ ch @ ( ins @ p ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_3_assms_I5_J,axiom,
% 2.85/1.56 ! [X: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X @ ( ins @ pq ) )
% 2.85/1.56 => ~ ( exprChannel @ X @ m ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_4_assms_I1_J,axiom,
% 2.85/1.56 ( ( subcomponents @ pq )
% 2.85/1.56 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_5_locStream__def,axiom,
% 2.85/1.56 ( locStream
% 2.85/1.56 = ( ^ [X2: secrecy_specID] :
% 2.85/1.56 ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z )
% 2.85/1.56 @ ( loc @ X2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_6_correctCompositionIn__L1,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 2.85/1.56 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.85/1.56 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_7_correctCompositionIn__L2,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.85/1.56 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.85/1.56 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_8_correctCompositionIn__prop1,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 2.85/1.56 => ( ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 2.85/1.56 | ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_9_singletonI,axiom,
% 2.85/1.56 ! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_10_singletonI,axiom,
% 2.85/1.56 ! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_11_TBtheorem4b__P,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( ineM @ P @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ M ) )
% 2.85/1.56 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_12_TBtheorem4b__PQ,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ( ineM @ P @ M @ E )
% 2.85/1.56 | ( ineM @ Q @ M @ E ) )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.85/1.56 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ M )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_13_TBlemma3b,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 2.85/1.56 ( ~ ( ineM @ P @ M @ E )
% 2.85/1.56 => ( ~ ( ineM @ Q @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( member1967978193chanID @ Ch @ M )
% 2.85/1.56 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 2.85/1.56 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_14_inStream__def,axiom,
% 2.85/1.56 ( inStream
% 2.85/1.56 = ( ^ [X2: secrecy_specID] :
% 2.85/1.56 ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z )
% 2.85/1.56 @ ( ins @ X2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_15_insertCI,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.85/1.56 ( ( ~ ( member1967978193chanID @ A @ B )
% 2.85/1.56 => ( A = B2 ) )
% 2.85/1.56 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_16_insertCI,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.85/1.56 ( ( ~ ( member740727610specID @ A @ B )
% 2.85/1.56 => ( A = B2 ) )
% 2.85/1.56 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_17_insert__iff,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 2.85/1.56 = ( ( A = B2 )
% 2.85/1.56 | ( member1967978193chanID @ A @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_18_insert__iff,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 2.85/1.56 = ( ( A = B2 )
% 2.85/1.56 | ( member740727610specID @ A @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_19_insert__absorb2,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X3 @ A2 ) )
% 2.85/1.56 = ( insert1671894227specID @ X3 @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_20_insert__absorb2,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ X3 @ A2 ) )
% 2.85/1.56 = ( insert751661162chanID @ X3 @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_21_empty__iff,axiom,
% 2.85/1.56 ! [C: secrecy_specID] :
% 2.85/1.56 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_22_empty__iff,axiom,
% 2.85/1.56 ! [C: secrecy_chanID] :
% 2.85/1.56 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_23_all__not__in__conv,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ! [X2: secrecy_specID] :
% 2.85/1.56 ~ ( member740727610specID @ X2 @ A2 ) )
% 2.85/1.56 = ( A2 = bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_24_all__not__in__conv,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ! [X2: secrecy_chanID] :
% 2.85/1.56 ~ ( member1967978193chanID @ X2 @ A2 ) )
% 2.85/1.56 = ( A2 = bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_25_Collect__empty__eq,axiom,
% 2.85/1.56 ! [P: secrecy_specID > $o] :
% 2.85/1.56 ( ( ( collec1545797240specID @ P )
% 2.85/1.56 = bot_bo1785112429specID )
% 2.85/1.56 = ( ! [X2: secrecy_specID] :
% 2.85/1.56 ~ ( P @ X2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_26_Collect__empty__eq,axiom,
% 2.85/1.56 ! [P: secrecy_chanID > $o] :
% 2.85/1.56 ( ( ( collec625564175chanID @ P )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 = ( ! [X2: secrecy_chanID] :
% 2.85/1.56 ~ ( P @ X2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_27_empty__Collect__eq,axiom,
% 2.85/1.56 ! [P: secrecy_specID > $o] :
% 2.85/1.56 ( ( bot_bo1785112429specID
% 2.85/1.56 = ( collec1545797240specID @ P ) )
% 2.85/1.56 = ( ! [X2: secrecy_specID] :
% 2.85/1.56 ~ ( P @ X2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_28_empty__Collect__eq,axiom,
% 2.85/1.56 ! [P: secrecy_chanID > $o] :
% 2.85/1.56 ( ( bot_bo443197316chanID
% 2.85/1.56 = ( collec625564175chanID @ P ) )
% 2.85/1.56 = ( ! [X2: secrecy_chanID] :
% 2.85/1.56 ~ ( P @ X2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_29_ineM__def,axiom,
% 2.85/1.56 ( ineM
% 2.85/1.56 = ( ^ [SP: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.85/1.56 ? [Ch3: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.85/1.56 & ( member1967978193chanID @ Ch3 @ M2 )
% 2.85/1.56 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_30_ineM__L1,axiom,
% 2.85/1.56 ! [Ch: secrecy_chanID,M: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch @ M )
% 2.85/1.56 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 2.85/1.56 => ( ( exprChannel @ Ch @ E )
% 2.85/1.56 => ( ineM @ P @ M @ E ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_31_ex__in__conv,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ? [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 2.85/1.56 = ( A2 != bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_32_ex__in__conv,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ? [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 2.85/1.56 = ( A2 != bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_33_equals0I,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ! [Y2: secrecy_specID] :
% 2.85/1.56 ~ ( member740727610specID @ Y2 @ A2 )
% 2.85/1.56 => ( A2 = bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_34_equals0I,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ! [Y2: secrecy_chanID] :
% 2.85/1.56 ~ ( member1967978193chanID @ Y2 @ A2 )
% 2.85/1.56 => ( A2 = bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_35_equals0D,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,A: secrecy_specID] :
% 2.85/1.56 ( ( A2 = bot_bo1785112429specID )
% 2.85/1.56 => ~ ( member740727610specID @ A @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_36_equals0D,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,A: secrecy_chanID] :
% 2.85/1.56 ( ( A2 = bot_bo443197316chanID )
% 2.85/1.56 => ~ ( member1967978193chanID @ A @ A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_37_emptyE,axiom,
% 2.85/1.56 ! [A: secrecy_specID] :
% 2.85/1.56 ~ ( member740727610specID @ A @ bot_bo1785112429specID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_38_emptyE,axiom,
% 2.85/1.56 ! [A: secrecy_chanID] :
% 2.85/1.56 ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_39_mk__disjoint__insert,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ A @ A2 )
% 2.85/1.56 => ? [B3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( insert751661162chanID @ A @ B3 ) )
% 2.85/1.56 & ~ ( member1967978193chanID @ A @ B3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_40_mk__disjoint__insert,axiom,
% 2.85/1.56 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ A @ A2 )
% 2.85/1.56 => ? [B3: set_Secrecy_specID] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( insert1671894227specID @ A @ B3 ) )
% 2.85/1.56 & ~ ( member740727610specID @ A @ B3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_41_insert__commute,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,Y3: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ Y3 @ A2 ) )
% 2.85/1.56 = ( insert1671894227specID @ Y3 @ ( insert1671894227specID @ X3 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_42_insert__commute,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,Y3: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ Y3 @ A2 ) )
% 2.85/1.56 = ( insert751661162chanID @ Y3 @ ( insert751661162chanID @ X3 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_43_insert__eq__iff,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( member1967978193chanID @ A @ A2 )
% 2.85/1.56 => ( ~ ( member1967978193chanID @ B2 @ B )
% 2.85/1.56 => ( ( ( insert751661162chanID @ A @ A2 )
% 2.85/1.56 = ( insert751661162chanID @ B2 @ B ) )
% 2.85/1.56 = ( ( ( A = B2 )
% 2.85/1.56 => ( A2 = B ) )
% 2.85/1.56 & ( ( A != B2 )
% 2.85/1.56 => ? [C2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( insert751661162chanID @ B2 @ C2 ) )
% 2.85/1.56 & ~ ( member1967978193chanID @ B2 @ C2 )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert751661162chanID @ A @ C2 ) )
% 2.85/1.56 & ~ ( member1967978193chanID @ A @ C2 ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_44_insert__eq__iff,axiom,
% 2.85/1.56 ! [A: secrecy_specID,A2: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ~ ( member740727610specID @ A @ A2 )
% 2.85/1.56 => ( ~ ( member740727610specID @ B2 @ B )
% 2.85/1.56 => ( ( ( insert1671894227specID @ A @ A2 )
% 2.85/1.56 = ( insert1671894227specID @ B2 @ B ) )
% 2.85/1.56 = ( ( ( A = B2 )
% 2.85/1.56 => ( A2 = B ) )
% 2.85/1.56 & ( ( A != B2 )
% 2.85/1.56 => ? [C2: set_Secrecy_specID] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( insert1671894227specID @ B2 @ C2 ) )
% 2.85/1.56 & ~ ( member740727610specID @ B2 @ C2 )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert1671894227specID @ A @ C2 ) )
% 2.85/1.56 & ~ ( member740727610specID @ A @ C2 ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_45_insert__absorb,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ A @ A2 )
% 2.85/1.56 => ( ( insert751661162chanID @ A @ A2 )
% 2.85/1.56 = A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_46_insert__absorb,axiom,
% 2.85/1.56 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ A @ A2 )
% 2.85/1.56 => ( ( insert1671894227specID @ A @ A2 )
% 2.85/1.56 = A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_47_insert__ident,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( member1967978193chanID @ X3 @ A2 )
% 2.85/1.56 => ( ~ ( member1967978193chanID @ X3 @ B )
% 2.85/1.56 => ( ( ( insert751661162chanID @ X3 @ A2 )
% 2.85/1.56 = ( insert751661162chanID @ X3 @ B ) )
% 2.85/1.56 = ( A2 = B ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_48_insert__ident,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ~ ( member740727610specID @ X3 @ A2 )
% 2.85/1.56 => ( ~ ( member740727610specID @ X3 @ B )
% 2.85/1.56 => ( ( ( insert1671894227specID @ X3 @ A2 )
% 2.85/1.56 = ( insert1671894227specID @ X3 @ B ) )
% 2.85/1.56 = ( A2 = B ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_49_Set_Oset__insert,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X3 @ A2 )
% 2.85/1.56 => ~ ! [B3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( insert751661162chanID @ X3 @ B3 ) )
% 2.85/1.56 => ( member1967978193chanID @ X3 @ B3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_50_Set_Oset__insert,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ X3 @ A2 )
% 2.85/1.56 => ~ ! [B3: set_Secrecy_specID] :
% 2.85/1.56 ( ( A2
% 2.85/1.56 = ( insert1671894227specID @ X3 @ B3 ) )
% 2.85/1.56 => ( member740727610specID @ X3 @ B3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_51_insertI2,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ A @ B )
% 2.85/1.56 => ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_52_insertI2,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ A @ B )
% 2.85/1.56 => ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_53_insertI1,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_54_insertI1,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_55_insertE,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B2: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B2 @ A2 ) )
% 2.85/1.56 => ( ( A != B2 )
% 2.85/1.56 => ( member1967978193chanID @ A @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_56_insertE,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B2: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ A @ ( insert1671894227specID @ B2 @ A2 ) )
% 2.85/1.56 => ( ( A != B2 )
% 2.85/1.56 => ( member740727610specID @ A @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_57_TBtheorem3b,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ~ ( ineM @ P @ M @ E )
% 2.85/1.56 => ( ~ ( ineM @ Q @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_58_TBtheorem1b,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( ineM @ PQ @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( ineM @ P @ M @ E )
% 2.85/1.56 | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_59_singleton__inject,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B2: secrecy_specID] :
% 2.85/1.56 ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
% 2.85/1.56 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.85/1.56 => ( A = B2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_60_singleton__inject,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B2: secrecy_chanID] :
% 2.85/1.56 ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
% 2.85/1.56 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.85/1.56 => ( A = B2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_61_insert__not__empty,axiom,
% 2.85/1.56 ! [A: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( insert1671894227specID @ A @ A2 )
% 2.85/1.56 != bot_bo1785112429specID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_62_insert__not__empty,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( insert751661162chanID @ A @ A2 )
% 2.85/1.56 != bot_bo443197316chanID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_63_doubleton__eq__iff,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 2.85/1.56 ( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.85/1.56 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 2.85/1.56 = ( ( ( A = C )
% 2.85/1.56 & ( B2 = D ) )
% 2.85/1.56 | ( ( A = D )
% 2.85/1.56 & ( B2 = C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_64_doubleton__eq__iff,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 2.85/1.56 ( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.85/1.56 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 2.85/1.56 = ( ( ( A = C )
% 2.85/1.56 & ( B2 = D ) )
% 2.85/1.56 | ( ( A = D )
% 2.85/1.56 & ( B2 = C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_65_singleton__iff,axiom,
% 2.85/1.56 ! [B2: secrecy_specID,A: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 2.85/1.56 = ( B2 = A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_66_singleton__iff,axiom,
% 2.85/1.56 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 2.85/1.56 = ( B2 = A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_67_singletonD,axiom,
% 2.85/1.56 ! [B2: secrecy_specID,A: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 2.85/1.56 => ( B2 = A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_68_singletonD,axiom,
% 2.85/1.56 ! [B2: secrecy_chanID,A: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 2.85/1.56 => ( B2 = A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_69_TBtheorem4b__notP1,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ineM @ P @ M @ E )
% 2.85/1.56 => ( ~ ( ineM @ Q @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ M )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_70_TBtheorem4b__notPQ,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.85/1.56 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_71_mem__Collect__eq,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,P: secrecy_chanID > $o] :
% 2.85/1.56 ( ( member1967978193chanID @ A @ ( collec625564175chanID @ P ) )
% 2.85/1.56 = ( P @ A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_72_mem__Collect__eq,axiom,
% 2.85/1.56 ! [A: secrecy_specID,P: secrecy_specID > $o] :
% 2.85/1.56 ( ( member740727610specID @ A @ ( collec1545797240specID @ P ) )
% 2.85/1.56 = ( P @ A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_73_Collect__mem__eq,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( collec625564175chanID
% 2.85/1.56 @ ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ A2 ) )
% 2.85/1.56 = A2 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_74_Collect__mem__eq,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( collec1545797240specID
% 2.85/1.56 @ ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ A2 ) )
% 2.85/1.56 = A2 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_75_Collect__cong,axiom,
% 2.85/1.56 ! [P: secrecy_chanID > $o,Q: secrecy_chanID > $o] :
% 2.85/1.56 ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( P @ X4 )
% 2.85/1.56 = ( Q @ X4 ) )
% 2.85/1.56 => ( ( collec625564175chanID @ P )
% 2.85/1.56 = ( collec625564175chanID @ Q ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_76_Collect__cong,axiom,
% 2.85/1.56 ! [P: secrecy_specID > $o,Q: secrecy_specID > $o] :
% 2.85/1.56 ( ! [X4: secrecy_specID] :
% 2.85/1.56 ( ( P @ X4 )
% 2.85/1.56 = ( Q @ X4 ) )
% 2.85/1.56 => ( ( collec1545797240specID @ P )
% 2.85/1.56 = ( collec1545797240specID @ Q ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_77_TBtheorem4b__notP2,axiom,
% 2.85/1.56 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( ineM @ Q @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_78_the__elem__eq,axiom,
% 2.85/1.56 ! [X3: secrecy_specID] :
% 2.85/1.56 ( ( the_el827131246specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.85/1.56 = X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_79_the__elem__eq,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID] :
% 2.85/1.56 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.85/1.56 = X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_80_bot__apply,axiom,
% 2.85/1.56 ( bot_bo1012329985anID_o
% 2.85/1.56 = ( ^ [X2: secrecy_chanID] : bot_bot_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_81_bot__apply,axiom,
% 2.85/1.56 ( bot_bo1767780696ecID_o
% 2.85/1.56 = ( ^ [X2: secrecy_specID] : bot_bot_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_82_TBtheorem4a__PQ,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ( ine @ P @ E )
% 2.85/1.56 | ( ine @ Q @ E ) )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.85/1.56 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_83_TBtheorem4a__P,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( ine @ P @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_84_is__singletonI,axiom,
% 2.85/1.56 ! [X3: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_85_is__singletonI,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_86_TBtheorem4a__empty,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ( ine @ P @ E )
% 2.85/1.56 | ( ine @ Q @ E ) )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( ( loc @ PQ )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_87_ine__exprChannelSingle__def,axiom,
% 2.85/1.56 ( ine_ex1303305700Single
% 2.85/1.56 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.85/1.56 & ( exprChannel @ Ch3 @ E2 )
% 2.85/1.56 & ! [X2: secrecy_chanID,T: nat] :
% 2.85/1.56 ( ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 2.85/1.56 & ( X2 != Ch3 ) )
% 2.85/1.56 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_88_ine__empty__exprChannelSet,axiom,
% 2.85/1.56 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.85/1.56 => ( ( ChSet = bot_bo443197316chanID )
% 2.85/1.56 => ~ ( ine @ P @ E ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_89_ine__exprChannelSet__Single,axiom,
% 2.85/1.56 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 2.85/1.56 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_90_ine__exprChannelSingle__Set,axiom,
% 2.85/1.56 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 2.85/1.56 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_91_ine__nonempty__exprChannelSet,axiom,
% 2.85/1.56 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.85/1.56 => ( ( ChSet != bot_bo443197316chanID )
% 2.85/1.56 => ( ine @ P @ E ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_92_bot__set__def,axiom,
% 2.85/1.56 ( bot_bo1785112429specID
% 2.85/1.56 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_93_bot__set__def,axiom,
% 2.85/1.56 ( bot_bo443197316chanID
% 2.85/1.56 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_94_not__ine__ineM,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( ine @ P @ E )
% 2.85/1.56 => ~ ( ineM @ P @ M @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_95_ineM__ine,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( ineM @ P @ M @ E )
% 2.85/1.56 => ( ine @ P @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_96_is__singleton__the__elem,axiom,
% 2.85/1.56 ( is_sin1501507247specID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_specID] :
% 2.85/1.56 ( A3
% 2.85/1.56 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_97_is__singleton__the__elem,axiom,
% 2.85/1.56 ( is_sin581274182chanID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_chanID] :
% 2.85/1.56 ( A3
% 2.85/1.56 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_98_ine__def,axiom,
% 2.85/1.56 ( ine
% 2.85/1.56 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.85/1.56 ? [Ch3: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 2.85/1.56 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_99_ine__ins__neg1,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M3: secrecy_Expression,X3: secrecy_chanID] :
% 2.85/1.56 ( ~ ( ine @ P @ M3 )
% 2.85/1.56 => ( ( exprChannel @ X3 @ M3 )
% 2.85/1.56 => ~ ( member1967978193chanID @ X3 @ ( ins @ P ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_100_is__singletonI_H,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( A2 != bot_bo1785112429specID )
% 2.85/1.56 => ( ! [X4: secrecy_specID,Y2: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ X4 @ A2 )
% 2.85/1.56 => ( ( member740727610specID @ Y2 @ A2 )
% 2.85/1.56 => ( X4 = Y2 ) ) )
% 2.85/1.56 => ( is_sin1501507247specID @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_101_is__singletonI_H,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A2 != bot_bo443197316chanID )
% 2.85/1.56 => ( ! [X4: secrecy_chanID,Y2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ A2 )
% 2.85/1.56 => ( ( member1967978193chanID @ Y2 @ A2 )
% 2.85/1.56 => ( X4 = Y2 ) ) )
% 2.85/1.56 => ( is_sin581274182chanID @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_102_bot__fun__def,axiom,
% 2.85/1.56 ( bot_bo1012329985anID_o
% 2.85/1.56 = ( ^ [X2: secrecy_chanID] : bot_bot_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_103_bot__fun__def,axiom,
% 2.85/1.56 ( bot_bo1767780696ecID_o
% 2.85/1.56 = ( ^ [X2: secrecy_specID] : bot_bot_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_104_TBtheorem4a__notP2,axiom,
% 2.85/1.56 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( ine @ Q @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_105_TBtheorem4a__notPQ,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.85/1.56 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_106_TBtheorem4a__notP1,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ine @ P @ E )
% 2.85/1.56 => ( ~ ( ine @ Q @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_107_ine__exprChannelSet__def,axiom,
% 2.85/1.56 ( ine_exprChannelSet
% 2.85/1.56 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.85/1.56 ( ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 2.85/1.56 => ( ( member1967978193chanID @ X2 @ ( ins @ SP ) )
% 2.85/1.56 & ( exprChannel @ X2 @ E2 ) ) )
% 2.85/1.56 & ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 2.85/1.56 & ( member1967978193chanID @ X2 @ ( ins @ SP ) ) )
% 2.85/1.56 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_108_is__singletonE,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( is_sin1501507247specID @ A2 )
% 2.85/1.56 => ~ ! [X4: secrecy_specID] :
% 2.85/1.56 ( A2
% 2.85/1.56 != ( insert1671894227specID @ X4 @ bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_109_is__singletonE,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( is_sin581274182chanID @ A2 )
% 2.85/1.56 => ~ ! [X4: secrecy_chanID] :
% 2.85/1.56 ( A2
% 2.85/1.56 != ( insert751661162chanID @ X4 @ bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_110_is__singleton__def,axiom,
% 2.85/1.56 ( is_sin1501507247specID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_specID] :
% 2.85/1.56 ? [X2: secrecy_specID] :
% 2.85/1.56 ( A3
% 2.85/1.56 = ( insert1671894227specID @ X2 @ bot_bo1785112429specID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_111_is__singleton__def,axiom,
% 2.85/1.56 ( is_sin581274182chanID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_chanID] :
% 2.85/1.56 ? [X2: secrecy_chanID] :
% 2.85/1.56 ( A3
% 2.85/1.56 = ( insert751661162chanID @ X2 @ bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_112_TBtheorem1a,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( ine @ PQ @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ( ( ine @ P @ E )
% 2.85/1.56 | ( ine @ Q @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_113_TBtheorem3a,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ~ ( ine @ P @ E )
% 2.85/1.56 => ( ~ ( ine @ Q @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correctCompositionIn @ PQ )
% 2.85/1.56 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_114_subcomponents__loc,axiom,
% 2.85/1.56 ! [X3: secrecy_specID] :
% 2.85/1.56 ( ( correc965049635ionLoc @ X3 )
% 2.85/1.56 => ( ( ( subcomponents @ X3 )
% 2.85/1.56 = bot_bo1785112429specID )
% 2.85/1.56 => ( ( loc @ X3 )
% 2.85/1.56 = bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_115_Set_Ois__empty__def,axiom,
% 2.85/1.56 ( is_emp1849217361specID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_116_Set_Ois__empty__def,axiom,
% 2.85/1.56 ( is_emp928984296chanID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_117_TBtheorem5a__empty,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ( eout @ P @ E )
% 2.85/1.56 | ( eout @ Q @ E ) )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( ( loc @ PQ )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_118_bot__empty__eq,axiom,
% 2.85/1.56 ( bot_bo1767780696ecID_o
% 2.85/1.56 = ( ^ [X2: secrecy_specID] : ( member740727610specID @ X2 @ bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_119_bot__empty__eq,axiom,
% 2.85/1.56 ( bot_bo1012329985anID_o
% 2.85/1.56 = ( ^ [X2: secrecy_chanID] : ( member1967978193chanID @ X2 @ bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_120_Collect__empty__eq__bot,axiom,
% 2.85/1.56 ! [P: secrecy_specID > $o] :
% 2.85/1.56 ( ( ( collec1545797240specID @ P )
% 2.85/1.56 = bot_bo1785112429specID )
% 2.85/1.56 = ( P = bot_bo1767780696ecID_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_121_Collect__empty__eq__bot,axiom,
% 2.85/1.56 ! [P: secrecy_chanID > $o] :
% 2.85/1.56 ( ( ( collec625564175chanID @ P )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 = ( P = bot_bo1012329985anID_o ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_122_pairwise__singleton,axiom,
% 2.85/1.56 ! [P: secrecy_specID > secrecy_specID > $o,A2: secrecy_specID] : ( pairwi514744696specID @ P @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_123_pairwise__singleton,axiom,
% 2.85/1.56 ! [P: secrecy_chanID > secrecy_chanID > $o,A2: secrecy_chanID] : ( pairwi1741995279chanID @ P @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_124_singleton__insert__inj__eq,axiom,
% 2.85/1.56 ! [B2: secrecy_specID,A: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ( insert1671894227specID @ B2 @ bot_bo1785112429specID )
% 2.85/1.56 = ( insert1671894227specID @ A @ A2 ) )
% 2.85/1.56 = ( ( A = B2 )
% 2.85/1.56 & ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_125_singleton__insert__inj__eq,axiom,
% 2.85/1.56 ! [B2: secrecy_chanID,A: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( insert751661162chanID @ B2 @ bot_bo443197316chanID )
% 2.85/1.56 = ( insert751661162chanID @ A @ A2 ) )
% 2.85/1.56 = ( ( A = B2 )
% 2.85/1.56 & ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_126_order__refl,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X3 @ X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_127_order__refl,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID] : ( ord_le996703545specID @ X3 @ X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_128_subsetI,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ A2 )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ B ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ A2 @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_129_subsetI,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ! [X4: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ X4 @ A2 )
% 2.85/1.56 => ( member740727610specID @ X4 @ B ) )
% 2.85/1.56 => ( ord_le996703545specID @ A2 @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_130_subset__antisym,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ B )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B @ A2 )
% 2.85/1.56 => ( A2 = B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_131_subset__antisym,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A2 @ B )
% 2.85/1.56 => ( ( ord_le996703545specID @ B @ A2 )
% 2.85/1.56 => ( A2 = B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_132_empty__subsetI,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] : ( ord_le996703545specID @ bot_bo1785112429specID @ A2 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_133_empty__subsetI,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ bot_bo443197316chanID @ A2 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_134_subset__empty,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A2 @ bot_bo1785112429specID )
% 2.85/1.56 = ( A2 = bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_135_subset__empty,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ bot_bo443197316chanID )
% 2.85/1.56 = ( A2 = bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_136_insert__subset,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ ( insert751661162chanID @ X3 @ A2 ) @ B )
% 2.85/1.56 = ( ( member1967978193chanID @ X3 @ B )
% 2.85/1.56 & ( ord_le1802272080chanID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_137_insert__subset,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ ( insert1671894227specID @ X3 @ A2 ) @ B )
% 2.85/1.56 = ( ( member740727610specID @ X3 @ B )
% 2.85/1.56 & ( ord_le996703545specID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_138_singleton__insert__inj__eq_H,axiom,
% 2.85/1.56 ! [A: secrecy_specID,A2: set_Secrecy_specID,B2: secrecy_specID] :
% 2.85/1.56 ( ( ( insert1671894227specID @ A @ A2 )
% 2.85/1.56 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 2.85/1.56 = ( ( A = B2 )
% 2.85/1.56 & ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_139_singleton__insert__inj__eq_H,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.85/1.56 ( ( ( insert751661162chanID @ A @ A2 )
% 2.85/1.56 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 2.85/1.56 = ( ( A = B2 )
% 2.85/1.56 & ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_140_order__subst1,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_141_order__subst1,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,F: set_Secrecy_specID > set_Secrecy_chanID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le996703545specID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_142_order__subst1,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,F: set_Secrecy_chanID > set_Secrecy_specID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_143_order__subst1,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le996703545specID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_144_order__subst2,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ ( F @ B2 ) @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_145_order__subst2,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le996703545specID @ ( F @ B2 ) @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_146_order__subst2,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ ( F @ B2 ) @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_147_order__subst2,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le996703545specID @ ( F @ B2 ) @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_148_ord__eq__le__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A
% 2.85/1.56 = ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_149_ord__eq__le__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,F: set_Secrecy_chanID > set_Secrecy_specID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A
% 2.85/1.56 = ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_150_ord__eq__le__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,F: set_Secrecy_specID > set_Secrecy_chanID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( A
% 2.85/1.56 = ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le996703545specID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_151_ord__eq__le__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( A
% 2.85/1.56 = ( F @ B2 ) )
% 2.85/1.56 => ( ( ord_le996703545specID @ B2 @ C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ A @ ( F @ C ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_152_ord__le__eq__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( ( F @ B2 )
% 2.85/1.56 = C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_153_ord__le__eq__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,F: set_Secrecy_chanID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( ( F @ B2 )
% 2.85/1.56 = C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_154_ord__le__eq__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ B2 )
% 2.85/1.56 => ( ( ( F @ B2 )
% 2.85/1.56 = C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_155_ord__le__eq__subst,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,F: set_Secrecy_specID > set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ B2 )
% 2.85/1.56 => ( ( ( F @ B2 )
% 2.85/1.56 = C )
% 2.85/1.56 => ( ! [X4: set_Secrecy_specID,Y2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X4 @ Y2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ X4 ) @ ( F @ Y2 ) ) )
% 2.85/1.56 => ( ord_le996703545specID @ ( F @ A ) @ C ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_156_eq__iff,axiom,
% 2.85/1.56 ( ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z ) )
% 2.85/1.56 = ( ^ [X2: set_Secrecy_chanID,Y4: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X2 @ Y4 )
% 2.85/1.56 & ( ord_le1802272080chanID @ Y4 @ X2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_157_eq__iff,axiom,
% 2.85/1.56 ( ( ^ [Y: set_Secrecy_specID,Z: set_Secrecy_specID] : ( Y = Z ) )
% 2.85/1.56 = ( ^ [X2: set_Secrecy_specID,Y4: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X2 @ Y4 )
% 2.85/1.56 & ( ord_le996703545specID @ Y4 @ X2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_158_antisym,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 2.85/1.56 => ( X3 = Y3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_159_antisym,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X3 @ Y3 )
% 2.85/1.56 => ( ( ord_le996703545specID @ Y3 @ X3 )
% 2.85/1.56 => ( X3 = Y3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_160_eq__refl,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( X3 = Y3 )
% 2.85/1.56 => ( ord_le1802272080chanID @ X3 @ Y3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_161_eq__refl,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 2.85/1.56 ( ( X3 = Y3 )
% 2.85/1.56 => ( ord_le996703545specID @ X3 @ Y3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_162_order_Otrans,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ C )
% 2.85/1.56 => ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_163_order_Otrans,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le996703545specID @ B2 @ C )
% 2.85/1.56 => ( ord_le996703545specID @ A @ C ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_164_antisym__conv,axiom,
% 2.85/1.56 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 2.85/1.56 = ( X3 = Y3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_165_antisym__conv,axiom,
% 2.85/1.56 ! [Y3: set_Secrecy_specID,X3: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ Y3 @ X3 )
% 2.85/1.56 => ( ( ord_le996703545specID @ X3 @ Y3 )
% 2.85/1.56 = ( X3 = Y3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_166_order__class_Oorder_Oeq__iff,axiom,
% 2.85/1.56 ( ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z ) )
% 2.85/1.56 = ( ^ [A4: set_Secrecy_chanID,B4: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A4 @ B4 )
% 2.85/1.56 & ( ord_le1802272080chanID @ B4 @ A4 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_167_order__class_Oorder_Oeq__iff,axiom,
% 2.85/1.56 ( ( ^ [Y: set_Secrecy_specID,Z: set_Secrecy_specID] : ( Y = Z ) )
% 2.85/1.56 = ( ^ [A4: set_Secrecy_specID,B4: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A4 @ B4 )
% 2.85/1.56 & ( ord_le996703545specID @ B4 @ A4 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_168_ord__eq__le__trans,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A = B2 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ C )
% 2.85/1.56 => ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_169_ord__eq__le__trans,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( A = B2 )
% 2.85/1.56 => ( ( ord_le996703545specID @ B2 @ C )
% 2.85/1.56 => ( ord_le996703545specID @ A @ C ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_170_ord__le__eq__trans,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( B2 = C )
% 2.85/1.56 => ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_171_ord__le__eq__trans,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID,C: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ B2 )
% 2.85/1.56 => ( ( B2 = C )
% 2.85/1.56 => ( ord_le996703545specID @ A @ C ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_172_order__class_Oorder_Oantisym,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ A )
% 2.85/1.56 => ( A = B2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_173_order__class_Oorder_Oantisym,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ B2 )
% 2.85/1.56 => ( ( ord_le996703545specID @ B2 @ A )
% 2.85/1.56 => ( A = B2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_174_order__trans,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ Y3 @ Z2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ X3 @ Z2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_175_order__trans,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID,Z2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X3 @ Y3 )
% 2.85/1.56 => ( ( ord_le996703545specID @ Y3 @ Z2 )
% 2.85/1.56 => ( ord_le996703545specID @ X3 @ Z2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_176_dual__order_Orefl,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID] : ( ord_le996703545specID @ A @ A ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_177_in__mono,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,X3: secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ B )
% 2.85/1.56 => ( ( member1967978193chanID @ X3 @ A2 )
% 2.85/1.56 => ( member1967978193chanID @ X3 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_178_in__mono,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,X3: secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A2 @ B )
% 2.85/1.56 => ( ( member740727610specID @ X3 @ A2 )
% 2.85/1.56 => ( member740727610specID @ X3 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_179_subsetD,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ B )
% 2.85/1.56 => ( ( member1967978193chanID @ C @ A2 )
% 2.85/1.56 => ( member1967978193chanID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_180_subsetD,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A2 @ B )
% 2.85/1.56 => ( ( member740727610specID @ C @ A2 )
% 2.85/1.56 => ( member740727610specID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_181_pairwiseD,axiom,
% 2.85/1.56 ! [R: secrecy_chanID > secrecy_chanID > $o,S: set_Secrecy_chanID,X3: secrecy_chanID,Y3: secrecy_chanID] :
% 2.85/1.56 ( ( pairwi1741995279chanID @ R @ S )
% 2.85/1.56 => ( ( member1967978193chanID @ X3 @ S )
% 2.85/1.56 => ( ( member1967978193chanID @ Y3 @ S )
% 2.85/1.56 => ( ( X3 != Y3 )
% 2.85/1.56 => ( R @ X3 @ Y3 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_182_pairwiseD,axiom,
% 2.85/1.56 ! [R: secrecy_specID > secrecy_specID > $o,S: set_Secrecy_specID,X3: secrecy_specID,Y3: secrecy_specID] :
% 2.85/1.56 ( ( pairwi514744696specID @ R @ S )
% 2.85/1.56 => ( ( member740727610specID @ X3 @ S )
% 2.85/1.56 => ( ( member740727610specID @ Y3 @ S )
% 2.85/1.56 => ( ( X3 != Y3 )
% 2.85/1.56 => ( R @ X3 @ Y3 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_183_pairwiseI,axiom,
% 2.85/1.56 ! [S: set_Secrecy_chanID,R: secrecy_chanID > secrecy_chanID > $o] :
% 2.85/1.56 ( ! [X4: secrecy_chanID,Y2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ S )
% 2.85/1.56 => ( ( member1967978193chanID @ Y2 @ S )
% 2.85/1.56 => ( ( X4 != Y2 )
% 2.85/1.56 => ( R @ X4 @ Y2 ) ) ) )
% 2.85/1.56 => ( pairwi1741995279chanID @ R @ S ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_184_pairwiseI,axiom,
% 2.85/1.56 ! [S: set_Secrecy_specID,R: secrecy_specID > secrecy_specID > $o] :
% 2.85/1.56 ( ! [X4: secrecy_specID,Y2: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ X4 @ S )
% 2.85/1.56 => ( ( member740727610specID @ Y2 @ S )
% 2.85/1.56 => ( ( X4 != Y2 )
% 2.85/1.56 => ( R @ X4 @ Y2 ) ) ) )
% 2.85/1.56 => ( pairwi514744696specID @ R @ S ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_185_subset__eq,axiom,
% 2.85/1.56 ( ord_le1802272080chanID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] :
% 2.85/1.56 ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ A3 )
% 2.85/1.56 => ( member1967978193chanID @ X2 @ B5 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_186_subset__eq,axiom,
% 2.85/1.56 ( ord_le996703545specID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_specID,B5: set_Secrecy_specID] :
% 2.85/1.56 ! [X2: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ X2 @ A3 )
% 2.85/1.56 => ( member740727610specID @ X2 @ B5 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_187_subset__iff,axiom,
% 2.85/1.56 ( ord_le1802272080chanID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] :
% 2.85/1.56 ! [T: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ T @ A3 )
% 2.85/1.56 => ( member1967978193chanID @ T @ B5 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_188_subset__iff,axiom,
% 2.85/1.56 ( ord_le996703545specID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_specID,B5: set_Secrecy_specID] :
% 2.85/1.56 ! [T: secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ T @ A3 )
% 2.85/1.56 => ( member740727610specID @ T @ B5 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_189_bot_Oextremum__uniqueI,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ bot_bo1785112429specID )
% 2.85/1.56 => ( A = bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_190_bot_Oextremum__uniqueI,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ bot_bo443197316chanID )
% 2.85/1.56 => ( A = bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_191_bot_Oextremum__unique,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A @ bot_bo1785112429specID )
% 2.85/1.56 = ( A = bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_192_bot_Oextremum__unique,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ bot_bo443197316chanID )
% 2.85/1.56 = ( A = bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_193_bot_Oextremum,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID] : ( ord_le996703545specID @ bot_bo1785112429specID @ A ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_194_bot_Oextremum,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID] : ( ord_le1802272080chanID @ bot_bo443197316chanID @ A ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_195_subset__insertI2,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A2 @ B )
% 2.85/1.56 => ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_196_subset__insertI2,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ B )
% 2.85/1.56 => ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_197_subset__insertI,axiom,
% 2.85/1.56 ! [B: set_Secrecy_specID,A: secrecy_specID] : ( ord_le996703545specID @ B @ ( insert1671894227specID @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_198_subset__insertI,axiom,
% 2.85/1.56 ! [B: set_Secrecy_chanID,A: secrecy_chanID] : ( ord_le1802272080chanID @ B @ ( insert751661162chanID @ A @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_199_subset__insert,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( member1967978193chanID @ X3 @ A2 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ X3 @ B ) )
% 2.85/1.56 = ( ord_le1802272080chanID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_200_subset__insert,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ~ ( member740727610specID @ X3 @ A2 )
% 2.85/1.56 => ( ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ X3 @ B ) )
% 2.85/1.56 = ( ord_le996703545specID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_201_insert__mono,axiom,
% 2.85/1.56 ! [C3: set_Secrecy_specID,D2: set_Secrecy_specID,A: secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ C3 @ D2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( insert1671894227specID @ A @ C3 ) @ ( insert1671894227specID @ A @ D2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_202_insert__mono,axiom,
% 2.85/1.56 ! [C3: set_Secrecy_chanID,D2: set_Secrecy_chanID,A: secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ C3 @ D2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( insert751661162chanID @ A @ C3 ) @ ( insert751661162chanID @ A @ D2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_203_pairwise__empty,axiom,
% 2.85/1.56 ! [P: secrecy_specID > secrecy_specID > $o] : ( pairwi514744696specID @ P @ bot_bo1785112429specID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_204_pairwise__empty,axiom,
% 2.85/1.56 ! [P: secrecy_chanID > secrecy_chanID > $o] : ( pairwi1741995279chanID @ P @ bot_bo443197316chanID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_205_pairwise__insert,axiom,
% 2.85/1.56 ! [R2: secrecy_chanID > secrecy_chanID > $o,X3: secrecy_chanID,S2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( pairwi1741995279chanID @ R2 @ ( insert751661162chanID @ X3 @ S2 ) )
% 2.85/1.56 = ( ! [Y4: secrecy_chanID] :
% 2.85/1.56 ( ( ( member1967978193chanID @ Y4 @ S2 )
% 2.85/1.56 & ( Y4 != X3 ) )
% 2.85/1.56 => ( ( R2 @ X3 @ Y4 )
% 2.85/1.56 & ( R2 @ Y4 @ X3 ) ) )
% 2.85/1.56 & ( pairwi1741995279chanID @ R2 @ S2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_206_pairwise__insert,axiom,
% 2.85/1.56 ! [R2: secrecy_specID > secrecy_specID > $o,X3: secrecy_specID,S2: set_Secrecy_specID] :
% 2.85/1.56 ( ( pairwi514744696specID @ R2 @ ( insert1671894227specID @ X3 @ S2 ) )
% 2.85/1.56 = ( ! [Y4: secrecy_specID] :
% 2.85/1.56 ( ( ( member740727610specID @ Y4 @ S2 )
% 2.85/1.56 & ( Y4 != X3 ) )
% 2.85/1.56 => ( ( R2 @ X3 @ Y4 )
% 2.85/1.56 & ( R2 @ Y4 @ X3 ) ) )
% 2.85/1.56 & ( pairwi514744696specID @ R2 @ S2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_207_subset__singleton__iff,axiom,
% 2.85/1.56 ! [X5: set_Secrecy_specID,A: secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ X5 @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
% 2.85/1.56 = ( ( X5 = bot_bo1785112429specID )
% 2.85/1.56 | ( X5
% 2.85/1.56 = ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_208_subset__singleton__iff,axiom,
% 2.85/1.56 ! [X5: set_Secrecy_chanID,A: secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X5 @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
% 2.85/1.56 = ( ( X5 = bot_bo443197316chanID )
% 2.85/1.56 | ( X5
% 2.85/1.56 = ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_209_subset__singletonD,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,X3: secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A2 @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.85/1.56 => ( ( A2 = bot_bo1785112429specID )
% 2.85/1.56 | ( A2
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_210_subset__singletonD,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,X3: secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.85/1.56 => ( ( A2 = bot_bo443197316chanID )
% 2.85/1.56 | ( A2
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_211_TBtheorem2a,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( eout @ PQ @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( eout @ P @ E )
% 2.85/1.56 | ( eout @ Q @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_212_TBtheorem5a__notP1,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( eout @ P @ E )
% 2.85/1.56 => ( ~ ( eout @ Q @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_213_TBtheorem5a__notPQ,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.85/1.56 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_214_TBtheorem5a__notP2,axiom,
% 2.85/1.56 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( eout @ Q @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_215_TBtheorem5a__PQ,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ( eout @ P @ E )
% 2.85/1.56 | ( eout @ Q @ E ) )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.85/1.56 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_216_TBtheorem45a__P,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( eout @ P @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_217_TBtheorem2b,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( eoutM @ PQ @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( eoutM @ P @ M @ E )
% 2.85/1.56 | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_218_eoutM__def,axiom,
% 2.85/1.56 ( eoutM
% 2.85/1.56 = ( ^ [SP: secrecy_specID,M2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.85/1.56 ? [Ch3: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.85/1.56 & ( member1967978193chanID @ Ch3 @ M2 )
% 2.85/1.56 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_219_out__exprChannelSet__def,axiom,
% 2.85/1.56 ( out_exprChannelSet
% 2.85/1.56 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 2.85/1.56 ( ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ ChSet2 )
% 2.85/1.56 => ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 2.85/1.56 & ( exprChannel @ X2 @ E2 ) ) )
% 2.85/1.56 & ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( ~ ( member1967978193chanID @ X2 @ ChSet2 )
% 2.85/1.56 & ( member1967978193chanID @ X2 @ ( out @ SP ) ) )
% 2.85/1.56 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_220_out__exprChannelSingle__def,axiom,
% 2.85/1.56 ( out_ex985543062Single
% 2.85/1.56 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.85/1.56 & ( exprChannel @ Ch3 @ E2 )
% 2.85/1.56 & ! [X2: secrecy_chanID,T: nat] :
% 2.85/1.56 ( ( ( member1967978193chanID @ X2 @ ( out @ SP ) )
% 2.85/1.56 & ( X2 != Ch3 ) )
% 2.85/1.56 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_221_not__eout__eoutM,axiom,
% 2.85/1.56 ! [P: secrecy_specID,E: secrecy_Expression,M: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( eout @ P @ E )
% 2.85/1.56 => ~ ( eoutM @ P @ M @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_222_eoutM__eout,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( eoutM @ P @ M @ E )
% 2.85/1.56 => ( eout @ P @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_223_out__exprChannelSet__Single,axiom,
% 2.85/1.56 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 2.85/1.56 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_224_out__exprChannelSingle__Set,axiom,
% 2.85/1.56 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.85/1.56 ( ( out_ex985543062Single @ P @ Ch @ E )
% 2.85/1.56 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_225_eout__def,axiom,
% 2.85/1.56 ( eout
% 2.85/1.56 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.85/1.56 ? [Ch3: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 2.85/1.56 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_226_TBtheorem5b__notP2,axiom,
% 2.85/1.56 ! [Q: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( eoutM @ Q @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSet )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_227_TBtheore54b__P,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.85/1.56 ( ( eoutM @ P @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ M ) )
% 2.85/1.56 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_228_TBtheorem5b__PQ,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( ( eoutM @ P @ M @ E )
% 2.85/1.56 | ( eoutM @ Q @ M @ E ) )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 2.85/1.56 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ M )
% 2.85/1.56 & ( exprChannel @ Ch2 @ E )
% 2.85/1.56 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_229_TBtheorem5b__notP1,axiom,
% 2.85/1.56 ! [P: secrecy_specID,M: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.85/1.56 ( ( eoutM @ P @ M @ E )
% 2.85/1.56 => ( ~ ( eoutM @ Q @ M @ E )
% 2.85/1.56 => ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ? [Ch2: secrecy_chanID] :
% 2.85/1.56 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ M )
% 2.85/1.56 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_230_correctCompositionOut__prop1,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( member1967978193chanID @ X3 @ ( out @ PQ ) )
% 2.85/1.56 => ( ( member1967978193chanID @ X3 @ ( out @ P ) )
% 2.85/1.56 | ( member1967978193chanID @ X3 @ ( out @ Q ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_231_outStream__def,axiom,
% 2.85/1.56 ( outStream
% 2.85/1.56 = ( ^ [X2: secrecy_specID] :
% 2.85/1.56 ( ^ [Y: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y = Z )
% 2.85/1.56 @ ( out @ X2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_232_TBtheorem5b__notPQ,axiom,
% 2.85/1.56 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( subcomponents @ PQ )
% 2.85/1.56 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 2.85/1.56 => ( ( correc990227761ionOut @ PQ )
% 2.85/1.56 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.85/1.56 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.85/1.56 => ( ( M
% 2.85/1.56 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetP )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X4 @ ChSetQ )
% 2.85/1.56 => ( member1967978193chanID @ X4 @ ( loc @ PQ ) ) )
% 2.85/1.56 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_233_insert__subsetI,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,X5: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X3 @ A2 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ X5 @ A2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( insert751661162chanID @ X3 @ X5 ) @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_234_insert__subsetI,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,A2: set_Secrecy_specID,X5: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ X3 @ A2 )
% 2.85/1.56 => ( ( ord_le996703545specID @ X5 @ A2 )
% 2.85/1.56 => ( ord_le996703545specID @ ( insert1671894227specID @ X3 @ X5 ) @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_235_UnCI,axiom,
% 2.85/1.56 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ~ ( member740727610specID @ C @ B )
% 2.85/1.56 => ( member740727610specID @ C @ A2 ) )
% 2.85/1.56 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_236_UnCI,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ~ ( member1967978193chanID @ C @ B )
% 2.85/1.56 => ( member1967978193chanID @ C @ A2 ) )
% 2.85/1.56 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_237_Un__iff,axiom,
% 2.85/1.56 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 2.85/1.56 = ( ( member740727610specID @ C @ A2 )
% 2.85/1.56 | ( member740727610specID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_238_Un__iff,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 2.85/1.56 = ( ( member1967978193chanID @ C @ A2 )
% 2.85/1.56 | ( member1967978193chanID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_239_Un__empty,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( ( sup_su1712599557specID @ A2 @ B )
% 2.85/1.56 = bot_bo1785112429specID )
% 2.85/1.56 = ( ( A2 = bot_bo1785112429specID )
% 2.85/1.56 & ( B = bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_240_Un__empty,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( sup_su370684444chanID @ A2 @ B )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 = ( ( A2 = bot_bo443197316chanID )
% 2.85/1.56 & ( B = bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_241_Un__insert__left,axiom,
% 2.85/1.56 ! [A: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 2.85/1.56 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_242_Un__insert__left,axiom,
% 2.85/1.56 ! [A: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 2.85/1.56 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_243_Un__insert__right,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,A: secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 2.85/1.56 = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_244_Un__insert__right,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,A: secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 2.85/1.56 = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_245_Un__subset__iff,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 )
% 2.85/1.56 = ( ( ord_le1802272080chanID @ A2 @ C3 )
% 2.85/1.56 & ( ord_le1802272080chanID @ B @ C3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_246_Un__empty__left,axiom,
% 2.85/1.56 ! [B: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 2.85/1.56 = B ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_247_Un__empty__left,axiom,
% 2.85/1.56 ! [B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 2.85/1.56 = B ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_248_Un__empty__right,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 2.85/1.56 = A2 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_249_Un__empty__right,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 2.85/1.56 = A2 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_250_subset__Un__eq,axiom,
% 2.85/1.56 ( ord_le1802272080chanID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A3 @ B5 )
% 2.85/1.56 = B5 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_251_subset__UnE,axiom,
% 2.85/1.56 ! [C3: set_Secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ C3 @ ( sup_su370684444chanID @ A2 @ B ) )
% 2.85/1.56 => ~ ! [A5: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A5 @ A2 )
% 2.85/1.56 => ! [B6: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ B6 @ B )
% 2.85/1.56 => ( C3
% 2.85/1.56 != ( sup_su370684444chanID @ A5 @ B6 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_252_Un__absorb2,axiom,
% 2.85/1.56 ! [B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ B @ A2 )
% 2.85/1.56 => ( ( sup_su370684444chanID @ A2 @ B )
% 2.85/1.56 = A2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_253_Un__absorb1,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ B )
% 2.85/1.56 => ( ( sup_su370684444chanID @ A2 @ B )
% 2.85/1.56 = B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_254_Un__upper2,axiom,
% 2.85/1.56 ! [B: set_Secrecy_chanID,A2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ B @ ( sup_su370684444chanID @ A2 @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_255_Un__upper1,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( ord_le1802272080chanID @ A2 @ ( sup_su370684444chanID @ A2 @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_256_Un__least,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ C3 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B @ C3 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_257_Un__mono,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID,D2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ C3 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B @ D2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A2 @ B ) @ ( sup_su370684444chanID @ C3 @ D2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_258_ineM__Un1,axiom,
% 2.85/1.56 ! [P: secrecy_specID,A2: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ineM @ P @ A2 @ E )
% 2.85/1.56 => ( ineM @ P @ ( sup_su370684444chanID @ A2 @ B ) @ E ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_259_UnE,axiom,
% 2.85/1.56 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) )
% 2.85/1.56 => ( ~ ( member740727610specID @ C @ A2 )
% 2.85/1.56 => ( member740727610specID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_260_UnE,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) )
% 2.85/1.56 => ( ~ ( member1967978193chanID @ C @ A2 )
% 2.85/1.56 => ( member1967978193chanID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_261_UnI1,axiom,
% 2.85/1.56 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ C @ A2 )
% 2.85/1.56 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_262_UnI1,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ C @ A2 )
% 2.85/1.56 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_263_UnI2,axiom,
% 2.85/1.56 ! [C: secrecy_specID,B: set_Secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ C @ B )
% 2.85/1.56 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_264_UnI2,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ C @ B )
% 2.85/1.56 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A2 @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_265_bex__Un,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.85/1.56 ( ( ? [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 2.85/1.56 & ( P @ X2 ) ) )
% 2.85/1.56 = ( ? [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ A2 )
% 2.85/1.56 & ( P @ X2 ) )
% 2.85/1.56 | ? [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ B )
% 2.85/1.56 & ( P @ X2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_266_ball__Un,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 2.85/1.56 ( ( ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 2.85/1.56 => ( P @ X2 ) ) )
% 2.85/1.56 = ( ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ A2 )
% 2.85/1.56 => ( P @ X2 ) )
% 2.85/1.56 & ! [X2: secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ X2 @ B )
% 2.85/1.56 => ( P @ X2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_267_Un__assoc,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A2 @ B ) @ C3 )
% 2.85/1.56 = ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_268_Un__absorb,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A2 @ A2 )
% 2.85/1.56 = A2 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_269_Un__commute,axiom,
% 2.85/1.56 ( sup_su370684444chanID
% 2.85/1.56 = ( ^ [A3: set_Secrecy_chanID,B5: set_Secrecy_chanID] : ( sup_su370684444chanID @ B5 @ A3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_270_Un__left__absorb,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ A2 @ B ) )
% 2.85/1.56 = ( sup_su370684444chanID @ A2 @ B ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_271_Un__left__commute,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) )
% 2.85/1.56 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A2 @ C3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_272_singleton__Un__iff,axiom,
% 2.85/1.56 ! [X3: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( ( insert1671894227specID @ X3 @ bot_bo1785112429specID )
% 2.85/1.56 = ( sup_su1712599557specID @ A2 @ B ) )
% 2.85/1.56 = ( ( ( A2 = bot_bo1785112429specID )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.85/1.56 & ( B = bot_bo1785112429specID ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_273_singleton__Un__iff,axiom,
% 2.85/1.56 ! [X3: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( insert751661162chanID @ X3 @ bot_bo443197316chanID )
% 2.85/1.56 = ( sup_su370684444chanID @ A2 @ B ) )
% 2.85/1.56 = ( ( ( A2 = bot_bo443197316chanID )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.85/1.56 & ( B = bot_bo443197316chanID ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_274_Un__singleton__iff,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B: set_Secrecy_specID,X3: secrecy_specID] :
% 2.85/1.56 ( ( ( sup_su1712599557specID @ A2 @ B )
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.85/1.56 = ( ( ( A2 = bot_bo1785112429specID )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.85/1.56 & ( B = bot_bo1785112429specID ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_275_Un__singleton__iff,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B: set_Secrecy_chanID,X3: secrecy_chanID] :
% 2.85/1.56 ( ( ( sup_su370684444chanID @ A2 @ B )
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.85/1.56 = ( ( ( A2 = bot_bo443197316chanID )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.85/1.56 & ( B = bot_bo443197316chanID ) )
% 2.85/1.56 | ( ( A2
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 2.85/1.56 & ( B
% 2.85/1.56 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_276_insert__is__Un,axiom,
% 2.85/1.56 ( insert1671894227specID
% 2.85/1.56 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_277_insert__is__Un,axiom,
% 2.85/1.56 ( insert751661162chanID
% 2.85/1.56 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_278_subset__emptyI,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID] :
% 2.85/1.56 ( ! [X4: secrecy_specID] :
% 2.85/1.56 ~ ( member740727610specID @ X4 @ A2 )
% 2.85/1.56 => ( ord_le996703545specID @ A2 @ bot_bo1785112429specID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_279_subset__emptyI,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ! [X4: secrecy_chanID] :
% 2.85/1.56 ~ ( member1967978193chanID @ X4 @ A2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_280_sup__bot_Oright__neutral,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 2.85/1.56 = A ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_281_sup__bot_Oright__neutral,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 2.85/1.56 = A ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_282_sup__bot_Oneutr__eq__iff,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 2.85/1.56 ( ( bot_bo1785112429specID
% 2.85/1.56 = ( sup_su1712599557specID @ A @ B2 ) )
% 2.85/1.56 = ( ( A = bot_bo1785112429specID )
% 2.85/1.56 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_283_sup__bot_Oneutr__eq__iff,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( bot_bo443197316chanID
% 2.85/1.56 = ( sup_su370684444chanID @ A @ B2 ) )
% 2.85/1.56 = ( ( A = bot_bo443197316chanID )
% 2.85/1.56 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_284_sup__bot_Oleft__neutral,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
% 2.85/1.56 = A ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_285_sup__bot_Oleft__neutral,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
% 2.85/1.56 = A ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_286_le__sup__iff,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ X3 @ Y3 ) @ Z2 )
% 2.85/1.56 = ( ( ord_le1802272080chanID @ X3 @ Z2 )
% 2.85/1.56 & ( ord_le1802272080chanID @ Y3 @ Z2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_287_sup_Obounded__iff,axiom,
% 2.85/1.56 ! [B2: set_Secrecy_chanID,C: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ B2 @ C ) @ A )
% 2.85/1.56 = ( ( ord_le1802272080chanID @ B2 @ A )
% 2.85/1.56 & ( ord_le1802272080chanID @ C @ A ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_288_sup__bot__left,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X3 )
% 2.85/1.56 = X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_289_sup__bot__left,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X3 )
% 2.85/1.56 = X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_290_sup__bot__right,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID] :
% 2.85/1.56 ( ( sup_su1712599557specID @ X3 @ bot_bo1785112429specID )
% 2.85/1.56 = X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_291_sup__bot__right,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ X3 @ bot_bo443197316chanID )
% 2.85/1.56 = X3 ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_292_bot__eq__sup__iff,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 2.85/1.56 ( ( bot_bo1785112429specID
% 2.85/1.56 = ( sup_su1712599557specID @ X3 @ Y3 ) )
% 2.85/1.56 = ( ( X3 = bot_bo1785112429specID )
% 2.85/1.56 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_293_bot__eq__sup__iff,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( bot_bo443197316chanID
% 2.85/1.56 = ( sup_su370684444chanID @ X3 @ Y3 ) )
% 2.85/1.56 = ( ( X3 = bot_bo443197316chanID )
% 2.85/1.56 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_294_sup__eq__bot__iff,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID,Y3: set_Secrecy_specID] :
% 2.85/1.56 ( ( ( sup_su1712599557specID @ X3 @ Y3 )
% 2.85/1.56 = bot_bo1785112429specID )
% 2.85/1.56 = ( ( X3 = bot_bo1785112429specID )
% 2.85/1.56 & ( Y3 = bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_295_sup__eq__bot__iff,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( sup_su370684444chanID @ X3 @ Y3 )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 = ( ( X3 = bot_bo443197316chanID )
% 2.85/1.56 & ( Y3 = bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_296_sup__bot_Oeq__neutr__iff,axiom,
% 2.85/1.56 ! [A: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 2.85/1.56 ( ( ( sup_su1712599557specID @ A @ B2 )
% 2.85/1.56 = bot_bo1785112429specID )
% 2.85/1.56 = ( ( A = bot_bo1785112429specID )
% 2.85/1.56 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_297_sup__bot_Oeq__neutr__iff,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ( sup_su370684444chanID @ A @ B2 )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 = ( ( A = bot_bo443197316chanID )
% 2.85/1.56 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_298_inf__sup__ord_I4_J,axiom,
% 2.85/1.56 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ Y3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_299_inf__sup__ord_I3_J,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_300_le__supE,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,X3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A @ B2 ) @ X3 )
% 2.85/1.56 => ~ ( ( ord_le1802272080chanID @ A @ X3 )
% 2.85/1.56 => ~ ( ord_le1802272080chanID @ B2 @ X3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_301_le__supI,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,X3: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ X3 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ X3 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A @ B2 ) @ X3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_302_sup__ge1,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_303_sup__ge2,axiom,
% 2.85/1.56 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] : ( ord_le1802272080chanID @ Y3 @ ( sup_su370684444chanID @ X3 @ Y3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_304_le__supI1,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X3 @ A )
% 2.85/1.56 => ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_305_le__supI2,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X3 @ B2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ X3 @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_306_sup_Omono,axiom,
% 2.85/1.56 ! [C: set_Secrecy_chanID,A: set_Secrecy_chanID,D: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ C @ A )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ D @ B2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ C @ D ) @ ( sup_su370684444chanID @ A @ B2 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_307_sup__mono,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,C: set_Secrecy_chanID,B2: set_Secrecy_chanID,D: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ C )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ B2 @ D )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ A @ B2 ) @ ( sup_su370684444chanID @ C @ D ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_308_sup__least,axiom,
% 2.85/1.56 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ Z2 @ X3 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ Y3 @ Z2 ) @ X3 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_309_le__iff__sup,axiom,
% 2.85/1.56 ( ord_le1802272080chanID
% 2.85/1.56 = ( ^ [X2: set_Secrecy_chanID,Y4: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ X2 @ Y4 )
% 2.85/1.56 = Y4 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_310_sup_OorderE,axiom,
% 2.85/1.56 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ B2 @ A )
% 2.85/1.56 => ( A
% 2.85/1.56 = ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_311_sup_OorderI,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( A
% 2.85/1.56 = ( sup_su370684444chanID @ A @ B2 ) )
% 2.85/1.56 => ( ord_le1802272080chanID @ B2 @ A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_312_sup__unique,axiom,
% 2.85/1.56 ! [F: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID,X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.85/1.56 ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ X4 @ ( F @ X4 @ Y2 ) )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ Y2 @ ( F @ X4 @ Y2 ) )
% 2.85/1.56 => ( ! [X4: set_Secrecy_chanID,Y2: set_Secrecy_chanID,Z3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ Y2 @ X4 )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ Z3 @ X4 )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( F @ Y2 @ Z3 ) @ X4 ) ) )
% 2.85/1.56 => ( ( sup_su370684444chanID @ X3 @ Y3 )
% 2.85/1.56 = ( F @ X3 @ Y3 ) ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_313_sup_Oabsorb1,axiom,
% 2.85/1.56 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ B2 @ A )
% 2.85/1.56 => ( ( sup_su370684444chanID @ A @ B2 )
% 2.85/1.56 = A ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_314_sup_Oabsorb2,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 => ( ( sup_su370684444chanID @ A @ B2 )
% 2.85/1.56 = B2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_315_sup__absorb1,axiom,
% 2.85/1.56 ! [Y3: set_Secrecy_chanID,X3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ Y3 @ X3 )
% 2.85/1.56 => ( ( sup_su370684444chanID @ X3 @ Y3 )
% 2.85/1.56 = X3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_316_sup__absorb2,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 2.85/1.56 => ( ( sup_su370684444chanID @ X3 @ Y3 )
% 2.85/1.56 = Y3 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_317_sup_OboundedE,axiom,
% 2.85/1.56 ! [B2: set_Secrecy_chanID,C: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ ( sup_su370684444chanID @ B2 @ C ) @ A )
% 2.85/1.56 => ~ ( ( ord_le1802272080chanID @ B2 @ A )
% 2.85/1.56 => ~ ( ord_le1802272080chanID @ C @ A ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_318_sup_OboundedI,axiom,
% 2.85/1.56 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ B2 @ A )
% 2.85/1.56 => ( ( ord_le1802272080chanID @ C @ A )
% 2.85/1.56 => ( ord_le1802272080chanID @ ( sup_su370684444chanID @ B2 @ C ) @ A ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_319_sup_Oorder__iff,axiom,
% 2.85/1.56 ( ord_le1802272080chanID
% 2.85/1.56 = ( ^ [B4: set_Secrecy_chanID,A4: set_Secrecy_chanID] :
% 2.85/1.56 ( A4
% 2.85/1.56 = ( sup_su370684444chanID @ A4 @ B4 ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_320_sup_Ocobounded1,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID] : ( ord_le1802272080chanID @ A @ ( sup_su370684444chanID @ A @ B2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_321_sup_Ocobounded2,axiom,
% 2.85/1.56 ! [B2: set_Secrecy_chanID,A: set_Secrecy_chanID] : ( ord_le1802272080chanID @ B2 @ ( sup_su370684444chanID @ A @ B2 ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_322_sup_Oabsorb__iff1,axiom,
% 2.85/1.56 ( ord_le1802272080chanID
% 2.85/1.56 = ( ^ [B4: set_Secrecy_chanID,A4: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A4 @ B4 )
% 2.85/1.56 = A4 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_323_sup_Oabsorb__iff2,axiom,
% 2.85/1.56 ( ord_le1802272080chanID
% 2.85/1.56 = ( ^ [A4: set_Secrecy_chanID,B4: set_Secrecy_chanID] :
% 2.85/1.56 ( ( sup_su370684444chanID @ A4 @ B4 )
% 2.85/1.56 = B4 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_324_sup_OcoboundedI1,axiom,
% 2.85/1.56 ! [C: set_Secrecy_chanID,A: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ C @ A )
% 2.85/1.56 => ( ord_le1802272080chanID @ C @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_325_sup_OcoboundedI2,axiom,
% 2.85/1.56 ! [C: set_Secrecy_chanID,B2: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ C @ B2 )
% 2.85/1.56 => ( ord_le1802272080chanID @ C @ ( sup_su370684444chanID @ A @ B2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_326_correctInOutLoc__def,axiom,
% 2.85/1.56 ( correctInOutLoc
% 2.85/1.56 = ( ^ [X2: secrecy_specID] :
% 2.85/1.56 ( ( ( inf_in1474033538chanID @ ( ins @ X2 ) @ ( out @ X2 ) )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 & ( ( inf_in1474033538chanID @ ( ins @ X2 ) @ ( loc @ X2 ) )
% 2.85/1.56 = bot_bo443197316chanID )
% 2.85/1.56 & ( ( inf_in1474033538chanID @ ( loc @ X2 ) @ ( out @ X2 ) )
% 2.85/1.56 = bot_bo443197316chanID ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_327_subset__Compl__singleton,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_specID,B2: secrecy_specID] :
% 2.85/1.56 ( ( ord_le996703545specID @ A2 @ ( uminus238526242specID @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) ) )
% 2.85/1.56 = ( ~ ( member740727610specID @ B2 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_328_subset__Compl__singleton,axiom,
% 2.85/1.56 ! [A2: set_Secrecy_chanID,B2: secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A2 @ ( uminus1044094777chanID @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) ) )
% 2.85/1.56 = ( ~ ( member1967978193chanID @ B2 @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_329_IntI,axiom,
% 2.85/1.56 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ C @ A2 )
% 2.85/1.56 => ( ( member740727610specID @ C @ B )
% 2.85/1.56 => ( member740727610specID @ C @ ( inf_in668465003specID @ A2 @ B ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_330_IntI,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ C @ A2 )
% 2.85/1.56 => ( ( member1967978193chanID @ C @ B )
% 2.85/1.56 => ( member1967978193chanID @ C @ ( inf_in1474033538chanID @ A2 @ B ) ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_331_Int__iff,axiom,
% 2.85/1.56 ! [C: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ C @ ( inf_in668465003specID @ A2 @ B ) )
% 2.85/1.56 = ( ( member740727610specID @ C @ A2 )
% 2.85/1.56 & ( member740727610specID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_332_Int__iff,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ C @ ( inf_in1474033538chanID @ A2 @ B ) )
% 2.85/1.56 = ( ( member1967978193chanID @ C @ A2 )
% 2.85/1.56 & ( member1967978193chanID @ C @ B ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_333_ComplI,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ~ ( member1967978193chanID @ C @ A2 )
% 2.85/1.56 => ( member1967978193chanID @ C @ ( uminus1044094777chanID @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_334_ComplI,axiom,
% 2.85/1.56 ! [C: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ~ ( member740727610specID @ C @ A2 )
% 2.85/1.56 => ( member740727610specID @ C @ ( uminus238526242specID @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_335_Compl__iff,axiom,
% 2.85/1.56 ! [C: secrecy_chanID,A2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( member1967978193chanID @ C @ ( uminus1044094777chanID @ A2 ) )
% 2.85/1.56 = ( ~ ( member1967978193chanID @ C @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_336_Compl__iff,axiom,
% 2.85/1.56 ! [C: secrecy_specID,A2: set_Secrecy_specID] :
% 2.85/1.56 ( ( member740727610specID @ C @ ( uminus238526242specID @ A2 ) )
% 2.85/1.56 = ( ~ ( member740727610specID @ C @ A2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_337_le__inf__iff,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID,Y3: set_Secrecy_chanID,Z2: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ X3 @ ( inf_in1474033538chanID @ Y3 @ Z2 ) )
% 2.85/1.56 = ( ( ord_le1802272080chanID @ X3 @ Y3 )
% 2.85/1.56 & ( ord_le1802272080chanID @ X3 @ Z2 ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_338_inf_Obounded__iff,axiom,
% 2.85/1.56 ! [A: set_Secrecy_chanID,B2: set_Secrecy_chanID,C: set_Secrecy_chanID] :
% 2.85/1.56 ( ( ord_le1802272080chanID @ A @ ( inf_in1474033538chanID @ B2 @ C ) )
% 2.85/1.56 = ( ( ord_le1802272080chanID @ A @ B2 )
% 2.85/1.56 & ( ord_le1802272080chanID @ A @ C ) ) ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_339_inf__bot__left,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID] :
% 2.85/1.56 ( ( inf_in668465003specID @ bot_bo1785112429specID @ X3 )
% 2.85/1.56 = bot_bo1785112429specID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_340_inf__bot__left,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( inf_in1474033538chanID @ bot_bo443197316chanID @ X3 )
% 2.85/1.56 = bot_bo443197316chanID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_341_inf__bot__right,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_specID] :
% 2.85/1.56 ( ( inf_in668465003specID @ X3 @ bot_bo1785112429specID )
% 2.85/1.56 = bot_bo1785112429specID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_342_inf__bot__right,axiom,
% 2.85/1.56 ! [X3: set_Secrecy_chanID] :
% 2.85/1.56 ( ( inf_in1474033538chanID @ X3 @ bot_bo443197316chanID )
% 2.85/1.56 = bot_bo443197316chanID ) ).
% 2.85/1.56
% 2.85/1.56 thf(fact_343_Int__insert__left__if0,axiom,
% 2.85/1.56 ! [A: secrecy_specID,C3: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.56 ( ~ ( member740727610specID @ A @ C3 )
% 2.85/1.56 => ( ( inf_in668465003specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 2.85/1.57 = ( inf_in668465003specID @ B @ C3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_344_Int__insert__left__if0,axiom,
% 2.85/1.57 ! [A: secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.57 ( ~ ( member1967978193chanID @ A @ C3 )
% 2.85/1.57 => ( ( inf_in1474033538chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 2.85/1.57 = ( inf_in1474033538chanID @ B @ C3 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_345_Int__insert__left__if1,axiom,
% 2.85/1.57 ! [A: secrecy_specID,C3: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.57 ( ( member740727610specID @ A @ C3 )
% 2.85/1.57 => ( ( inf_in668465003specID @ ( insert1671894227specID @ A @ B ) @ C3 )
% 2.85/1.57 = ( insert1671894227specID @ A @ ( inf_in668465003specID @ B @ C3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_346_Int__insert__left__if1,axiom,
% 2.85/1.57 ! [A: secrecy_chanID,C3: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.57 ( ( member1967978193chanID @ A @ C3 )
% 2.85/1.57 => ( ( inf_in1474033538chanID @ ( insert751661162chanID @ A @ B ) @ C3 )
% 2.85/1.57 = ( insert751661162chanID @ A @ ( inf_in1474033538chanID @ B @ C3 ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_347_insert__inter__insert,axiom,
% 2.85/1.57 ! [A: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.57 ( ( inf_in668465003specID @ ( insert1671894227specID @ A @ A2 ) @ ( insert1671894227specID @ A @ B ) )
% 2.85/1.57 = ( insert1671894227specID @ A @ ( inf_in668465003specID @ A2 @ B ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_348_insert__inter__insert,axiom,
% 2.85/1.57 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.57 ( ( inf_in1474033538chanID @ ( insert751661162chanID @ A @ A2 ) @ ( insert751661162chanID @ A @ B ) )
% 2.85/1.57 = ( insert751661162chanID @ A @ ( inf_in1474033538chanID @ A2 @ B ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_349_Int__insert__right__if0,axiom,
% 2.85/1.57 ! [A: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.57 ( ~ ( member740727610specID @ A @ A2 )
% 2.85/1.57 => ( ( inf_in668465003specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 2.85/1.57 = ( inf_in668465003specID @ A2 @ B ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_350_Int__insert__right__if0,axiom,
% 2.85/1.57 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.57 ( ~ ( member1967978193chanID @ A @ A2 )
% 2.85/1.57 => ( ( inf_in1474033538chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 2.85/1.57 = ( inf_in1474033538chanID @ A2 @ B ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_351_Int__insert__right__if1,axiom,
% 2.85/1.57 ! [A: secrecy_specID,A2: set_Secrecy_specID,B: set_Secrecy_specID] :
% 2.85/1.57 ( ( member740727610specID @ A @ A2 )
% 2.85/1.57 => ( ( inf_in668465003specID @ A2 @ ( insert1671894227specID @ A @ B ) )
% 2.85/1.57 = ( insert1671894227specID @ A @ ( inf_in668465003specID @ A2 @ B ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_352_Int__insert__right__if1,axiom,
% 2.85/1.57 ! [A: secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.57 ( ( member1967978193chanID @ A @ A2 )
% 2.85/1.57 => ( ( inf_in1474033538chanID @ A2 @ ( insert751661162chanID @ A @ B ) )
% 2.85/1.57 = ( insert751661162chanID @ A @ ( inf_in1474033538chanID @ A2 @ B ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_353_Int__subset__iff,axiom,
% 2.85/1.57 ! [C3: set_Secrecy_chanID,A2: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 2.85/1.57 ( ( ord_le1802272080chanID @ C3 @ ( inf_in1474033538chanID @ A2 @ B ) )
% 2.85/1.57 = ( ( ord_le1802272080chanID @ C3 @ A2 )
% 2.85/1.57 & ( ord_le1802272080chanID @ C3 @ B ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_354_Int__Un__eq_I4_J,axiom,
% 2.85/1.57 ! [T2: set_Secrecy_chanID,S: set_Secrecy_chanID] :
% 2.85/1.57 ( ( sup_su370684444chanID @ T2 @ ( inf_in1474033538chanID @ S @ T2 ) )
% 2.85/1.57 = T2 ) ).
% 2.85/1.57
% 2.85/1.57 thf(conj_0,conjecture,
% 2.85/1.57 member1967978193chanID @ ch @ ( loc @ pq ) ).
% 2.85/1.57 ------------------------
% 2.92/1.60 % (12958)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/183Mi)
% 2.92/1.61 % (12961)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/2Mi)
% 2.92/1.61 % (12959)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_12739 for (2999ds/4Mi)
% 2.92/1.61 % (12962)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_12739 for (2999ds/2Mi)
% 2.92/1.61 % (12963)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_12739 for (2999ds/275Mi)
% 2.92/1.61 % (12964)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/18Mi)
% 2.92/1.61 % (12960)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_12739 for (2999ds/27Mi)
% 2.92/1.61 % (12961)Instruction limit reached!
% 2.92/1.61 % (12961)------------------------------
% 2.92/1.61 % (12961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (12961)Termination reason: Unknown
% 2.92/1.61 % (12961)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (12961)Memory used [KB]: 1407
% 2.92/1.61 % (12961)Time elapsed: 0.004 s
% 2.92/1.61 % (12961)Instructions burned: 2 (million)
% 2.92/1.61 % (12961)------------------------------
% 2.92/1.61 % (12961)------------------------------
% 2.92/1.61 % (12962)Instruction limit reached!
% 2.92/1.61 % (12962)------------------------------
% 2.92/1.61 % (12962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (12962)Termination reason: Unknown
% 2.92/1.61 % (12962)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (12962)Memory used [KB]: 1407
% 2.92/1.61 % (12962)Time elapsed: 0.004 s
% 2.92/1.61 % (12962)Instructions burned: 3 (million)
% 2.92/1.61 % (12962)------------------------------
% 2.92/1.61 % (12962)------------------------------
% 2.92/1.61 % (12959)Instruction limit reached!
% 2.92/1.61 % (12959)------------------------------
% 2.92/1.61 % (12959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (12959)Termination reason: Unknown
% 2.92/1.61 % (12959)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (12959)Memory used [KB]: 1407
% 2.92/1.61 % (12959)Time elapsed: 0.005 s
% 2.92/1.61 % (12959)Instructions burned: 5 (million)
% 2.92/1.61 % (12959)------------------------------
% 2.92/1.61 % (12959)------------------------------
% 2.92/1.62 % (12964)Instruction limit reached!
% 2.92/1.62 % (12964)------------------------------
% 2.92/1.62 % (12964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (12964)Termination reason: Unknown
% 2.92/1.62 % (12964)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (12964)Memory used [KB]: 1663
% 2.92/1.62 % (12964)Time elapsed: 0.013 s
% 2.92/1.62 % (12964)Instructions burned: 18 (million)
% 2.92/1.62 % (12964)------------------------------
% 2.92/1.62 % (12964)------------------------------
% 2.92/1.62 % (12960)Instruction limit reached!
% 2.92/1.62 % (12960)------------------------------
% 2.92/1.62 % (12960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (12960)Termination reason: Unknown
% 2.92/1.62 % (12960)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (12960)Memory used [KB]: 1918
% 2.92/1.62 % (12960)Time elapsed: 0.018 s
% 2.92/1.62 % (12960)Instructions burned: 28 (million)
% 2.92/1.62 % (12960)------------------------------
% 2.92/1.62 % (12960)------------------------------
% 2.92/1.62 % (12965)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/3Mi)
% 2.92/1.63 % (12966)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_12739 for (2999ds/37Mi)
% 2.92/1.63 % (12965)Instruction limit reached!
% 2.92/1.63 % (12965)------------------------------
% 2.92/1.63 % (12965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (12965)Termination reason: Unknown
% 2.92/1.63 % (12965)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (12965)Memory used [KB]: 1407
% 2.92/1.63 % (12965)Time elapsed: 0.004 s
% 2.92/1.63 % (12965)Instructions burned: 4 (million)
% 2.92/1.63 % (12965)------------------------------
% 2.92/1.63 % (12965)------------------------------
% 2.92/1.63 % (12967)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_12739 for (2999ds/15Mi)
% 2.92/1.63 % (12963)Refutation not found, incomplete strategy
% 2.92/1.63 % (12963)------------------------------
% 2.92/1.63 % (12963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (12963)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.63
% 2.92/1.63
% 2.92/1.63 % (12963)Memory used [KB]: 6396
% 2.92/1.63 % (12963)Time elapsed: 0.030 s
% 2.92/1.63 % (12963)Instructions burned: 49 (million)
% 2.92/1.63 % (12963)------------------------------
% 2.92/1.63 % (12963)------------------------------
% 2.92/1.63 % (12968)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_12739 for (2999ds/3Mi)
% 2.92/1.64 % (12967)Instruction limit reached!
% 2.92/1.64 % (12967)------------------------------
% 2.92/1.64 % (12967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (12967)Termination reason: Unknown
% 2.92/1.64 % (12967)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (12967)Memory used [KB]: 1663
% 2.92/1.64 % (12967)Time elapsed: 0.011 s
% 2.92/1.64 % (12967)Instructions burned: 16 (million)
% 2.92/1.64 % (12967)------------------------------
% 2.92/1.64 % (12967)------------------------------
% 2.92/1.64 % (12968)Instruction limit reached!
% 2.92/1.64 % (12968)------------------------------
% 2.92/1.64 % (12968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (12968)Termination reason: Unknown
% 2.92/1.64 % (12968)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (12968)Memory used [KB]: 1407
% 2.92/1.64 % (12968)Time elapsed: 0.004 s
% 2.92/1.64 % (12968)Instructions burned: 3 (million)
% 2.92/1.64 % (12968)------------------------------
% 2.92/1.64 % (12968)------------------------------
% 2.92/1.64 % (12970)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/7Mi)
% 2.92/1.64 % (12969)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_12739 for (2999ds/1041Mi)
% 2.92/1.64 % (12970)Instruction limit reached!
% 2.92/1.64 % (12970)------------------------------
% 2.92/1.64 % (12970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (12970)Termination reason: Unknown
% 2.92/1.64 % (12970)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (12970)Memory used [KB]: 1535
% 2.92/1.64 % (12970)Time elapsed: 0.005 s
% 2.92/1.64 % (12970)Instructions burned: 10 (million)
% 2.92/1.64 % (12970)------------------------------
% 2.92/1.64 % (12970)------------------------------
% 2.92/1.64 % (12966)Instruction limit reached!
% 2.92/1.64 % (12966)------------------------------
% 2.92/1.64 % (12966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (12966)Termination reason: Unknown
% 2.92/1.64 % (12966)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (12966)Memory used [KB]: 2174
% 2.92/1.64 % (12966)Time elapsed: 0.021 s
% 2.92/1.64 % (12966)Instructions burned: 38 (million)
% 2.92/1.64 % (12966)------------------------------
% 2.92/1.64 % (12966)------------------------------
% 2.92/1.65 % (12972)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_12739 for (2999ds/3Mi)
% 2.92/1.65 % (12972)Instruction limit reached!
% 2.92/1.65 % (12972)------------------------------
% 2.92/1.65 % (12972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (12972)Termination reason: Unknown
% 2.92/1.65 % (12972)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (12972)Memory used [KB]: 1407
% 2.92/1.65 % (12972)Time elapsed: 0.003 s
% 2.92/1.65 % (12972)Instructions burned: 5 (million)
% 2.92/1.65 % (12972)------------------------------
% 2.92/1.65 % (12972)------------------------------
% 2.92/1.65 % (12974)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/7Mi)
% 2.92/1.65 % (12958)Instruction limit reached!
% 2.92/1.65 % (12958)------------------------------
% 2.92/1.65 % (12958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (12958)Termination reason: Unknown
% 2.92/1.65 % (12958)Termination phase: Saturation
% 2.92/1.65
% 2.92/1.65 % (12958)Memory used [KB]: 7291
% 2.92/1.65 % (12958)Time elapsed: 0.054 s
% 2.92/1.65 % (12958)Instructions burned: 186 (million)
% 2.92/1.65 % (12958)------------------------------
% 2.92/1.65 % (12958)------------------------------
% 2.92/1.65 % (12973)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_12739 for (2999ds/3Mi)
% 2.92/1.65 % (12971)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/16Mi)
% 2.92/1.65 % (12974)Instruction limit reached!
% 2.92/1.65 % (12974)------------------------------
% 2.92/1.65 % (12974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (12974)Termination reason: Unknown
% 2.92/1.65 % (12974)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (12974)Memory used [KB]: 1535
% 2.92/1.65 % (12974)Time elapsed: 0.004 s
% 2.92/1.65 % (12974)Instructions burned: 9 (million)
% 2.92/1.65 % (12974)------------------------------
% 2.92/1.65 % (12974)------------------------------
% 2.92/1.65 % (12973)Instruction limit reached!
% 2.92/1.65 % (12973)------------------------------
% 2.92/1.65 % (12973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (12973)Termination reason: Unknown
% 2.92/1.65 % (12973)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (12973)Memory used [KB]: 1407
% 2.92/1.65 % (12973)Time elapsed: 0.003 s
% 2.92/1.65 % (12973)Instructions burned: 4 (million)
% 2.92/1.65 % (12973)------------------------------
% 2.92/1.65 % (12973)------------------------------
% 2.92/1.66 % (12976)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/4Mi)
% 2.92/1.66 % (12976)Instruction limit reached!
% 2.92/1.66 % (12976)------------------------------
% 2.92/1.66 % (12976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (12976)Termination reason: Unknown
% 2.92/1.66 % (12976)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (12976)Memory used [KB]: 1535
% 2.92/1.66 % (12976)Time elapsed: 0.004 s
% 2.92/1.66 % (12976)Instructions burned: 6 (million)
% 2.92/1.66 % (12976)------------------------------
% 2.92/1.66 % (12976)------------------------------
% 2.92/1.66 % (12977)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/18Mi)
% 2.92/1.66 % (12975)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/3Mi)
% 2.92/1.66 % (12971)Instruction limit reached!
% 2.92/1.66 % (12971)------------------------------
% 2.92/1.66 % (12971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (12971)Termination reason: Unknown
% 2.92/1.66 % (12971)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (12971)Memory used [KB]: 1663
% 2.92/1.66 % (12971)Time elapsed: 0.012 s
% 2.92/1.66 % (12971)Instructions burned: 17 (million)
% 2.92/1.66 % (12971)------------------------------
% 2.92/1.66 % (12971)------------------------------
% 2.92/1.66 % (12978)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/710Mi)
% 2.92/1.66 % (12975)Instruction limit reached!
% 2.92/1.66 % (12975)------------------------------
% 2.92/1.66 % (12975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (12975)Termination reason: Unknown
% 2.92/1.66 % (12975)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (12975)Memory used [KB]: 1407
% 2.92/1.66 % (12975)Time elapsed: 0.004 s
% 2.92/1.66 % (12975)Instructions burned: 4 (million)
% 2.92/1.66 % (12975)------------------------------
% 2.92/1.66 % (12975)------------------------------
% 2.92/1.67 % (12979)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/6Mi)
% 2.92/1.67 % (12977)Instruction limit reached!
% 2.92/1.67 % (12977)------------------------------
% 2.92/1.67 % (12977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (12977)Termination reason: Unknown
% 2.92/1.67 % (12977)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (12977)Memory used [KB]: 1791
% 2.92/1.67 % (12977)Time elapsed: 0.007 s
% 2.92/1.67 % (12977)Instructions burned: 19 (million)
% 2.92/1.67 % (12977)------------------------------
% 2.92/1.67 % (12977)------------------------------
% 2.92/1.67 % (12979)Instruction limit reached!
% 2.92/1.67 % (12979)------------------------------
% 2.92/1.67 % (12979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (12979)Termination reason: Unknown
% 2.92/1.67 % (12979)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (12979)Memory used [KB]: 1407
% 2.92/1.67 % (12979)Time elapsed: 0.004 s
% 2.92/1.67 % (12979)Instructions burned: 6 (million)
% 2.92/1.67 % (12979)------------------------------
% 2.92/1.67 % (12979)------------------------------
% 2.92/1.67 % (12980)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_12739 for (2999ds/902Mi)
% 2.92/1.68 % (12982)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/5Mi)
% 2.92/1.68 % (12983)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_12739 for (2999ds/6Mi)
% 2.92/1.68 % (12982)Instruction limit reached!
% 2.92/1.68 % (12982)------------------------------
% 2.92/1.68 % (12982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (12982)Termination reason: Unknown
% 2.92/1.68 % (12982)Termination phase: shuffling
% 2.92/1.68
% 2.92/1.68 % (12982)Memory used [KB]: 1407
% 2.92/1.68 % (12982)Time elapsed: 0.003 s
% 2.92/1.68 % (12982)Instructions burned: 6 (million)
% 2.92/1.68 % (12982)------------------------------
% 2.92/1.68 % (12982)------------------------------
% 2.92/1.68 % (12978)Refutation not found, incomplete strategy
% 2.92/1.68 % (12978)------------------------------
% 2.92/1.68 % (12978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (12978)Termination reason: Refutation not found, incomplete strategy
% 2.92/1.68
% 2.92/1.68
% 2.92/1.68 % (12978)Memory used [KB]: 6396
% 2.92/1.68 % (12978)Time elapsed: 0.016 s
% 2.92/1.68 % (12978)Instructions burned: 49 (million)
% 2.92/1.68 % (12978)------------------------------
% 2.92/1.68 % (12978)------------------------------
% 2.92/1.68 % (12983)Instruction limit reached!
% 2.92/1.68 % (12983)------------------------------
% 2.92/1.68 % (12983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.68 % (12983)Termination reason: Unknown
% 2.92/1.68 % (12983)Termination phase: shuffling
% 2.92/1.68
% 2.92/1.68 % (12983)Memory used [KB]: 1535
% 2.92/1.68 % (12983)Time elapsed: 0.003 s
% 2.92/1.68 % (12983)Instructions burned: 7 (million)
% 2.92/1.68 % (12983)------------------------------
% 2.92/1.68 % (12983)------------------------------
% 2.92/1.68 % (12984)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_12739 for (2999ds/377Mi)
% 2.92/1.68 % (12981)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_12739 for (2999ds/21Mi)
% 2.92/1.69 % (12985)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_12739 for (2998ds/779Mi)
% 2.92/1.69 % (12986)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_12739 for (2998ds/19Mi)
% 2.92/1.69 % (12987)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_12739 for (2998ds/879Mi)
% 2.92/1.69 % (12981)Instruction limit reached!
% 2.92/1.69 % (12981)------------------------------
% 2.92/1.69 % (12981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.69 % (12981)Termination reason: Unknown
% 2.92/1.69 % (12981)Termination phase: shuffling
% 2.92/1.69
% 2.92/1.69 % (12981)Memory used [KB]: 1791
% 2.92/1.69 % (12981)Time elapsed: 0.015 s
% 2.92/1.69 % (12981)Instructions burned: 22 (million)
% 2.92/1.69 % (12981)------------------------------
% 2.92/1.69 % (12981)------------------------------
% 2.92/1.69 % (12986)Instruction limit reached!
% 2.92/1.69 % (12986)------------------------------
% 2.92/1.69 % (12986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.69 % (12986)Termination reason: Unknown
% 2.92/1.69 % (12986)Termination phase: shuffling
% 2.92/1.69
% 2.92/1.69 % (12986)Memory used [KB]: 1791
% 2.92/1.69 % (12986)Time elapsed: 0.007 s
% 2.92/1.69 % (12986)Instructions burned: 22 (million)
% 2.92/1.69 % (12986)------------------------------
% 2.92/1.69 % (12986)------------------------------
% 2.92/1.70 % (12989)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_12739 for (2998ds/3Mi)
% 2.92/1.70 % (12989)Instruction limit reached!
% 2.92/1.70 % (12989)------------------------------
% 2.92/1.70 % (12989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.70 % (12989)Termination reason: Unknown
% 2.92/1.70 % (12989)Termination phase: shuffling
% 2.92/1.70
% 2.92/1.70 % (12989)Memory used [KB]: 1407
% 2.92/1.70 % (12989)Time elapsed: 0.002 s
% 2.92/1.70 % (12989)Instructions burned: 3 (million)
% 2.92/1.70 % (12989)------------------------------
% 2.92/1.70 % (12989)------------------------------
% 2.92/1.71 % (12988)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_12739 for (2998ds/17Mi)
% 2.92/1.71 % (12990)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_12739 for (2998ds/30Mi)
% 2.92/1.72 % (12988)Instruction limit reached!
% 2.92/1.72 % (12988)------------------------------
% 2.92/1.72 % (12988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.72 % (12988)Termination reason: Unknown
% 2.92/1.72 % (12988)Termination phase: shuffling
% 2.92/1.72
% 2.92/1.72 % (12988)Memory used [KB]: 1663
% 2.92/1.72 % (12988)Time elapsed: 0.011 s
% 2.92/1.72 % (12988)Instructions burned: 18 (million)
% 2.92/1.72 % (12988)------------------------------
% 2.92/1.72 % (12988)------------------------------
% 2.92/1.72 % (12990)Instruction limit reached!
% 2.92/1.72 % (12990)------------------------------
% 2.92/1.72 % (12990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.72 % (12990)Termination reason: Unknown
% 2.92/1.72 % (12990)Termination phase: Property scanning
% 2.92/1.72
% 2.92/1.72 % (12990)Memory used [KB]: 1918
% 2.92/1.72 % (12990)Time elapsed: 0.011 s
% 2.92/1.72 % (12990)Instructions burned: 32 (million)
% 2.92/1.72 % (12990)------------------------------
% 2.92/1.72 % (12990)------------------------------
% 2.92/1.73 % (12987)First to succeed.
% 2.92/1.73 % (12987)Refutation found. Thanks to Tanya!
% 2.92/1.73 % SZS status Theorem for DTF2THF_12739
% 2.92/1.73 % SZS output start Proof for DTF2THF_12739
% 2.92/1.73 thf(type_def_5, type, set_Secrecy_chanID: $tType).
% 2.92/1.73 thf(type_def_7, type, set_Secrecy_specID: $tType).
% 2.92/1.73 thf(type_def_8, type, secrecy_chanID: $tType).
% 2.92/1.73 thf(type_def_9, type, secrecy_specID: $tType).
% 2.92/1.73 thf(type_def_10, type, secrecy_Expression: $tType).
% 2.92/1.73 thf(type_def_11, type, nat: $tType).
% 2.92/1.73 thf(func_def_0, type, set_Secrecy_specID: $tType).
% 2.92/1.73 thf(func_def_1, type, set_Secrecy_chanID: $tType).
% 2.92/1.73 thf(func_def_2, type, secrecy_Expression: $tType).
% 2.92/1.73 thf(func_def_3, type, secrecy_specID: $tType).
% 2.92/1.73 thf(func_def_4, type, secrecy_chanID: $tType).
% 2.92/1.73 thf(func_def_5, type, nat: $tType).
% 2.92/1.73 thf(func_def_6, type, uminus1044094777chanID: set_Secrecy_chanID > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_7, type, uminus238526242specID: set_Secrecy_specID > set_Secrecy_specID).
% 2.92/1.73 thf(func_def_8, type, inf_in1474033538chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_9, type, inf_in668465003specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 2.92/1.73 thf(func_def_10, type, sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_11, type, sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 2.92/1.73 thf(func_def_12, type, bot_bo1012329985anID_o: secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_13, type, bot_bo1767780696ecID_o: secrecy_specID > $o).
% 2.92/1.73 thf(func_def_15, type, bot_bo443197316chanID: set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_16, type, bot_bo1785112429specID: set_Secrecy_specID).
% 2.92/1.73 thf(func_def_17, type, ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_18, type, ord_le996703545specID: set_Secrecy_specID > set_Secrecy_specID > $o).
% 2.92/1.73 thf(func_def_19, type, eout: secrecy_specID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_20, type, eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_21, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_22, type, ine: secrecy_specID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_23, type, ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_24, type, ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_25, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_26, type, out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_27, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 2.92/1.73 thf(func_def_28, type, collec625564175chanID: (secrecy_chanID > $o) > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_29, type, collec1545797240specID: (secrecy_specID > $o) > set_Secrecy_specID).
% 2.92/1.73 thf(func_def_30, type, insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_31, type, insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID).
% 2.92/1.73 thf(func_def_32, type, is_emp928984296chanID: set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_33, type, is_emp1849217361specID: set_Secrecy_specID > $o).
% 2.92/1.73 thf(func_def_34, type, is_sin581274182chanID: set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_35, type, is_sin1501507247specID: set_Secrecy_specID > $o).
% 2.92/1.73 thf(func_def_36, type, pairwi1741995279chanID: (secrecy_chanID > secrecy_chanID > $o) > set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_37, type, pairwi514744696specID: (secrecy_specID > secrecy_specID > $o) > set_Secrecy_specID > $o).
% 2.92/1.73 thf(func_def_38, type, the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_39, type, the_el827131246specID: set_Secrecy_specID > secrecy_specID).
% 2.92/1.73 thf(func_def_40, type, correctCompositionIn: secrecy_specID > $o).
% 2.92/1.73 thf(func_def_41, type, correc965049635ionLoc: secrecy_specID > $o).
% 2.92/1.73 thf(func_def_42, type, correc990227761ionOut: secrecy_specID > $o).
% 2.92/1.73 thf(func_def_43, type, correctInOutLoc: secrecy_specID > $o).
% 2.92/1.73 thf(func_def_44, type, inStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_45, type, ins: secrecy_specID > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_46, type, loc: secrecy_specID > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_47, type, locStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_48, type, out: secrecy_specID > set_Secrecy_chanID).
% 2.92/1.73 thf(func_def_49, type, outStream: secrecy_specID > set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_50, type, subcomponents: secrecy_specID > set_Secrecy_specID).
% 2.92/1.73 thf(func_def_51, type, member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o).
% 2.92/1.73 thf(func_def_52, type, member740727610specID: secrecy_specID > set_Secrecy_specID > $o).
% 2.92/1.73 thf(func_def_53, type, p: secrecy_specID).
% 2.92/1.73 thf(func_def_54, type, pq: secrecy_specID).
% 2.92/1.73 thf(func_def_55, type, q: secrecy_specID).
% 2.92/1.73 thf(func_def_56, type, ch: secrecy_chanID).
% 2.92/1.73 thf(func_def_57, type, m: secrecy_Expression).
% 2.92/1.73 thf(func_def_73, type, sK0: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 2.92/1.73 thf(func_def_74, type, sK1: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_75, type, sK2: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 2.92/1.73 thf(func_def_76, type, sK3: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 2.92/1.73 thf(func_def_77, type, sK4: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_78, type, sK5: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_79, type, sK6: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_80, type, sK7: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_81, type, sK8: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_82, type, sK9: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 2.92/1.73 thf(func_def_83, type, sK10: secrecy_specID > set_Secrecy_chanID > secrecy_chanID).
% 2.92/1.73 thf(func_def_84, type, sK11: set_Secrecy_chanID > secrecy_specID > secrecy_chanID).
% 2.92/1.73 thf(f1158,plain,(
% 2.92/1.73 $false),
% 2.92/1.73 inference(subsumption_resolution,[status(thm)],[f1157,f1100])).
% 2.92/1.73 thf(f1100,plain,(
% 2.92/1.73 ((exprChannel @ ch @ m) = $true)),
% 2.92/1.73 inference(cnf_transformation,[status(thm)],[f686])).
% 2.92/1.73 thf(f686,plain,(
% 2.92/1.73 ((exprChannel @ ch @ m) = $true)),
% 2.92/1.73 inference(fool_elimination,[status(thm)],[f685])).
% 2.92/1.73 thf(f685,plain,(
% 2.92/1.73 (exprChannel @ ch @ m)),
% 2.92/1.73 inference(rectify,[status(thm)],[f2])).
% 2.92/1.73 thf(f2,axiom,(
% 2.92/1.73 (exprChannel @ ch @ m)),
% 2.92/1.73 file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_1_assms_I4_J)).
% 2.92/1.73 thf(f1157,plain,(
% 2.92/1.73 ((exprChannel @ ch @ m) != $true)),
% 2.92/1.73 inference(trivial_inequality_removal,[status(thm)],[f1156])).
% 2.92/1.73 thf(f1156,plain,(
% 2.92/1.73 ($true != $true) | ((exprChannel @ ch @ m) != $true)),
% 2.92/1.73 inference(superposition,[status(thm)],[f1120,f1154])).
% 2.92/1.73 thf(f1154,plain,(
% 2.92/1.73 ($true = (member1967978193chanID @ ch @ (ins @ pq)))),
% 2.92/1.73 inference(subsumption_resolution,[status(thm)],[f1153,f1109])).
% 2.92/1.73 thf(f1109,plain,(
% 2.92/1.73 ((member1967978193chanID @ ch @ (loc @ pq)) != $true)),
% 2.92/1.73 inference(cnf_transformation,[status(thm)],[f983])).
% 2.92/1.73 thf(f983,plain,(
% 2.92/1.73 ((member1967978193chanID @ ch @ (loc @ pq)) != $true)),
% 2.92/1.73 inference(flattening,[status(thm)],[f576])).
% 2.92/1.73 thf(f576,plain,(
% 2.92/1.73 ~((member1967978193chanID @ ch @ (loc @ pq)) = $true)),
% 2.92/1.73 inference(fool_elimination,[status(thm)],[f575])).
% 2.92/1.73 thf(f575,plain,(
% 2.92/1.73 ~(member1967978193chanID @ ch @ (loc @ pq))),
% 2.92/1.73 inference(rectify,[status(thm)],[f357])).
% 2.92/1.73 thf(f357,negated_conjecture,(
% 2.92/1.73 ~(member1967978193chanID @ ch @ (loc @ pq))),
% 2.92/1.73 inference(negated_conjecture,[status(cth)],[f356])).
% 2.92/1.73 thf(f356,conjecture,(
% 2.92/1.73 (member1967978193chanID @ ch @ (loc @ pq))),
% 2.92/1.73 file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',conj_0)).
% 2.92/1.73 thf(f1153,plain,(
% 2.92/1.73 ((member1967978193chanID @ ch @ (loc @ pq)) = $true) | ($true = (member1967978193chanID @ ch @ (ins @ pq)))),
% 2.92/1.73 inference(subsumption_resolution,[status(thm)],[f1152,f1084])).
% 2.92/1.73 thf(f1084,plain,(
% 2.92/1.73 ((correctCompositionIn @ pq) = $true)),
% 2.92/1.73 inference(cnf_transformation,[status(thm)],[f540])).
% 2.92/1.73 thf(f540,plain,(
% 2.92/1.73 ((correctCompositionIn @ pq) = $true)),
% 2.92/1.73 inference(fool_elimination,[status(thm)],[f539])).
% 2.92/1.73 thf(f539,plain,(
% 2.92/1.73 (correctCompositionIn @ pq)),
% 2.92/1.73 inference(rectify,[status(thm)],[f1])).
% 2.92/1.73 thf(f1,axiom,(
% 2.92/1.73 (correctCompositionIn @ pq)),
% 2.92/1.73 file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_0_assms_I2_J)).
% 2.92/1.73 thf(f1152,plain,(
% 2.92/1.73 ((correctCompositionIn @ pq) != $true) | ((member1967978193chanID @ ch @ (loc @ pq)) = $true) | ($true = (member1967978193chanID @ ch @ (ins @ pq)))),
% 2.92/1.73 inference(equality_resolution,[status(thm)],[f1150])).
% 2.92/1.73 thf(f1150,plain,(
% 2.92/1.73 ( ! [X0 : secrecy_specID] : (((subcomponents @ pq) != (subcomponents @ X0)) | ($true = (member1967978193chanID @ ch @ (ins @ X0))) | ($true = (member1967978193chanID @ ch @ (loc @ X0))) | ($true != (correctCompositionIn @ X0))) )),
% 2.92/1.73 inference(trivial_inequality_removal,[status(thm)],[f1149])).
% 2.92/1.73 thf(f1149,plain,(
% 2.92/1.73 ( ! [X0 : secrecy_specID] : (($true = (member1967978193chanID @ ch @ (ins @ X0))) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true = (member1967978193chanID @ ch @ (loc @ X0))) | ($true != (correctCompositionIn @ X0)) | ($true != $true)) )),
% 2.92/1.73 inference(superposition,[status(thm)],[f1148,f1121])).
% 2.92/1.73 thf(f1121,plain,(
% 2.92/1.73 ((member1967978193chanID @ ch @ (ins @ p)) = $true)),
% 2.92/1.73 inference(cnf_transformation,[status(thm)],[f800])).
% 2.92/1.73 thf(f800,plain,(
% 2.92/1.73 ((member1967978193chanID @ ch @ (ins @ p)) = $true)),
% 2.92/1.73 inference(fool_elimination,[status(thm)],[f799])).
% 2.92/1.73 thf(f799,plain,(
% 2.92/1.73 (member1967978193chanID @ ch @ (ins @ p))),
% 2.92/1.73 inference(rectify,[status(thm)],[f3])).
% 2.92/1.73 thf(f3,axiom,(
% 2.92/1.73 (member1967978193chanID @ ch @ (ins @ p))),
% 2.92/1.73 file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_2_assms_I3_J)).
% 2.92/1.73 thf(f1148,plain,(
% 2.92/1.73 ( ! [X0 : secrecy_specID,X1 : secrecy_chanID] : (($true != (member1967978193chanID @ X1 @ (ins @ p))) | ($true = (member1967978193chanID @ X1 @ (loc @ X0))) | ((member1967978193chanID @ X1 @ (ins @ X0)) = $true) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true != (correctCompositionIn @ X0))) )),
% 2.92/1.73 inference(superposition,[status(thm)],[f1082,f1110])).
% 2.92/1.73 thf(f1110,plain,(
% 2.92/1.73 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 2.92/1.73 inference(cnf_transformation,[status(thm)],[f5])).
% 2.92/1.73 thf(f5,axiom,(
% 2.92/1.73 ((subcomponents @ pq) = (insert1671894227specID @ p @ (insert1671894227specID @ q @ bot_bo1785112429specID)))),
% 2.92/1.73 file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_4_assms_I1_J)).
% 2.92/1.73 thf(f1082,plain,(
% 2.92/1.73 ( ! [X2 : secrecy_specID,X3 : secrecy_specID,X0 : secrecy_specID,X1 : secrecy_chanID] : (((subcomponents @ X0) != (insert1671894227specID @ X2 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) | ($true = (member1967978193chanID @ X1 @ (loc @ X0))) | ($true != (correctCompositionIn @ X0)) | ((member1967978193chanID @ X1 @ (ins @ X0)) = $true) | ((member1967978193chanID @ X1 @ (ins @ X2)) != $true)) )),
% 2.92/1.73 inference(cnf_transformation,[status(thm)],[f1052])).
% 2.92/1.73 thf(f1052,plain,(
% 2.92/1.73 ! [X0 : secrecy_specID,X1 : secrecy_chanID,X2 : secrecy_specID,X3 : secrecy_specID] : (($true = (member1967978193chanID @ X1 @ (loc @ X0))) | ((subcomponents @ X0) != (insert1671894227specID @ X2 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) | ((member1967978193chanID @ X1 @ (ins @ X2)) != $true) | ($true != (correctCompositionIn @ X0)) | ((member1967978193chanID @ X1 @ (ins @ X0)) = $true))),
% 2.92/1.73 inference(flattening,[status(thm)],[f1051])).
% 2.92/1.73 thf(f1051,plain,(
% 2.92/1.73 ! [X0 : secrecy_specID,X1 : secrecy_chanID,X2 : secrecy_specID,X3 : secrecy_specID] : ((((((member1967978193chanID @ X1 @ (ins @ X0)) = $true) | ((member1967978193chanID @ X1 @ (ins @ X2)) != $true)) | ($true = (member1967978193chanID @ X1 @ (loc @ X0)))) | ($true != (correctCompositionIn @ X0))) | ((subcomponents @ X0) != (insert1671894227specID @ X2 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))))),
% 2.92/1.73 inference(ennf_transformation,[status(thm)],[f989])).
% 2.92/1.73 thf(f989,plain,(
% 2.92/1.73 ! [X0 : secrecy_specID,X1 : secrecy_chanID,X2 : secrecy_specID,X3 : secrecy_specID] : (((subcomponents @ X0) = (insert1671894227specID @ X2 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) => (($true = (correctCompositionIn @ X0)) => (($true != (member1967978193chanID @ X1 @ (loc @ X0))) => (((member1967978193chanID @ X1 @ (ins @ X2)) = $true) => ((member1967978193chanID @ X1 @ (ins @ X0)) = $true)))))),
% 2.92/1.73 inference(flattening,[status(thm)],[f862])).
% 2.92/1.73 thf(f862,plain,(
% 2.92/1.73 ! [X0 : secrecy_specID,X1 : secrecy_chanID,X2 : secrecy_specID,X3 : secrecy_specID] : (((subcomponents @ X0) = (insert1671894227specID @ X2 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) => (($true = (correctCompositionIn @ X0)) => (~($true = (member1967978193chanID @ X1 @ (loc @ X0))) => (((member1967978193chanID @ X1 @ (ins @ X2)) = $true) => ((member1967978193chanID @ X1 @ (ins @ X0)) = $true)))))),
% 2.92/1.73 inference(fool_elimination,[status(thm)],[f861])).
% 2.92/1.73 thf(f861,plain,(
% 2.92/1.73 ! [X0 : secrecy_specID,X1 : secrecy_chanID,X2 : secrecy_specID,X3 : secrecy_specID] : (((subcomponents @ X0) = (insert1671894227specID @ X2 @ (insert1671894227specID @ X3 @ bot_bo1785112429specID))) => ((correctCompositionIn @ X0) => (~(member1967978193chanID @ X1 @ (loc @ X0)) => ((member1967978193chanID @ X1 @ (ins @ X2)) => (member1967978193chanID @ X1 @ (ins @ X0))))))),
% 2.92/1.73 inference(rectify,[status(thm)],[f7])).
% 2.92/1.73 thf(f7,axiom,(
% 2.92/1.73 ! [X4 : secrecy_specID,X7 : secrecy_chanID,X5 : secrecy_specID,X6 : secrecy_specID] : (((subcomponents @ X4) = (insert1671894227specID @ X5 @ (insert1671894227specID @ X6 @ bot_bo1785112429specID))) => ((correctCompositionIn @ X4) => (~(member1967978193chanID @ X7 @ (loc @ X4)) => ((member1967978193chanID @ X7 @ (ins @ X5)) => (member1967978193chanID @ X7 @ (ins @ X4))))))),
% 2.92/1.73 file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_6_correctCompositionIn__L1)).
% 2.92/1.73 thf(f1120,plain,(
% 2.92/1.73 ( ! [X0 : secrecy_chanID] : (((member1967978193chanID @ X0 @ (ins @ pq)) != $true) | ((exprChannel @ X0 @ m) != $true)) )),
% 2.92/1.73 inference(cnf_transformation,[status(thm)],[f1022])).
% 2.92/1.73 thf(f1022,plain,(
% 2.92/1.73 ! [X0 : secrecy_chanID] : (((member1967978193chanID @ X0 @ (ins @ pq)) != $true) | ((exprChannel @ X0 @ m) != $true))),
% 2.92/1.73 inference(ennf_transformation,[status(thm)],[f1005])).
% 2.92/1.73 thf(f1005,plain,(
% 2.92/1.73 ! [X0 : secrecy_chanID] : (((member1967978193chanID @ X0 @ (ins @ pq)) = $true) => ((exprChannel @ X0 @ m) != $true))),
% 2.92/1.73 inference(flattening,[status(thm)],[f426])).
% 2.92/1.73 thf(f426,plain,(
% 2.92/1.73 ! [X0 : secrecy_chanID] : (((member1967978193chanID @ X0 @ (ins @ pq)) = $true) => ~((exprChannel @ X0 @ m) = $true))),
% 2.92/1.73 inference(fool_elimination,[status(thm)],[f425])).
% 2.92/1.73 thf(f425,plain,(
% 2.92/1.73 ! [X0 : secrecy_chanID] : ((member1967978193chanID @ X0 @ (ins @ pq)) => ~(exprChannel @ X0 @ m))),
% 2.92/1.73 inference(rectify,[status(thm)],[f4])).
% 2.92/1.73 thf(f4,axiom,(
% 2.92/1.73 ! [X0 : secrecy_chanID] : ((member1967978193chanID @ X0 @ (ins @ pq)) => ~(exprChannel @ X0 @ m))),
% 2.92/1.73 file('/export/starexec/sandbox2/tmp/tmp.lKBVdO4VxJ/DTF2THF_12739.p',fact_3_assms_I5_J)).
% 2.92/1.73 % SZS output end Proof for DTF2THF_12739
% 2.92/1.73 % (12987)------------------------------
% 2.92/1.73 % (12987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (12987)Termination reason: Refutation
% 2.92/1.73
% 2.92/1.73 % (12987)Memory used [KB]: 6652
% 2.92/1.73 % (12987)Time elapsed: 0.039 s
% 2.92/1.73 % (12987)Instructions burned: 127 (million)
% 2.92/1.73 % (12987)------------------------------
% 2.92/1.73 % (12987)------------------------------
% 2.92/1.73 % (12957)Success in time 0.165 s
%------------------------------------------------------------------------------