%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP091^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:43 AM UTC 2026
% Result : Theorem 20.34s 6.02s
% Output : Refutation 22.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 294
% Syntax : Number of formulae : 590 ( 284 unt; 0 typ; 0 def)
% Number of atoms : 2202 ( 744 equ; 6 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 7033 ( 509 ~; 96 |; 230 &;5178 @)
% ( 0 <=>;1020 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 11 con; 0-3 aty)
% Number of variables : 1716 ( 82 ^;1556 !; 78 ?;1716 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_S529945141ession_type,type,
list_S529945141ession: $tType ).
thf(set_Secrecy_Secrets_type,type,
set_Secrecy_Secrets: $tType ).
thf(set_Secrecy_specID_type,type,
set_Secrecy_specID: $tType ).
thf(set_Secrecy_chanID_type,type,
set_Secrecy_chanID: $tType ).
thf(set_Secrecy_Keys_type,type,
set_Secrecy_Keys: $tType ).
thf(set_Secrecy_KS_type,type,
set_Secrecy_KS: $tType ).
thf(secrecy_Expression_type,type,
secrecy_Expression: $tType ).
thf(secrecy_Secrets_type,type,
secrecy_Secrets: $tType ).
thf(secrecy_specID_type,type,
secrecy_specID: $tType ).
thf(secrecy_chanID_type,type,
secrecy_chanID: $tType ).
thf(secrecy_Keys_type,type,
secrecy_Keys: $tType ).
thf(secrecy_KS_type,type,
secrecy_KS: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(localSecrets_decl,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(knowle233900195orrect_decl,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(knowle945212990e_know_decl,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(sup_su1301156759ecy_KS_decl,type,
sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(sup_su1029080330ecrets_decl,type,
sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
thf(sup_su370684444chanID_decl,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(sup_su1712599557specID_decl,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(mem_Se1967555118ession_decl,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(bot_bot_Secrecy_KS_o_decl,type,
bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
thf(bot_bo1909946299rets_o_decl,type,
bot_bo1909946299rets_o: secrecy_Secrets > $o ).
thf(bot_bo1943466239ecy_KS_decl,type,
bot_bo1943466239ecy_KS: set_Secrecy_KS ).
thf(bot_bo1124690338ecrets_decl,type,
bot_bo1124690338ecrets: set_Secrecy_Secrets ).
thf(bot_bo443197316chanID_decl,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(bot_bo1785112429specID_decl,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(ord_le1802272080chanID_decl,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(correctCompositionKS_decl,type,
correctCompositionKS: secrecy_specID > $o ).
thf(eout_decl,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(eoutM_decl,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(exprChannel_decl,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(ine_decl,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(ineM_decl,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(ine_exprChannelSet_decl,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(ine_ex1303305700Single_decl,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(notSpe1586871396tsExpr_decl,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(out_exprChannelSet_decl,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(out_ex985543062Single_decl,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(specKeys_decl,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(specKeysSecrets_decl,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(specSecrets_decl,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(secrecy_kE_decl,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(secrecy_sE_decl,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(secrec1016742679ession_decl,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(secrecy_kKS_decl,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(secrecy_sKS_decl,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(collect_Secrecy_KS_decl,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(collec836099393ecrets_decl,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(insert_Secrecy_KS_decl,type,
insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(insert751661162chanID_decl,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(insert1671894227specID_decl,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(is_emp1849217361specID_decl,type,
is_emp1849217361specID: set_Secrecy_specID > $o ).
thf(is_sin1442426433ecy_KS_decl,type,
is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
thf(is_sin1002224330ecrets_decl,type,
is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
thf(is_sin1501507247specID_decl,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(the_el827131246specID_decl,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(correctCompositionIn_decl,type,
correctCompositionIn: secrecy_specID > $o ).
thf(correc965049635ionLoc_decl,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(correc990227761ionOut_decl,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(inStream_decl,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(ins_decl,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(loc_decl,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(locStream_decl,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(out_decl,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(outStream_decl,type,
outStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(subcomponents_decl,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(member_Secrecy_KS_decl,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(member_Secrecy_Keys_decl,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(member2138796287ecrets_decl,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(member1967978193chanID_decl,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(member740727610specID_decl,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(p_decl,type,
p: secrecy_specID ).
thf(pq_decl,type,
pq: secrecy_specID ).
thf(q_decl,type,
q: secrecy_specID ).
thf(m_decl,type,
m: secrecy_KS ).
thf(secret_decl,type,
secret: secrecy_Secrets ).
thf(283,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
=> ( ! [E: secrecy_Keys] :
( ( D
= ( secrecy_kKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
& ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
=> ( ! [E: secrecy_Secrets] :
( ( D
= ( secrecy_sKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
& ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_LocalSecretsComposition__neg) ).
thf(1322,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
=> ( ! [E: secrecy_Keys] :
( ( D
= ( secrecy_kKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
& ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
=> ( ! [E: secrecy_Secrets] :
( ( D
= ( secrecy_sKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
& ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(149,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member1967978193chanID @ E @ ( out @ A ) )
| ( member1967978193chanID @ E @ ( out @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ( eout @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_TBtheorem5a__PQ) ).
thf(809,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member1967978193chanID @ E @ ( out @ A ) )
| ( member1967978193chanID @ E @ ( out @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ( eout @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(249,axiom,
! [A: set_Secrecy_KS] :
( ( ! [B: secrecy_KS] :
~ ( member_Secrecy_KS @ B @ A ) )
= ( A = bot_bo1943466239ecy_KS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_all__not__in__conv) ).
thf(1190,plain,
! [A: set_Secrecy_KS] :
( ( ! [B: secrecy_KS] :
~ ( member_Secrecy_KS @ B @ A ) )
= ( A = bot_bo1943466239ecy_KS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(18,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID,D: set_Secrecy_chanID] :
( ~ ( member1967978193chanID @ A @ B )
=> ( ~ ( member1967978193chanID @ C @ D )
=> ( ( ( insert751661162chanID @ A @ B )
= ( insert751661162chanID @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Secrecy_chanID] :
( ( B
= ( insert751661162chanID @ C @ E ) )
& ~ ( member1967978193chanID @ C @ E )
& ( D
= ( insert751661162chanID @ A @ E ) )
& ~ ( member1967978193chanID @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__eq__iff) ).
thf(347,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID,D: set_Secrecy_chanID] :
( ~ ( member1967978193chanID @ A @ B )
=> ( ~ ( member1967978193chanID @ C @ D )
=> ( ( ( insert751661162chanID @ A @ B )
= ( insert751661162chanID @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Secrecy_chanID] :
( ( B
= ( insert751661162chanID @ C @ E ) )
& ~ ( member1967978193chanID @ C @ E )
& ( D
= ( insert751661162chanID @ A @ E ) )
& ~ ( member1967978193chanID @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(262,axiom,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_KS2Expression_Osimps_I2_J) ).
thf(1237,plain,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(177,axiom,
( ineM
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( ins @ A ) )
& ( member1967978193chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_ineM__def) ).
thf(909,plain,
( ineM
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( ins @ A ) )
& ( member1967978193chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(172,axiom,
( eoutM
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( out @ A ) )
& ( member1967978193chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_eoutM__def) ).
thf(893,plain,
( eoutM
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( out @ A ) )
& ( member1967978193chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(281,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS,D: set_Secrecy_KS] :
( ~ ( member_Secrecy_KS @ A @ B )
=> ( ~ ( member_Secrecy_KS @ C @ D )
=> ( ( ( insert_Secrecy_KS @ A @ B )
= ( insert_Secrecy_KS @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Secrecy_KS] :
( ( B
= ( insert_Secrecy_KS @ C @ E ) )
& ~ ( member_Secrecy_KS @ C @ E )
& ( D
= ( insert_Secrecy_KS @ A @ E ) )
& ~ ( member_Secrecy_KS @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_insert__eq__iff) ).
thf(1315,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS,D: set_Secrecy_KS] :
( ~ ( member_Secrecy_KS @ A @ B )
=> ( ~ ( member_Secrecy_KS @ C @ D )
=> ( ( ( insert_Secrecy_KS @ A @ B )
= ( insert_Secrecy_KS @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Secrecy_KS] :
( ( B
= ( insert_Secrecy_KS @ C @ E ) )
& ~ ( member_Secrecy_KS @ C @ E )
& ( D
= ( insert_Secrecy_KS @ A @ E ) )
& ~ ( member_Secrecy_KS @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(141,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ D )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ F )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_TBtheorem4b__notPQ) ).
thf(777,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ D )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ F )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(226,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_correctCompositionKS__exprChannel__s__Pex) ).
thf(1110,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(57,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= bot_bo443197316chanID )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_sup__bot_Oeq__neutr__iff) ).
thf(481,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= bot_bo443197316chanID )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(252,axiom,
! [A: secrecy_KS > $o,B: secrecy_KS] :
( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
=> ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_KS_Oinduct) ).
thf(1200,plain,
! [A: secrecy_KS > $o,B: secrecy_KS] :
( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
=> ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(194,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eoutM @ D @ B @ C )
| ( eoutM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_TBtheorem2b) ).
thf(977,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eoutM @ D @ B @ C )
| ( eoutM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(255,axiom,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ A @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( member_Secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_LocalSecretsComposition1) ).
thf(1211,plain,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ A @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( member_Secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(217,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ~ ( member_Secrecy_KS @ A @ B )
=> ( ~ ( member_Secrecy_KS @ A @ C )
=> ( ( ( insert_Secrecy_KS @ A @ B )
= ( insert_Secrecy_KS @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_insert__ident) ).
thf(1068,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ~ ( member_Secrecy_KS @ A @ B )
=> ( ~ ( member_Secrecy_KS @ A @ C )
=> ( ( ( insert_Secrecy_KS @ A @ B )
= ( insert_Secrecy_KS @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(199,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_sup__bot_Oright__neutral) ).
thf(994,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(253,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
= ( ( ine @ A @ ( secrecy_kE @ B ) )
| ( member_Secrecy_KS @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_know_Osimps_I1_J) ).
thf(1205,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
= ( ( ine @ A @ ( secrecy_kE @ B ) )
| ( member_Secrecy_KS @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(114,axiom,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
( A
= ( insert1671894227specID @ ( the_el827131246specID @ A ) @ bot_bo1785112429specID ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_is__singleton__the__elem) ).
thf(677,plain,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
( A
= ( insert1671894227specID @ ( the_el827131246specID @ A ) @ bot_bo1785112429specID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(211,axiom,
( out_exprChannelSet
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
=> ( ( member1967978193chanID @ D @ ( out @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member1967978193chanID @ D @ B )
& ( member1967978193chanID @ D @ ( out @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_out__exprChannelSet__def) ).
thf(1041,plain,
( out_exprChannelSet
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
=> ( ( member1967978193chanID @ D @ ( out @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member1967978193chanID @ D @ B )
& ( member1967978193chanID @ D @ ( out @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(69,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_UnI1) ).
thf(523,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(88,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_Un__absorb) ).
thf(582,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(30,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C )
= ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_Un__assoc) ).
thf(385,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C )
= ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(184,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ D @ ( ins @ A ) )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
| ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_correctCompositionIn__L2) ).
thf(930,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ D @ ( ins @ A ) )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
| ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(286,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_insertI2) ).
thf(1342,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(135,axiom,
! [A: set_Secrecy_specID] :
( ( is_sin1501507247specID @ A )
=> ~ ! [B: secrecy_specID] :
( A
!= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_is__singletonE) ).
thf(747,plain,
! [A: set_Secrecy_specID] :
( ( is_sin1501507247specID @ A )
=> ~ ! [B: secrecy_specID] :
( A
!= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(179,axiom,
correc965049635ionLoc @ pq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_cCompLoc) ).
thf(913,plain,
correc965049635ionLoc @ pq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(35,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_sup__bot_Oright__neutral) ).
thf(404,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(174,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( out @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ D ) )
& ( member1967978193chanID @ F @ B ) )
=> ( eoutM @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_TBtheore54b__P) ).
thf(898,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( out @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ D ) )
& ( member1967978193chanID @ F @ B ) )
=> ( eoutM @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(4,axiom,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( insert751661162chanID @ B @ ( insert751661162chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_insert__commute) ).
thf(301,plain,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( insert751661162chanID @ B @ ( insert751661162chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( bot_bo1785112429specID
= ( sup_su1712599557specID @ A @ B ) )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_sup__bot_Oneutr__eq__iff) ).
thf(436,plain,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( bot_bo1785112429specID
= ( sup_su1712599557specID @ A @ B ) )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(10,axiom,
! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_singletonI) ).
thf(320,plain,
! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(82,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
=> ( ~ ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_UnE) ).
thf(565,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
=> ( ~ ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(84,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
= ( sup_su370684444chanID @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_Un__left__absorb) ).
thf(570,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
= ( sup_su370684444chanID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(126,axiom,
( sup_su1301156759ecy_KS
= ( ^ [A: set_Secrecy_KS,B: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_Un__commute) ).
thf(719,plain,
( sup_su1301156759ecy_KS
= ( ^ [A: set_Secrecy_KS,B: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(17,axiom,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( ( A = B )
| ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_insert__iff) ).
thf(344,plain,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( ( A = B )
| ( member1967978193chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(231,axiom,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
=> ( ( knowle945212990e_know @ C @ A )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_know__composition2) ).
thf(1132,plain,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
=> ( ( knowle945212990e_know @ C @ A )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(215,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ D )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ~ ( ine @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_TBtheorem4a__notPQ) ).
thf(1055,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ D )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ~ ( ine @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(128,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ B )
!= bot_bo1785112429specID ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_insert__not__empty) ).
thf(724,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ B )
!= bot_bo1785112429specID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(90,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= bot_bo1785112429specID )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_sup__bot_Oeq__neutr__iff) ).
thf(587,plain,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= bot_bo1785112429specID )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(101,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_Un__empty__left) ).
thf(619,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(181,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( exprChannel @ C @ B )
=> ~ ( member1967978193chanID @ C @ ( ins @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_ine__ins__neg1) ).
thf(917,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( exprChannel @ C @ B )
=> ~ ( member1967978193chanID @ C @ ( ins @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(123,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
= ( ( ( A = bot_bo1785112429specID )
& ( B
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
| ( ( A
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
& ( B = bot_bo1785112429specID ) )
| ( ( A
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
& ( B
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_Un__singleton__iff) ).
thf(702,plain,
! [A: set_Secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
= ( ( ( A = bot_bo1785112429specID )
& ( B
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
| ( ( A
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
& ( B = bot_bo1785112429specID ) )
| ( ( A
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
& ( B
= ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(136,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets > $o] :
( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_mem__Collect__eq) ).
thf(751,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets > $o] :
( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(185,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ~ ( eout @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( out_ex985543062Single @ A @ E @ B )
& ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ~ ( eout @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_TBtheorem5a__notP1) ).
thf(934,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ~ ( eout @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( out_ex985543062Single @ A @ E @ B )
& ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ~ ( eout @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(21,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
= ( ( ( A = bot_bo443197316chanID )
& ( B
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) )
| ( ( A
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
& ( B = bot_bo443197316chanID ) )
| ( ( A
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
& ( B
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_Un__singleton__iff) ).
thf(357,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
= ( ( ( A = bot_bo443197316chanID )
& ( B
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) )
| ( ( A
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
& ( B = bot_bo443197316chanID ) )
| ( ( A
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
& ( B
= ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(175,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Un__empty__left) ).
thf(902,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(235,axiom,
! [A: secrecy_KS] :
~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_empty__iff) ).
thf(1147,plain,
! [A: secrecy_KS] :
~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(264,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
=> ( ~ ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_UnE) ).
thf(1247,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
=> ( ~ ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(282,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
( ( ? [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ A )
& ( C @ D ) )
| ? [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_bex__Un) ).
thf(1319,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
( ( ? [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ A )
& ( C @ D ) )
| ? [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(288,axiom,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ D @ ( secrecy_kE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ C @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_LocalSecretsComposition__ine1__k) ).
thf(1347,plain,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ D @ ( secrecy_kE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ C @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(39,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_insertI1) ).
thf(416,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(48,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_sup__bot_Oleft__neutral) ).
thf(448,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(260,axiom,
! [A: secrecy_KS] :
~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_emptyE) ).
thf(1232,plain,
! [A: secrecy_KS] :
~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(47,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ? [C: set_Secrecy_specID] :
( ( B
= ( insert1671894227specID @ A @ C ) )
& ~ ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_mk__disjoint__insert) ).
thf(443,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ? [C: set_Secrecy_specID] :
( ( B
= ( insert1671894227specID @ A @ C ) )
& ~ ( member740727610specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(148,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( ( sup_su1301156759ecy_KS @ A @ B )
= bot_bo1943466239ecy_KS )
= ( ( A = bot_bo1943466239ecy_KS )
& ( B = bot_bo1943466239ecy_KS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_sup__bot_Oeq__neutr__iff) ).
thf(806,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( ( sup_su1301156759ecy_KS @ A @ B )
= bot_bo1943466239ecy_KS )
= ( ( A = bot_bo1943466239ecy_KS )
& ( B = bot_bo1943466239ecy_KS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(214,axiom,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( ~ ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ C ) )
=> ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_UnCI) ).
thf(1051,plain,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( ~ ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ C ) )
=> ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(176,axiom,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ( ~ ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_know__composition__neg__ine__k) ).
thf(905,plain,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ( ~ ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(278,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_correctCompositionKS__exprChannel__k__Qex) ).
thf(1302,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(138,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( ( loc @ D )
= bot_bo443197316chanID )
=> ( eout @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_TBtheorem5a__empty) ).
thf(756,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( ( loc @ D )
= bot_bo443197316chanID )
=> ( eout @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(232,axiom,
! [A: secrecy_KS,B: secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_singletonD) ).
thf(1136,plain,
! [A: secrecy_KS,B: secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(155,axiom,
( is_emp1849217361specID
= ( ^ [A: set_Secrecy_specID] : ( A = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Set_Ois__empty__def) ).
thf(834,plain,
( is_emp1849217361specID
= ( ^ [A: set_Secrecy_specID] : ( A = bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(243,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
= ( ( ine @ A @ ( secrecy_sE @ B ) )
| ( member_Secrecy_KS @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_know_Osimps_I2_J) ).
thf(1169,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
= ( ( ine @ A @ ( secrecy_sE @ B ) )
| ( member_Secrecy_KS @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(256,axiom,
! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
= ( ( A = B )
| ( member_Secrecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_insert__iff) ).
thf(1215,plain,
! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
= ( ( A = B )
| ( member_Secrecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(131,axiom,
( eout
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member1967978193chanID @ C @ ( out @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_eout__def) ).
thf(734,plain,
( eout
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member1967978193chanID @ C @ ( out @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(218,axiom,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ C @ ( secrecy_sE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ D @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_LocalSecretsComposition__ine2__s) ).
thf(1072,plain,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ C @ ( secrecy_sE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ D @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(140,axiom,
! [A: set_Secrecy_Secrets] :
( ( collec836099393ecrets
@ ^ [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Collect__mem__eq) ).
thf(774,plain,
! [A: set_Secrecy_Secrets] :
( ( collec836099393ecrets
@ ^ [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(289,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_correctCompositionKS__exprChannel__k__Pex) ).
thf(1351,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(287,axiom,
~ ( ine @ q @ ( secrecy_sE @ secret ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_sg6a) ).
thf(1345,plain,
~ ( ine @ q @ ( secrecy_sE @ secret ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(43,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member_Secrecy_Keys @ C @ ( specKeys @ A ) )
=> ? [D: secrecy_specID] :
( ( member740727610specID @ D @ ( subcomponents @ A ) )
& ( member_Secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_correctCompositionKS__subcomp1) ).
thf(428,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member_Secrecy_Keys @ C @ ( specKeys @ A ) )
=> ? [D: secrecy_specID] :
( ( member740727610specID @ D @ ( subcomponents @ A ) )
& ( member_Secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
= ( sup_su370684444chanID @ B @ C ) )
= ( ( ( B = bot_bo443197316chanID )
& ( C
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) )
| ( ( B
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
& ( C = bot_bo443197316chanID ) )
| ( ( B
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
& ( C
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_singleton__Un__iff) ).
thf(312,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
= ( sup_su370684444chanID @ B @ C ) )
= ( ( ( B = bot_bo443197316chanID )
& ( C
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) )
| ( ( B
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
& ( C = bot_bo443197316chanID ) )
| ( ( B
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
& ( C
= ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(95,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_ex985543062Single @ A @ B @ C )
=> ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_out__exprChannelSingle__Set) ).
thf(602,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_ex985543062Single @ A @ B @ C )
=> ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(195,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
( ( member1967978193chanID @ A @ B )
=> ( ( member1967978193chanID @ A @ ( ins @ C ) )
=> ( ( exprChannel @ A @ D )
=> ( ineM @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ineM__L1) ).
thf(981,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
( ( member1967978193chanID @ A @ B )
=> ( ( member1967978193chanID @ A @ ( ins @ C ) )
=> ( ( exprChannel @ A @ D )
=> ( ineM @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(6,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C )
= ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Un__insert__left) ).
thf(307,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C )
= ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(182,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ( out_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ E )
=> ( member1967978193chanID @ F @ ( loc @ C ) ) )
=> ~ ( eout @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_TBtheorem5a__notP2) ).
thf(920,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ( out_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ E )
=> ( member1967978193chanID @ F @ ( loc @ C ) ) )
=> ~ ( eout @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(28,axiom,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_emptyE) ).
thf(380,plain,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(71,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( eoutM @ A @ B @ C )
=> ( eout @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_eoutM__eout) ).
thf(529,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( eoutM @ A @ B @ C )
=> ( eout @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(143,axiom,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ~ ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_not__know__k__not__eout) ).
thf(793,plain,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ~ ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(24,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ~ ! [C: set_Secrecy_chanID] :
( ( B
= ( insert751661162chanID @ A @ C ) )
=> ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Set_Oset__insert) ).
thf(366,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ~ ! [C: set_Secrecy_chanID] :
( ( B
= ( insert751661162chanID @ A @ C ) )
=> ( member1967978193chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(73,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_sup__bot_Oleft__neutral) ).
thf(534,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(66,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID,D: set_Secrecy_specID] :
( ~ ( member740727610specID @ A @ B )
=> ( ~ ( member740727610specID @ C @ D )
=> ( ( ( insert1671894227specID @ A @ B )
= ( insert1671894227specID @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Secrecy_specID] :
( ( B
= ( insert1671894227specID @ C @ E ) )
& ~ ( member740727610specID @ C @ E )
& ( D
= ( insert1671894227specID @ A @ E ) )
& ~ ( member740727610specID @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_insert__eq__iff) ).
thf(512,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID,D: set_Secrecy_specID] :
( ~ ( member740727610specID @ A @ B )
=> ( ~ ( member740727610specID @ C @ D )
=> ( ( ( insert1671894227specID @ A @ B )
= ( insert1671894227specID @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Secrecy_specID] :
( ( B
= ( insert1671894227specID @ C @ E ) )
& ~ ( member740727610specID @ C @ E )
& ( D
= ( insert1671894227specID @ A @ E ) )
& ~ ( member740727610specID @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(187,axiom,
( inStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( ins @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_inStream__def) ).
thf(942,plain,
( inStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( ins @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(46,axiom,
! [A: set_Secrecy_chanID] :
( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A )
=> ( A = bot_bo443197316chanID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_equals0I) ).
thf(439,plain,
! [A: set_Secrecy_chanID] :
( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A )
=> ( A = bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(213,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ~ ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_TBtheorem3a) ).
thf(1047,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ~ ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(145,axiom,
! [A: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_is__singletonI) ).
thf(798,plain,
! [A: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(240,axiom,
( m
= ( secrecy_sKS @ secret ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_a2) ).
thf(1163,plain,
( m
= ( secrecy_sKS @ secret ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(221,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_correctCompositionKS__exprChannel__s__Qex) ).
thf(1091,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(267,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
= ( ( member_Secrecy_KS @ A @ B )
| ( member_Secrecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_Un__iff) ).
thf(1255,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
= ( ( member_Secrecy_KS @ A @ B )
| ( member_Secrecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(245,axiom,
! [A: set_Secrecy_KS] :
( ( ? [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
= ( A != bot_bo1943466239ecy_KS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_ex__in__conv) ).
thf(1174,plain,
! [A: set_Secrecy_KS] :
( ( ? [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
= ( A != bot_bo1943466239ecy_KS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(150,axiom,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_UnI2) ).
thf(820,plain,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(142,axiom,
! [A: secrecy_chanID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
( ( exprChannel @ A @ ( secrecy_sE @ B ) )
=> ( ~ ( ine @ C @ ( secrecy_sE @ B ) )
=> ( ~ ( ine @ D @ ( secrecy_sE @ B ) )
=> ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
& ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_LocalSecretsComposition__exprChannel__s) ).
thf(788,plain,
! [A: secrecy_chanID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
( ( exprChannel @ A @ ( secrecy_sE @ B ) )
=> ( ~ ( ine @ C @ ( secrecy_sE @ B ) )
=> ( ~ ( ine @ D @ ( secrecy_sE @ B ) )
=> ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
& ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(36,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= bot_bo443197316chanID )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_Un__empty) ).
thf(407,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= bot_bo443197316chanID )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(105,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Expression_Oinject_I1_J) ).
thf(630,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(52,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( ( A = B )
| ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_insert__iff) ).
thf(467,plain,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( ( A = B )
| ( member740727610specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(58,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
= ( ( member1967978193chanID @ A @ B )
| ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Un__iff) ).
thf(484,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
= ( ( member1967978193chanID @ A @ B )
| ( member1967978193chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(291,axiom,
! [A: set_Secrecy_KS] :
( ( collect_Secrecy_KS
@ ^ [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Collect__mem__eq) ).
thf(1365,plain,
! [A: set_Secrecy_KS] :
( ( collect_Secrecy_KS
@ ^ [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(103,axiom,
( sup_su370684444chanID
= ( ^ [A: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( sup_su370684444chanID @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_Un__commute) ).
thf(625,plain,
( sup_su370684444chanID
= ( ^ [A: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( sup_su370684444chanID @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(168,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
= ( sup_su1301156759ecy_KS @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_Un__left__absorb) ).
thf(879,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
= ( sup_su1301156759ecy_KS @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(170,axiom,
( insert_Secrecy_KS
= ( ^ [A: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_insert__is__Un) ).
thf(889,plain,
( insert_Secrecy_KS
= ( ^ [A: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(116,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ D @ ( ins @ A ) )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
| ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_correctCompositionIn__prop1) ).
thf(682,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ D @ ( ins @ A ) )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
| ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(276,axiom,
! [A: set_Secrecy_KS] :
( ( A != bot_bo1943466239ecy_KS )
=> ( ! [B: secrecy_KS,C: secrecy_KS] :
( ( member_Secrecy_KS @ B @ A )
=> ( ( member_Secrecy_KS @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1442426433ecy_KS @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_is__singletonI_H) ).
thf(1291,plain,
! [A: set_Secrecy_KS] :
( ( A != bot_bo1943466239ecy_KS )
=> ( ! [B: secrecy_KS,C: secrecy_KS] :
( ( member_Secrecy_KS @ B @ A )
=> ( ( member_Secrecy_KS @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1442426433ecy_KS @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(193,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_Un__empty__right) ).
thf(974,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(78,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
= ( ( member740727610specID @ A @ B )
| ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Un__iff) ).
thf(551,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
= ( ( member740727610specID @ A @ B )
| ( member740727610specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(230,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_KS_Odistinct_I1_J) ).
thf(1128,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(68,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( ~ ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ C ) )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_UnCI) ).
thf(519,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( ~ ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ C ) )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(121,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( member1967978193chanID @ D @ ( out @ A ) )
=> ( ( member1967978193chanID @ D @ ( out @ B ) )
| ( member1967978193chanID @ D @ ( out @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_correctCompositionOut__prop1) ).
thf(697,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( member1967978193chanID @ D @ ( out @ A ) )
=> ( ( member1967978193chanID @ D @ ( out @ B ) )
| ( member1967978193chanID @ D @ ( out @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(234,axiom,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ C @ ( secrecy_kE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ D @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_LocalSecretsComposition__ine2__k) ).
thf(1143,plain,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ C @ ( secrecy_kE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ D @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(31,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( ~ ( member740727610specID @ A @ B )
=> ( A = C ) )
=> ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insertCI) ).
thf(388,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( ~ ( member740727610specID @ A @ B )
=> ( A = C ) )
=> ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(92,axiom,
! [A: set_Secrecy_specID] :
( ( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A ) )
= ( A = bot_bo1785112429specID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_all__not__in__conv) ).
thf(593,plain,
! [A: set_Secrecy_specID] :
( ( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A ) )
= ( A = bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(98,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
=> ( ~ ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_UnE) ).
thf(610,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
=> ( ~ ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(62,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_UnI2) ).
thf(499,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(294,axiom,
member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_sg5) ).
thf(1375,plain,
member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(228,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_UnI2) ).
thf(1121,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(79,axiom,
! [A: set_Secrecy_specID] :
( ( ? [B: secrecy_specID] : ( member740727610specID @ B @ A ) )
= ( A != bot_bo1785112429specID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_ex__in__conv) ).
thf(554,plain,
! [A: set_Secrecy_specID] :
( ( ? [B: secrecy_specID] : ( member740727610specID @ B @ A ) )
= ( A != bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(74,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( bot_bo443197316chanID
= ( sup_su370684444chanID @ A @ B ) )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_sup__bot_Oneutr__eq__iff) ).
thf(537,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( bot_bo443197316chanID
= ( sup_su370684444chanID @ A @ B ) )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(70,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_UnI1) ).
thf(526,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(115,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member2138796287ecrets @ C @ ( specSecrets @ B ) )
=> ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_correctCompositionKS__subcomp4) ).
thf(679,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member2138796287ecrets @ C @ ( specSecrets @ B ) )
=> ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(117,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( bot_bo1943466239ecy_KS
= ( sup_su1301156759ecy_KS @ A @ B ) )
= ( ( A = bot_bo1943466239ecy_KS )
& ( B = bot_bo1943466239ecy_KS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_sup__bot_Oneutr__eq__iff) ).
thf(686,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( bot_bo1943466239ecy_KS
= ( sup_su1301156759ecy_KS @ A @ B ) )
= ( ( A = bot_bo1943466239ecy_KS )
& ( B = bot_bo1943466239ecy_KS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(55,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( ineM @ A @ B @ C )
=> ( ine @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ineM__ine) ).
thf(476,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( ineM @ A @ B @ C )
=> ( ine @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(205,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
=> ( ( exprChannel @ D @ E )
=> ( ! [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
=> ~ ( exprChannel @ F @ E ) )
=> ( member1967978193chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_correctCompositionInLoc__exprChannel) ).
thf(1016,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
=> ( ( exprChannel @ D @ E )
=> ( ! [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ A ) )
=> ~ ( exprChannel @ F @ E ) )
=> ( member1967978193chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(91,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
= ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_Un__left__commute) ).
thf(590,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
= ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(102,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_insertI2) ).
thf(622,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(200,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_insert__commute) ).
thf(997,plain,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(122,axiom,
correctCompositionIn @ pq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_cCompI) ).
thf(701,plain,
correctCompositionIn @ pq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(270,axiom,
( notSpe1586871396tsExpr
= ( ^ [A: secrecy_specID,B: list_S529945141ession] :
( ! [C: secrecy_Keys] :
( ( mem_Se1967555118ession @ ( secrecy_kE @ C ) @ B )
=> ~ ( member_Secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
& ! [C: secrecy_Secrets] :
( ( mem_Se1967555118ession @ ( secrecy_sE @ C ) @ B )
=> ~ ( member_Secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_notSpecKeysSecretsExpr__def) ).
thf(1266,plain,
( notSpe1586871396tsExpr
= ( ^ [A: secrecy_specID,B: list_S529945141ession] :
( ! [C: secrecy_Keys] :
( ( mem_Se1967555118ession @ ( secrecy_kE @ C ) @ B )
=> ~ ( member_Secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
& ! [C: secrecy_Secrets] :
( ( mem_Se1967555118ession @ ( secrecy_sE @ C ) @ B )
=> ~ ( member_Secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(127,axiom,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_singletonD) ).
thf(721,plain,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(25,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( ( insert751661162chanID @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__absorb) ).
thf(371,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( ( insert751661162chanID @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(236,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
| ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_correctCompositionKS__PQ) ).
thf(1150,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
| ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(265,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_not__know__s__not__ine) ).
thf(1249,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(196,axiom,
! [A: set_Secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
= ( insert_Secrecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Un__insert__right) ).
thf(984,plain,
! [A: set_Secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
= ( insert_Secrecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(178,axiom,
( bot_bo1909946299rets_o
= ( ^ [A: secrecy_Secrets] : ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_bot__empty__eq) ).
thf(911,plain,
( bot_bo1909946299rets_o
= ( ^ [A: secrecy_Secrets] : ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(284,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_correctCompositionKS__exprChannel__s__Q) ).
thf(1333,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(186,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine @ C @ B )
| ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_TBtheorem1a) ).
thf(938,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine @ C @ B )
| ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(111,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ( G
= ( sup_su370684444chanID @ D @ F ) )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ D )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ F )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_TBtheorem5b__notPQ) ).
thf(657,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ( G
= ( sup_su370684444chanID @ D @ F ) )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ D )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member1967978193chanID @ H @ F )
=> ( member1967978193chanID @ H @ ( loc @ A ) ) )
=> ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(33,axiom,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_empty__iff) ).
thf(398,plain,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(113,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( ( sup_su1301156759ecy_KS @ A @ B )
= bot_bo1943466239ecy_KS )
= ( ( A = bot_bo1943466239ecy_KS )
& ( B = bot_bo1943466239ecy_KS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Un__empty) ).
thf(674,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
( ( ( sup_su1301156759ecy_KS @ A @ B )
= bot_bo1943466239ecy_KS )
= ( ( A = bot_bo1943466239ecy_KS )
& ( B = bot_bo1943466239ecy_KS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(106,axiom,
! [A: secrecy_specID,B: secrecy_specID] :
( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
= ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_singleton__inject) ).
thf(633,plain,
! [A: secrecy_specID,B: secrecy_specID] :
( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
= ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(22,axiom,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
=> ( ( A != B )
=> ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_insertE) ).
thf(360,plain,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
=> ( ( A != B )
=> ( member1967978193chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(207,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Expression_Odistinct_I1_J) ).
thf(1026,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(242,axiom,
! [A: secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_singletonI) ).
thf(1167,plain,
! [A: secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(3,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_insertI2) ).
thf(298,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(266,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_correctCompositionKS__negP) ).
thf(1251,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(42,axiom,
! [A: secrecy_Secrets] :
~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_emptyE) ).
thf(425,plain,
! [A: secrecy_Secrets] :
~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(224,axiom,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ D @ ( secrecy_sE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ C @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_LocalSecretsComposition__ine1__s) ).
thf(1103,plain,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ D @ ( secrecy_sE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ C @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(160,axiom,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_KS2Expression_Osimps_I1_J) ).
thf(856,plain,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(134,axiom,
( ine
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member1967978193chanID @ C @ ( ins @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ine__def) ).
thf(745,plain,
( ine
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member1967978193chanID @ C @ ( ins @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(85,axiom,
! [A: set_Secrecy_chanID] :
( ( ? [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
= ( A != bot_bo443197316chanID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_ex__in__conv) ).
thf(573,plain,
! [A: set_Secrecy_chanID] :
( ( ? [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
= ( A != bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(118,axiom,
! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_singletonI) ).
thf(689,plain,
! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1,conjecture,
~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(296,plain,
~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(237,axiom,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_chanID] :
( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( exprChannel @ C @ ( secrecy_kE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( specKeysSecrets @ B ) )
=> ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_LocalSecretsComposition__neg__loc__k) ).
thf(1154,plain,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_chanID] :
( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( exprChannel @ C @ ( secrecy_kE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( specKeysSecrets @ B ) )
=> ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(130,axiom,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
? [B: secrecy_specID] :
( A
= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_is__singleton__def) ).
thf(732,plain,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
? [B: secrecy_specID] :
( A
= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(158,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member1967978193chanID @ E @ ( ins @ A ) )
| ( member1967978193chanID @ E @ ( ins @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_TBtheorem4a__PQ) ).
thf(843,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member1967978193chanID @ E @ ( ins @ A ) )
| ( member1967978193chanID @ E @ ( ins @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(133,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
=> ( ( eout @ A @ ( secrecy_kE @ B ) )
=> ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_eoutKnowCorrect__L1k) ).
thf(743,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
=> ( ( eout @ A @ ( secrecy_kE @ B ) )
=> ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(87,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= bot_bo1785112429specID )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Un__empty) ).
thf(579,plain,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= bot_bo1785112429specID )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(229,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_LocalSecretsComposition__neg1__k) ).
thf(1124,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(38,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_Un__empty__right) ).
thf(413,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(203,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_not__know__k__not__ine) ).
thf(1007,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(120,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
( ( ( sup_su1301156759ecy_KS @ A @ B )
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
= ( ( ( A = bot_bo1943466239ecy_KS )
& ( B
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) )
| ( ( A
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
& ( B = bot_bo1943466239ecy_KS ) )
| ( ( A
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
& ( B
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Un__singleton__iff) ).
thf(694,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
( ( ( sup_su1301156759ecy_KS @ A @ B )
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
= ( ( ( A = bot_bo1943466239ecy_KS )
& ( B
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) )
| ( ( A
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
& ( B = bot_bo1943466239ecy_KS ) )
| ( ( A
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
& ( B
= ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(166,axiom,
knowle945212990e_know @ pq @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_knowPQ) ).
thf(875,plain,
knowle945212990e_know @ pq @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(152,axiom,
( outStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( out @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_outStream__def) ).
thf(826,plain,
( outStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( out @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(233,axiom,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
=> ( ( knowle945212990e_know @ B @ A )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_know__composition1) ).
thf(1139,plain,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
=> ( ( knowle945212990e_know @ B @ A )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(280,axiom,
! [A: secrecy_KS,B: secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_singleton__iff) ).
thf(1312,plain,
! [A: secrecy_KS,B: secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(225,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
= ( ( eout @ A @ ( secrecy_sE @ B ) )
= ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_eout__know__s) ).
thf(1107,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
= ( ( eout @ A @ ( secrecy_sE @ B ) )
= ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(14,axiom,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
= ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_singleton__inject) ).
thf(335,plain,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
= ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(147,axiom,
( insert1671894227specID
= ( ^ [A: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_insert__is__Un) ).
thf(804,plain,
( insert1671894227specID
= ( ^ [A: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(268,axiom,
! [A: secrecy_KS,B: secrecy_KS > $o] :
( ( member_Secrecy_KS @ A @ ( collect_Secrecy_KS @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_mem__Collect__eq) ).
thf(1258,plain,
! [A: secrecy_KS,B: secrecy_KS > $o] :
( ( member_Secrecy_KS @ A @ ( collect_Secrecy_KS @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(189,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ( loc @ D )
= bot_bo443197316chanID )
=> ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_TBtheorem4a__empty) ).
thf(947,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ( loc @ D )
= bot_bo443197316chanID )
=> ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(75,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_sup__bot__left) ).
thf(540,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(112,axiom,
( ine_ex1303305700Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member1967978193chanID @ B @ ( ins @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID,E: nat] :
( ( ( member1967978193chanID @ D @ ( ins @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_ine__exprChannelSingle__def) ).
thf(672,plain,
( ine_ex1303305700Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member1967978193chanID @ B @ ( ins @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID] :
( ( ( member1967978193chanID @ D @ ( ins @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(96,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_sup__bot__left) ).
thf(604,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(154,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS )
= ( sup_su1301156759ecy_KS @ B @ C ) )
= ( ( ( B = bot_bo1943466239ecy_KS )
& ( C
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) )
| ( ( B
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
& ( C = bot_bo1943466239ecy_KS ) )
| ( ( B
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
& ( C
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_singleton__Un__iff) ).
thf(831,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS )
= ( sup_su1301156759ecy_KS @ B @ C ) )
= ( ( ( B = bot_bo1943466239ecy_KS )
& ( C
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) )
| ( ( B
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
& ( C = bot_bo1943466239ecy_KS ) )
| ( ( B
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
& ( C
= ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(274,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_correctCompositionKS__exprChannel__k__P) ).
thf(1282,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(227,axiom,
! [A: set_Secrecy_KS] :
( ! [B: secrecy_KS] :
~ ( member_Secrecy_KS @ B @ A )
=> ( A = bot_bo1943466239ecy_KS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_equals0I) ).
thf(1117,plain,
! [A: set_Secrecy_KS] :
( ! [B: secrecy_KS] :
~ ( member_Secrecy_KS @ B @ A )
=> ( A = bot_bo1943466239ecy_KS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(132,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
( ~ ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( out_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ D ) ) )
=> ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_TBtheorem5b__notP2) ).
thf(736,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
( ~ ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( out_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ D ) ) )
=> ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(27,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C )
= ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Un__insert__left) ).
thf(377,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C )
= ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(162,axiom,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
=> ( ~ ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_UnE) ).
thf(863,plain,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
=> ( ~ ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(49,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_UnI2) ).
thf(451,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(83,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ~ ( ineM @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_not__ine__ineM) ).
thf(567,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ~ ( ineM @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(65,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
=> ( ( A != B )
=> ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_insertE) ).
thf(509,plain,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
=> ( ( A != B )
=> ( member740727610specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(212,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ineM @ D @ B @ C )
| ( ineM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_TBtheorem1b) ).
thf(1043,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ineM @ D @ B @ C )
| ( ineM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(94,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
( ( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ A )
=> ( C @ D ) )
& ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_ball__Un) ).
thf(599,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
( ( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ A )
=> ( C @ D ) )
& ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(295,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ C ) )
=> ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_LocalSecretsComposition__neg__k) ).
thf(1376,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ C ) )
=> ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(220,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ! [E: secrecy_Keys] :
( ( D
= ( secrecy_kKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
& ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
=> ( ! [E: secrecy_Secrets] :
( ( D
= ( secrecy_sKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
& ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_LocalSecretsComposition__neg1) ).
thf(1080,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ! [E: secrecy_Keys] :
( ( D
= ( secrecy_kKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
& ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
=> ( ! [E: secrecy_Secrets] :
( ( D
= ( secrecy_sKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
& ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(173,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
= ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_Un__left__commute) ).
thf(895,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
= ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(246,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_correctCompositionKS__negQ) ).
thf(1177,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(191,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ D ) )
& ( member1967978193chanID @ F @ B ) )
=> ( ineM @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_TBtheorem4b__P) ).
thf(959,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ ( ins @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ D ) )
& ( member1967978193chanID @ F @ B ) )
=> ( ineM @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(107,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ~ ( member1967978193chanID @ D @ ( loc @ A ) )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
=> ( member1967978193chanID @ D @ ( ins @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_correctCompositionIn__L1) ).
thf(636,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ~ ( member1967978193chanID @ D @ ( loc @ A ) )
=> ( ( member1967978193chanID @ D @ ( ins @ B ) )
=> ( member1967978193chanID @ D @ ( ins @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(32,axiom,
! [A: set_Secrecy_specID] :
( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A )
=> ( A = bot_bo1785112429specID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_equals0I) ).
thf(394,plain,
! [A: set_Secrecy_specID] :
( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A )
=> ( A = bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(201,axiom,
! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle945212990e_know @ A @ B )
=> ( ~ ( knowle945212990e_know @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ D )
=> ( ( correctCompositionIn @ D )
=> ~ ( knowle945212990e_know @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_know__composition__neg1) ).
thf(1000,plain,
! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle945212990e_know @ A @ B )
=> ( ~ ( knowle945212990e_know @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ D )
=> ( ( correctCompositionIn @ D )
=> ~ ( knowle945212990e_know @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(64,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( ~ ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ C ) )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_UnCI) ).
thf(505,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( ~ ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ C ) )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(216,axiom,
( out_ex985543062Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member1967978193chanID @ B @ ( out @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID,E: nat] :
( ( ( member1967978193chanID @ D @ ( out @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_out__exprChannelSingle__def) ).
thf(1066,plain,
( out_ex985543062Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member1967978193chanID @ B @ ( out @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID] :
( ( ( member1967978193chanID @ D @ ( out @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(164,axiom,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_UnI1) ).
thf(868,plain,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ B )
=> ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(254,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_UnI1) ).
thf(1208,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(144,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_sup__bot__right) ).
thf(795,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(77,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_Un__empty__left) ).
thf(548,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(273,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ? [C: set_Secrecy_KS] :
( ( B
= ( insert_Secrecy_KS @ A @ C ) )
& ~ ( member_Secrecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mk__disjoint__insert) ).
thf(1277,plain,
! [A: secrecy_KS,B: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ? [C: set_Secrecy_KS] :
( ( B
= ( insert_Secrecy_KS @ A @ C ) )
& ~ ( member_Secrecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(285,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_insertI1) ).
thf(1340,plain,
! [A: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(20,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_insertI1) ).
thf(355,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(137,axiom,
( ine_exprChannelSet
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
=> ( ( member1967978193chanID @ D @ ( ins @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member1967978193chanID @ D @ B )
& ( member1967978193chanID @ D @ ( ins @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_ine__exprChannelSet__def) ).
thf(754,plain,
( ine_exprChannelSet
= ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
=> ( ( member1967978193chanID @ D @ ( ins @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member1967978193chanID @ D @ B )
& ( member1967978193chanID @ D @ ( ins @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(156,axiom,
! [A: secrecy_specID] :
( ( the_el827131246specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_the__elem__eq) ).
thf(836,plain,
! [A: secrecy_specID] :
( ( the_el827131246specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(54,axiom,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_emptyE) ).
thf(473,plain,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(219,axiom,
! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
=> ( ~ ( knowle945212990e_know @ C @ ( secrecy_sKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_know__composition__neg__ine__s) ).
thf(1076,plain,
! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
=> ( ~ ( knowle945212990e_know @ C @ ( secrecy_sKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(72,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B != bot_bo443197316chanID )
=> ( ine @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_ine__nonempty__exprChannelSet) ).
thf(531,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B != bot_bo443197316chanID )
=> ( ine @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(188,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
= ( ( eout @ A @ ( secrecy_kE @ B ) )
= ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_eout__know__k) ).
thf(944,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
= ( ( eout @ A @ ( secrecy_kE @ B ) )
= ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(183,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_sup__bot_Oleft__neutral) ).
thf(927,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(26,axiom,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_empty__iff) ).
thf(374,plain,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(110,axiom,
! [A: set_Secrecy_Secrets] :
( ( A != bot_bo1124690338ecrets )
=> ( ! [B: secrecy_Secrets,C: secrecy_Secrets] :
( ( member2138796287ecrets @ B @ A )
=> ( ( member2138796287ecrets @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1002224330ecrets @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_is__singletonI_H) ).
thf(648,plain,
! [A: set_Secrecy_Secrets] :
( ( A != bot_bo1124690338ecrets )
=> ( ! [B: secrecy_Secrets,C: secrecy_Secrets] :
( ( member2138796287ecrets @ B @ A )
=> ( ( member2138796287ecrets @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1002224330ecrets @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(59,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B = bot_bo443197316chanID )
=> ~ ( ine @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_ine__empty__exprChannelSet) ).
thf(487,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B = bot_bo443197316chanID )
=> ~ ( ine @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(100,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
=> ( ine_ex1303305700Single @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ine__exprChannelSet__Single) ).
thf(617,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
=> ( ine_ex1303305700Single @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(67,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_sup__bot_Oright__neutral) ).
thf(516,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(51,axiom,
! [A: set_Secrecy_specID] :
( ( A != bot_bo1785112429specID )
=> ( ! [B: secrecy_specID,C: secrecy_specID] :
( ( member740727610specID @ B @ A )
=> ( ( member740727610specID @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1501507247specID @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_is__singletonI_H) ).
thf(458,plain,
! [A: set_Secrecy_specID] :
( ( A != bot_bo1785112429specID )
=> ( ! [B: secrecy_specID,C: secrecy_specID] :
( ( member740727610specID @ B @ A )
=> ( ( member740727610specID @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1501507247specID @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(247,axiom,
! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
=> ( ( A != B )
=> ( member_Secrecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_insertE) ).
thf(1181,plain,
! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
=> ( ( A != B )
=> ( member_Secrecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(151,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_doubleton__eq__iff) ).
thf(823,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(80,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ~ ( eoutM @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_not__eout__eoutM) ).
thf(557,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ~ ( eoutM @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(108,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ~ ( ineM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ F @ C )
& ( member1967978193chanID @ F @ B )
& ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_TBtheorem4b__notP1) ).
thf(640,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ~ ( ineM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ F @ C )
& ( member1967978193chanID @ F @ B )
& ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(124,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ( ineM @ A @ B @ C )
| ( ineM @ D @ B @ C ) )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member1967978193chanID @ F @ ( ins @ A ) )
| ( member1967978193chanID @ F @ ( ins @ D ) ) )
& ( member1967978193chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ( ineM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_TBtheorem4b__PQ) ).
thf(705,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ( ineM @ A @ B @ C )
| ( ineM @ D @ B @ C ) )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member1967978193chanID @ F @ ( ins @ A ) )
| ( member1967978193chanID @ F @ ( ins @ D ) ) )
& ( member1967978193chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ( ineM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(259,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_correctCompositionKS__exprChannel__s__P) ).
thf(1225,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(190,axiom,
! [A: secrecy_chanID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
( ( exprChannel @ A @ ( secrecy_kE @ B ) )
=> ( ~ ( ine @ C @ ( secrecy_kE @ B ) )
=> ( ~ ( ine @ D @ ( secrecy_kE @ B ) )
=> ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
& ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_LocalSecretsComposition__exprChannel__k) ).
thf(954,plain,
! [A: secrecy_chanID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
( ( exprChannel @ A @ ( secrecy_kE @ B ) )
=> ( ~ ( ine @ C @ ( secrecy_kE @ B ) )
=> ( ~ ( ine @ D @ ( secrecy_kE @ B ) )
=> ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
& ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(292,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_correctCompositionKS__neg1) ).
thf(1368,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(222,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( ord_le1802272080chanID @ ( out @ A ) @ ( ins @ B ) )
=> ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ C ) )
=> ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_adv__not__know2) ).
thf(1098,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( ord_le1802272080chanID @ ( out @ A ) @ ( ins @ B ) )
=> ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ C ) )
=> ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(7,axiom,
( insert751661162chanID
= ( ^ [A: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_insert__is__Un) ).
thf(310,plain,
( insert751661162chanID
= ( ^ [A: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(277,axiom,
~ ( knowle945212990e_know @ q @ m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_not__knowQm) ).
thf(1300,plain,
~ ( knowle945212990e_know @ q @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(63,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( ( insert1671894227specID @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_insert__absorb) ).
thf(502,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( ( insert1671894227specID @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(261,axiom,
( bot_bot_Secrecy_KS_o
= ( ^ [A: secrecy_KS] : ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_bot__empty__eq) ).
thf(1235,plain,
( bot_bot_Secrecy_KS_o
= ( ^ [A: secrecy_KS] : ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(15,axiom,
! [A: secrecy_chanID,B: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
= ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_doubleton__eq__iff) ).
thf(338,plain,
! [A: secrecy_chanID,B: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
= ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(257,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
( ( ! [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ A )
=> ( C @ D ) )
& ! [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_ball__Un) ).
thf(1218,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
( ( ! [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ A )
=> ( C @ D ) )
& ! [D: secrecy_KS] :
( ( member_Secrecy_KS @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(210,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_Un__absorb) ).
thf(1038,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(89,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_ex1303305700Single @ A @ B @ C )
=> ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_ine__exprChannelSingle__Set) ).
thf(585,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_ex1303305700Single @ A @ B @ C )
=> ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(53,axiom,
! [A: set_Secrecy_chanID] :
( ( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A ) )
= ( A = bot_bo443197316chanID ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_all__not__in__conv) ).
thf(470,plain,
! [A: set_Secrecy_chanID] :
( ( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A ) )
= ( A = bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(86,axiom,
! [A: set_Secrecy_Secrets] :
( ( ? [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
= ( A != bot_bo1124690338ecrets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_ex__in__conv) ).
thf(576,plain,
! [A: set_Secrecy_Secrets] :
( ( ? [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
= ( A != bot_bo1124690338ecrets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(290,axiom,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
=> ( ( ( knowle945212990e_know @ B @ A )
| ( knowle945212990e_know @ C @ A ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_know__composition) ).
thf(1358,plain,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
=> ( ( ( knowle945212990e_know @ B @ A )
| ( knowle945212990e_know @ C @ A ) )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(206,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
= ( sup_su1712599557specID @ B @ C ) )
= ( ( ( B = bot_bo1785112429specID )
& ( C
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
| ( ( B
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
& ( C = bot_bo1785112429specID ) )
| ( ( B
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
& ( C
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_singleton__Un__iff) ).
thf(1023,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
= ( sup_su1712599557specID @ B @ C ) )
= ( ( ( B = bot_bo1785112429specID )
& ( C
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
| ( ( B
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
& ( C = bot_bo1785112429specID ) )
| ( ( B
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
& ( C
= ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(258,axiom,
! [A: secrecy_KS] :
( ! [B: secrecy_Keys] :
( A
!= ( secrecy_kKS @ B ) )
=> ~ ! [B: secrecy_Secrets] :
( A
!= ( secrecy_sKS @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_KS_Oexhaust) ).
thf(1221,plain,
! [A: secrecy_KS] :
( ! [B: secrecy_Keys] :
( A
!= ( secrecy_kKS @ B ) )
=> ~ ! [B: secrecy_Secrets] :
( A
!= ( secrecy_sKS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(293,axiom,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_chanID] :
( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( exprChannel @ C @ ( secrecy_sE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( specKeysSecrets @ B ) )
=> ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_LocalSecretsComposition__neg__loc__s) ).
thf(1372,plain,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_chanID] :
( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( exprChannel @ C @ ( secrecy_sE @ A ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( specKeysSecrets @ B ) )
=> ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(167,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ B ) @ C )
= ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Un__insert__left) ).
thf(876,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ B ) @ C )
= ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(161,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ~ ( ineM @ A @ B @ C )
=> ( ~ ( ineM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_TBtheorem3b) ).
thf(859,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ~ ( ineM @ A @ B @ C )
=> ( ~ ( ineM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(272,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ~ ! [C: set_Secrecy_KS] :
( ( B
= ( insert_Secrecy_KS @ A @ C ) )
=> ( member_Secrecy_KS @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Set_Oset__insert) ).
thf(1272,plain,
! [A: secrecy_KS,B: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ~ ! [C: set_Secrecy_KS] :
( ( B
= ( insert_Secrecy_KS @ A @ C ) )
=> ( member_Secrecy_KS @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(99,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ~ ! [C: set_Secrecy_specID] :
( ( B
= ( insert1671894227specID @ A @ C ) )
=> ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Set_Oset__insert) ).
thf(612,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ~ ! [C: set_Secrecy_specID] :
( ( B
= ( insert1671894227specID @ A @ C ) )
=> ( member740727610specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(263,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_correctCompositionKS__exprChannel__k__Q) ).
thf(1240,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member1967978193chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(198,axiom,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
= ( ( member2138796287ecrets @ A @ B )
| ( member2138796287ecrets @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_Un__iff) ).
thf(991,plain,
! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
= ( ( member2138796287ecrets @ A @ B )
| ( member2138796287ecrets @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(104,axiom,
! [A: set_Secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( insert1671894227specID @ B @ ( sup_su1712599557specID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Un__insert__right) ).
thf(627,plain,
! [A: set_Secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( insert1671894227specID @ B @ ( sup_su1712599557specID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(23,axiom,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_singleton__iff) ).
thf(363,plain,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(238,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( ~ ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ C ) )
=> ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_UnCI) ).
thf(1157,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( ~ ( member_Secrecy_KS @ A @ B )
=> ( member_Secrecy_KS @ A @ C ) )
=> ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(171,axiom,
( locStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( loc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_locStream__def) ).
thf(891,plain,
( locStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( loc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(275,axiom,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
=> ( ( eout @ B @ ( secrecy_sE @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
=> ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_eout__know__nonKS__s) ).
thf(1289,plain,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
=> ( ( eout @ B @ ( secrecy_sE @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
=> ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(192,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ( eoutM @ A @ B @ C )
| ( eoutM @ D @ B @ C ) )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member1967978193chanID @ F @ ( out @ A ) )
| ( member1967978193chanID @ F @ ( out @ D ) ) )
& ( member1967978193chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ( eoutM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_TBtheorem5b__PQ) ).
thf(963,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ( eoutM @ A @ B @ C )
| ( eoutM @ D @ B @ C ) )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member1967978193chanID @ F @ ( out @ A ) )
| ( member1967978193chanID @ F @ ( out @ D ) ) )
& ( member1967978193chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ( eoutM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(5,axiom,
! [A: set_Secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( insert751661162chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Un__insert__right) ).
thf(304,plain,
! [A: set_Secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( insert751661162chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(223,axiom,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_subPQ) ).
thf(1101,plain,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(19,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ~ ( member1967978193chanID @ A @ B )
=> ( ~ ( member1967978193chanID @ A @ C )
=> ( ( ( insert751661162chanID @ A @ B )
= ( insert751661162chanID @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_insert__ident) ).
thf(351,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ~ ( member1967978193chanID @ A @ B )
=> ( ~ ( member1967978193chanID @ A @ C )
=> ( ( ( insert751661162chanID @ A @ B )
= ( insert751661162chanID @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
( ( ? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ A )
& ( C @ D ) )
| ? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_bex__Un) ).
thf(401,plain,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
( ( ? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ A )
& ( C @ D ) )
| ? [D: secrecy_chanID] :
( ( member1967978193chanID @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(40,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ~ ( member740727610specID @ A @ B )
=> ( ~ ( member740727610specID @ A @ C )
=> ( ( ( insert1671894227specID @ A @ B )
= ( insert1671894227specID @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_insert__ident) ).
thf(418,plain,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ~ ( member740727610specID @ A @ B )
=> ( ~ ( member740727610specID @ A @ C )
=> ( ( ( insert1671894227specID @ A @ B )
= ( insert1671894227specID @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(208,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ ( insert1671894227specID @ A @ B ) )
= ( insert1671894227specID @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_insert__absorb2) ).
thf(1030,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ ( insert1671894227specID @ A @ B ) )
= ( insert1671894227specID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(180,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_KS_Oinject_I1_J) ).
thf(914,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(44,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_sup__bot__right) ).
thf(433,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(250,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ C ) )
=> ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_LocalSecretsComposition__neg__s) ).
thf(1193,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ C ) )
=> ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(56,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: set_Secrecy_chanID] :
( ( ineM @ A @ B @ C )
=> ( ineM @ A @ ( sup_su370684444chanID @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_ineM__Un1) ).
thf(478,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: set_Secrecy_chanID] :
( ( ineM @ A @ B @ C )
=> ( ineM @ A @ ( sup_su370684444chanID @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(139,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ D )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ~ ( eout @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_TBtheorem5a__notPQ) ).
thf(763,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ D )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ A ) ) )
=> ~ ( eout @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(29,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
=> ( out_ex985543062Single @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_out__exprChannelSet__Single) ).
thf(383,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
=> ( out_ex985543062Single @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(279,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( ( insert_Secrecy_KS @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_insert__absorb) ).
thf(1309,plain,
! [A: secrecy_KS,B: set_Secrecy_KS] :
( ( member_Secrecy_KS @ A @ B )
=> ( ( insert_Secrecy_KS @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(125,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Expression_Oinject_I2_J) ).
thf(716,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(239,axiom,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
=> ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_not__know__s__not__eout) ).
thf(1161,plain,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
=> ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(146,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ E @ B )
& ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ~ ( ine @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_TBtheorem4a__notP1) ).
thf(800,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ E @ B )
& ( member1967978193chanID @ E @ ( loc @ D ) ) )
=> ~ ( ine @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(9,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ? [C: set_Secrecy_chanID] :
( ( B
= ( insert751661162chanID @ A @ C ) )
& ~ ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_mk__disjoint__insert) ).
thf(315,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ? [C: set_Secrecy_chanID] :
( ( B
= ( insert751661162chanID @ A @ C ) )
& ~ ( member1967978193chanID @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(37,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_sup__bot__right) ).
thf(410,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(159,axiom,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ( eout @ B @ ( secrecy_kE @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
=> ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_eout__know__nonKS__k) ).
thf(854,plain,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ( eout @ B @ ( secrecy_kE @ A ) )
=> ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
=> ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(41,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member_Secrecy_Keys @ C @ ( specKeys @ B ) )
=> ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_correctCompositionKS__subcomp3) ).
thf(422,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member_Secrecy_Keys @ C @ ( specKeys @ B ) )
=> ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(163,axiom,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C )
= ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_Un__assoc) ).
thf(865,plain,
! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C )
= ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(12,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( ~ ( member1967978193chanID @ A @ B )
=> ( A = C ) )
=> ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_insertCI) ).
thf(326,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( ~ ( member1967978193chanID @ A @ B )
=> ( A = C ) )
=> ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_singletonD) ).
thf(341,plain,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(244,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
=> ( ( eout @ A @ ( secrecy_sE @ B ) )
=> ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_eoutKnowCorrect__L1s) ).
thf(1172,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
=> ( ( eout @ A @ ( secrecy_sE @ B ) )
=> ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(153,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_sup__bot__left) ).
thf(828,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(241,axiom,
~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_a22) ).
thf(1165,plain,
~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(209,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member2138796287ecrets @ C @ ( specSecrets @ A ) )
=> ? [D: secrecy_specID] :
( ( member740727610specID @ D @ ( subcomponents @ A ) )
& ( member2138796287ecrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_correctCompositionKS__subcomp2) ).
thf(1033,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member740727610specID @ B @ ( subcomponents @ A ) )
=> ( ( member2138796287ecrets @ C @ ( specSecrets @ A ) )
=> ? [D: secrecy_specID] :
( ( member740727610specID @ D @ ( subcomponents @ A ) )
& ( member2138796287ecrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(251,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_KS_Oinject_I2_J) ).
thf(1197,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(157,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eout @ C @ B )
| ( eout @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_TBtheorem2a) ).
thf(839,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eout @ C @ B )
| ( eout @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(129,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: secrecy_chanID] :
( ~ ( ineM @ A @ B @ C )
=> ( ~ ( ineM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ( member1967978193chanID @ F @ B )
=> ( ( member1967978193chanID @ F @ ( ins @ E ) )
=> ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_TBlemma3b) ).
thf(728,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: secrecy_chanID] :
( ~ ( ineM @ A @ B @ C )
=> ( ~ ( ineM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ( member1967978193chanID @ F @ B )
=> ( ( member1967978193chanID @ F @ ( ins @ E ) )
=> ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(197,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ~ ( eoutM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( out_ex985543062Single @ A @ F @ C )
& ( member1967978193chanID @ F @ B )
& ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_TBtheorem5b__notP1) ).
thf(987,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ~ ( eoutM @ D @ B @ C )
=> ( ( ( subcomponents @ E )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( out_ex985543062Single @ A @ F @ C )
& ( member1967978193chanID @ F @ B )
& ( member1967978193chanID @ F @ ( loc @ E ) ) )
=> ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(13,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ ( insert751661162chanID @ A @ B ) )
= ( insert751661162chanID @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_insert__absorb2) ).
thf(332,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ ( insert751661162chanID @ A @ B ) )
= ( insert751661162chanID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(269,axiom,
! [A: set_Secrecy_KS,B: secrecy_KS] :
( ( A = bot_bo1943466239ecy_KS )
=> ~ ( member_Secrecy_KS @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_equals0D) ).
thf(1261,plain,
! [A: set_Secrecy_KS,B: secrecy_KS] :
( ( A = bot_bo1943466239ecy_KS )
=> ~ ( member_Secrecy_KS @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(271,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_LocalSecretsComposition__neg1__s) ).
thf(1268,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ B ) )
=> ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ C ) )
=> ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(93,axiom,
! [A: secrecy_Secrets] :
~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_empty__iff) ).
thf(596,plain,
! [A: secrecy_Secrets] :
~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(109,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ? [E: secrecy_chanID] :
( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
=> ( ine @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_TBtheorem4a__P) ).
thf(644,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ? [E: secrecy_chanID] :
( ( member1967978193chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
=> ( ine @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(202,axiom,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_singleton__iff) ).
thf(1004,plain,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(119,axiom,
! [A: secrecy_specID] :
( ( correc965049635ionLoc @ A )
=> ( ( ( subcomponents @ A )
= bot_bo1785112429specID )
=> ( ( loc @ A )
= bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_subcomponents__loc) ).
thf(691,plain,
! [A: secrecy_specID] :
( ( correc965049635ionLoc @ A )
=> ( ( ( subcomponents @ A )
= bot_bo1785112429specID )
=> ( ( loc @ A )
= bot_bo443197316chanID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(165,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ? [E: secrecy_chanID] :
( ( member1967978193chanID @ E @ ( out @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
=> ( eout @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_TBtheorem45a__P) ).
thf(871,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ? [E: secrecy_chanID] :
( ( member1967978193chanID @ E @ ( out @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
=> ( eout @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(97,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Un__empty__right) ).
thf(607,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(11,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ B )
!= bot_bo443197316chanID ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_insert__not__empty) ).
thf(322,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ B )
!= bot_bo443197316chanID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(204,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ( ine_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ E )
=> ( member1967978193chanID @ F @ ( loc @ C ) ) )
=> ~ ( ine @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_TBtheorem4a__notP2) ).
thf(1009,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ( ine_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member1967978193chanID @ F @ E )
=> ( member1967978193chanID @ F @ ( loc @ C ) ) )
=> ~ ( ine @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(248,axiom,
! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
( ( ~ ( member_Secrecy_KS @ A @ B )
=> ( A = C ) )
=> ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insertCI) ).
thf(1184,plain,
! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
( ( ~ ( member_Secrecy_KS @ A @ B )
=> ( A = C ) )
=> ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(76,axiom,
! [A: set_Secrecy_chanID,B: secrecy_chanID] :
( ( A = bot_bo443197316chanID )
=> ~ ( member1967978193chanID @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_equals0D) ).
thf(543,plain,
! [A: set_Secrecy_chanID,B: secrecy_chanID] :
( ( A = bot_bo443197316chanID )
=> ~ ( member1967978193chanID @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(81,axiom,
! [A: set_Secrecy_specID,B: secrecy_specID] :
( ( A = bot_bo1785112429specID )
=> ~ ( member740727610specID @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_equals0D) ).
thf(560,plain,
! [A: set_Secrecy_specID,B: secrecy_specID] :
( ( A = bot_bo1785112429specID )
=> ~ ( member740727610specID @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(60,axiom,
! [A: set_Secrecy_Secrets,B: secrecy_Secrets] :
( ( A = bot_bo1124690338ecrets )
=> ~ ( member2138796287ecrets @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_equals0D) ).
thf(491,plain,
! [A: set_Secrecy_Secrets,B: secrecy_Secrets] :
( ( A = bot_bo1124690338ecrets )
=> ~ ( member2138796287ecrets @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(169,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
( ~ ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ine_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ D ) ) )
=> ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_TBtheorem4b__notP2) ).
thf(882,plain,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
( ~ ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ine_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member1967978193chanID @ G @ F )
=> ( member1967978193chanID @ G @ ( loc @ D ) ) )
=> ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(61,axiom,
! [A: set_Secrecy_Secrets] :
( ( ! [B: secrecy_Secrets] :
~ ( member2138796287ecrets @ B @ A ) )
= ( A = bot_bo1124690338ecrets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_all__not__in__conv) ).
thf(496,plain,
! [A: set_Secrecy_Secrets] :
( ( ! [B: secrecy_Secrets] :
~ ( member2138796287ecrets @ B @ A ) )
= ( A = bot_bo1124690338ecrets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(50,axiom,
! [A: set_Secrecy_Secrets] :
( ! [B: secrecy_Secrets] :
~ ( member2138796287ecrets @ B @ A )
=> ( A = bot_bo1124690338ecrets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_equals0I) ).
thf(454,plain,
! [A: set_Secrecy_Secrets] :
( ! [B: secrecy_Secrets] :
~ ( member2138796287ecrets @ B @ A )
=> ( A = bot_bo1124690338ecrets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1463,plain,
$false,
inference(e,[status(thm)],[1322,809,1190,347,1237,909,893,1315,777,1110,481,1200,977,1211,1068,994,1205,677,1041,523,582,385,930,1342,747,913,404,898,301,436,320,565,570,719,344,1132,1055,724,587,619,917,702,751,934,357,902,1147,1247,1319,1347,416,448,1232,443,806,1051,905,1302,756,1136,834,1169,1215,734,1072,774,1351,1345,428,312,602,981,307,920,380,529,793,366,534,512,942,439,1047,798,1163,1091,1255,1174,820,788,407,630,467,484,1365,625,879,889,682,1291,974,551,1128,519,697,1143,388,593,610,499,1375,1121,554,537,526,679,686,476,1016,590,622,997,701,1266,721,371,1150,1249,984,911,1333,938,657,398,674,633,360,1026,1167,298,1251,425,1103,856,745,573,689,296,1154,732,843,743,579,1124,413,1007,694,875,826,1139,1312,1107,335,804,1258,947,540,672,604,831,1282,1117,736,377,863,451,567,509,1043,599,1376,1080,895,1177,959,636,394,1000,505,1066,868,1208,795,548,1277,1340,355,754,836,473,1076,531,944,927,374,648,487,617,516,458,1181,823,557,640,705,1225,954,1368,1098,310,1300,502,1235,338,1218,1038,585,470,576,1358,1023,1221,1372,876,859,1272,612,1240,991,627,363,1157,891,1289,963,304,1101,351,401,418,1030,914,433,1193,478,763,383,1309,716,1161,800,315,410,854,422,865,326,341,1172,828,1165,1033,1197,839,728,987,332,1261,1268,596,644,1004,691,871,607,322,1009,1184,543,560,491,882,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP091^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n020.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:52:55 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.00/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.24/1.25 % [INFO] Parsing done (449ms).
% 2.24/1.27 % [INFO] Running in sequential loop mode.
% 3.45/1.65 % [INFO] eprover registered as external prover.
% 3.45/1.66 % [INFO] Scanning for conjecture ...
% 3.96/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ...
% 4.21/1.99 % [INFO] Axiom selection finished. Selected 293 axioms (removed 62 axioms).
% 5.23/2.29 % [INFO] Problem is higher-order (TPTP THF).
% 5.62/2.33 % [INFO] Type checking passed.
% 5.62/2.33 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 20.34/6.01 % External prover 'e' found a proof!
% 20.34/6.01 % [INFO] Killing All external provers ...
% 20.34/6.01 % Time passed: 5657ms (effective reasoning time: 4740ms)
% 20.34/6.01 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 20.34/6.02 % Axioms used in derivation (293): fact_6_cCompLoc, fact_60_ex__in__conv, fact_164_is__singletonI_H, fact_139_singletonD, fact_189_TBtheorem4b__PQ, fact_56_ex__in__conv, fact_153_KS2Expression_Osimps_I2_J, fact_342_eout__know__nonKS__s, fact_37_insert__iff, fact_155_KS2Expression_Osimps_I1_J, fact_50_all__not__in__conv, fact_278_Un__absorb, fact_134_singleton__iff, fact_20_LocalSecretsComposition__ine2__s, fact_211_bot__empty__eq, fact_177_correctCompositionIn__L2, fact_217_LocalSecretsComposition__neg__loc__k, fact_55_empty__iff, fact_161_is__singletonI_H, fact_11_KS_Odistinct_I1_J, fact_284_Un__left__commute, fact_328_out__exprChannelSingle__Set, fact_213_bot__empty__eq, fact_102_Collect__mem__eq, fact_323_correctCompositionKS__subcomp4, fact_256_UnE, fact_53_empty__iff, fact_227_know__composition1, fact_184_subcomponents__loc, fact_208_inStream__def, fact_133_doubleton__eq__iff, fact_312_sup__bot__left, fact_131_insert__not__empty, fact_344_TBtheore54b__P, fact_138_singleton__iff, fact_289_Un__empty__right, fact_291_singleton__Un__iff, fact_115_insertI2, fact_78_mk__disjoint__insert, fact_15_know__composition__neg1, fact_228_know__composition2, fact_124_insertE, fact_90_insert__absorb, fact_246_Un__iff, fact_41_insert__absorb2, fact_82_insert__commute, fact_128_singleton__inject, fact_114_insertI2, fact_236_notSpecKeysSecretsExpr__def, fact_252_Un__insert__right, fact_226_know__composition, fact_104_insert__ident, fact_301_sup__bot_Oright__neutral, fact_75_emptyE, fact_159_is__singleton__the__elem, fact_218_correctCompositionKS__exprChannel__s__Qex, fact_181_ineM__ine, fact_10_cCompI, fact_110_Set_Oset__insert, fact_68_equals0D, fact_337_TBtheorem5b__notP1, fact_295_Un__singleton__iff, fact_302_sup__bot_Oright__neutral, fact_97_mem__Collect__eq, fact_183_correctCompositionIn__L1, fact_28_singletonI, fact_77_mk__disjoint__insert, fact_261_UnI1, fact_187_TBtheorem4a__notPQ, fact_237_UnCI, fact_254_Un__insert__left, fact_255_Un__insert__left, fact_311_sup__bot_Oeq__neutr__iff, fact_85_insert__eq__iff, fact_334_eoutM__eout, fact_109_Set_Oset__insert, fact_27_singletonI, fact_285_Un__empty__left, fact_309_sup__bot_Oeq__neutr__iff, fact_234_LocalSecretsComposition__neg__s, fact_352_TBtheorem5a__PQ, fact_81_insert__commute, fact_271_bex__Un, fact_259_UnE, fact_306_sup__bot_Oleft__neutral, fact_333_not__eout__eoutM, fact_247_Un__empty, fact_204_TBtheorem4a__P, fact_327_TBtheorem5a__notP2, fact_232_correctCompositionKS__exprChannel__k__Qex, fact_145_the__elem__eq, fact_22_TBtheorem1a, fact_63_equals0I, fact_21_LocalSecretsComposition__neg1__s, fact_322_TBtheorem2a, fact_172_TBtheorem4a__empty, fact_29_LocalSecretsComposition1, fact_201_ine__exprChannelSet__Single, fact_195_ine__exprChannelSingle__def, fact_171_know_Osimps_I1_J, fact_290_Un__empty__right, fact_303_sup__bot_Oneutr__eq__iff, fact_349_out__exprChannelSet__def, fact_230_correctCompositionKS__exprChannel__k__Q, fact_282_Un__left__absorb, fact_149_LocalSecretsComposition__ine1__k, fact_286_Un__empty__left, fact_130_insert__not__empty, fact_307_sup__bot_Oleft__neutral, fact_272_bex__Un, fact_203_TBlemma3b, fact_292_singleton__Un__iff, fact_9_subPQ, fact_46_all__not__in__conv, fact_288_Un__empty__right, fact_324_correctCompositionKS__subcomp3, fact_5_sg6a, fact_71_emptyE, fact_175_Set_Ois__empty__def, fact_263_UnI1, fact_294_Un__singleton__iff, fact_281_Un__left__absorb, fact_353_outStream__def, fact_0_not__knowQm, fact_248_Un__empty, fact_266_UnI2, fact_65_equals0I, fact_88_insert__absorb, fact_147_LocalSecretsComposition__neg1__k, fact_220_correctCompositionKS__exprChannel__s__Q, fact_83_insert__eq__iff, fact_154_Expression_Oinject_I1_J, fact_151_is__singletonI, fact_320_correctCompositionKS__subcomp1, fact_249_Un__empty, fact_240_UnCI, fact_340_not__know__k__not__eout, fact_16_know__composition__neg__ine__s, fact_346_TBtheorem45a__P, fact_345_TBtheorem5b__PQ, fact_341_eout__know__k, fact_18_KS_Oexhaust, fact_185_TBtheorem4b__notPQ, fact_321_correctCompositionKS__subcomp2, fact_258_UnE, fact_113_insertI2, fact_163_is__singletonI_H, fact_305_sup__bot_Oneutr__eq__iff, fact_225_correctCompositionKS__negQ, fact_279_Un__commute, fact_297_insert__is__Un, fact_313_sup__bot__left, fact_158_Expression_Odistinct_I1_J, fact_148_LocalSecretsComposition__ine2__k, fact_17_not__know__s__not__ine, fact_269_UnI2, fact_54_empty__iff, fact_251_Un__insert__right, fact_329_out__exprChannelSet__Single, fact_12_KS_Oinduct, fact_129_singleton__inject, fact_196_LocalSecretsComposition__exprChannel__s, fact_30_insertCI, fact_3_sg5, fact_194_ineM__L1, fact_150_know__composition__neg__ine__k, fact_4_KS_Oinject_I2_J, fact_273_ball__Un, fact_182_TBtheorem4b__notP1, fact_216_LocalSecretsComposition__neg__loc__s, fact_188_TBtheorem4a__notP2, fact_338_eout__know__nonKS__k, fact_318_ineM__Un1, fact_40_insert__absorb2, fact_192_ine__ins__neg1, fact_73_emptyE, fact_275_Un__assoc, fact_61_equals0I, fact_222_correctCompositionKS__PQ, fact_66_equals0D, fact_197_LocalSecretsComposition__exprChannel__k, fact_296_Un__singleton__iff, fact_186_TBtheorem4b__notP2, fact_268_UnI2, fact_169_is__singleton__def, fact_314_sup__bot__left, fact_19_LocalSecretsComposition__ine1__s, fact_270_UnI2, fact_76_mk__disjoint__insert, fact_105_insert__ident, fact_119_insertI1, fact_23_TBtheorem3a, fact_143_singletonD, fact_336_TBtheorem5b__notP2, fact_308_sup__bot_Oleft__neutral, fact_64_equals0I, fact_98_Collect__mem__eq, fact_310_sup__bot_Oeq__neutr__iff, fact_304_sup__bot_Oneutr__eq__iff, fact_118_insertI1, fact_180_not__ine__ineM, fact_193_ineM__def, fact_315_sup__bot__right, fact_174_TBtheorem3b, fact_207_locStream__def, fact_347_eout__def, fact_103_insert__ident, fact_276_Un__assoc, fact_317_sup__bot__right, fact_59_ex__in__conv, fact_31_insertCI, fact_231_correctCompositionKS__exprChannel__k__Pex, fact_351_correctCompositionOut__prop1, fact_123_insertE, fact_58_ex__in__conv, fact_260_UnE, fact_191_ine__def, fact_206_TBtheorem4b__P, fact_93_mem__Collect__eq, fact_283_Un__left__commute, fact_319_TBtheorem5a__empty, fact_48_all__not__in__conv, fact_69_equals0D, fact_205_TBtheorem4a__PQ, fact_178_correctCompositionIn__prop1, fact_36_insert__iff, fact_235_LocalSecretsComposition__neg__k, fact_179_TBtheorem4a__notP1, fact_241_UnCI, fact_300_sup__bot_Oright__neutral, fact_144_LocalSecretsComposition__neg1, fact_2_knowPQ, fact_199_ine__empty__exprChannelSet, fact_316_sup__bot__right, fact_51_empty__iff, fact_280_Un__commute, fact_70_equals0D, fact_339_eoutKnowCorrect__L1k, fact_108_Set_Oset__insert, fact_239_UnCI, fact_250_Un__insert__right, fact_223_correctCompositionKS__neg1, fact_244_Un__iff, fact_325_TBtheorem5a__notP1, fact_221_correctCompositionKS__exprChannel__s__P, fact_331_eout__know__s, fact_132_doubleton__eq__iff, fact_49_all__not__in__conv, fact_299_insert__is__Un, fact_335_TBtheorem2b, fact_354_adv__not__know2, fact_190_ine__exprChannelSet__def, fact_265_UnI1, fact_35_insert__iff, fact_229_correctCompositionKS__exprChannel__k__P, fact_287_Un__empty__left, fact_125_insertE, fact_1_a2, fact_277_Un__absorb, fact_14_Expression_Oinject_I2_J, fact_348_eoutM__def, fact_13_KS_Oinject_I1_J, fact_166_not__know__k__not__ine, fact_293_singleton__Un__iff, fact_242_Un__iff, fact_32_insertCI, fact_350_out__exprChannelSingle__def, fact_7_a22, fact_264_UnI1, fact_142_singletonD, fact_200_ine__exprChannelSingle__Set, fact_332_not__know__s__not__eout, fact_8_know_Osimps_I2_J, fact_173_TBtheorem1b, fact_89_insert__absorb, fact_343_eoutKnowCorrect__L1s, fact_120_insertI1, fact_219_correctCompositionKS__exprChannel__s__Pex, fact_202_correctCompositionInLoc__exprChannel, fact_198_ine__nonempty__exprChannelSet, fact_74_emptyE, fact_137_singleton__iff, fact_24_singletonI, fact_298_insert__is__Un, fact_274_ball__Un, fact_326_TBtheorem5a__notPQ, fact_330_TBtheorem5b__notPQ, fact_253_Un__insert__left, fact_224_correctCompositionKS__negP, fact_233_LocalSecretsComposition__neg, fact_167_is__singletonE, fact_245_Un__iff, fact_84_insert__eq__iff
% 20.34/6.02 % No. of inferences in proof: 590
% 20.34/6.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5657 ms resp. 4740 ms w/o parsing
% 22.10/6.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.10/6.28 % [INFO] Killing All external provers ...
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