TSTP Solution File: ITP088^1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP088^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:43 EDT 2024
% Result : Theorem 25.39s 6.54s
% Output : Refutation 25.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 348
% Syntax : Number of formulae : 622 ( 262 unt; 76 typ; 0 def)
% Number of atoms : 2050 ( 674 equ; 4 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 6620 ( 483 ~; 86 |; 206 &;4871 @)
% ( 0 <=>; 974 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 9 con; 0-3 aty)
% Number of variables : 1636 ( 82 ^1480 !; 74 ?;1636 :)
% 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_type,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(knowle233900195orrect_type,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(knowle945212990e_know_type,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(sup_su1301156759ecy_KS_type,type,
sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
thf(sup_su552545507y_Keys_type,type,
sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
thf(sup_su370684444chanID_type,type,
sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(sup_su1712599557specID_type,type,
sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(mem_Se1967555118ession_type,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(bot_bo2072920570Keys_o_type,type,
bot_bo2072920570Keys_o: secrecy_Keys > $o ).
thf(bot_bo1012329985anID_o_type,type,
bot_bo1012329985anID_o: secrecy_chanID > $o ).
thf(bot_bo701486667y_Keys_type,type,
bot_bo701486667y_Keys: set_Secrecy_Keys ).
thf(bot_bo443197316chanID_type,type,
bot_bo443197316chanID: set_Secrecy_chanID ).
thf(bot_bo1785112429specID_type,type,
bot_bo1785112429specID: set_Secrecy_specID ).
thf(ord_le1802272080chanID_type,type,
ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
thf(correctCompositionKS_type,type,
correctCompositionKS: secrecy_specID > $o ).
thf(eout_type,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(eoutM_type,type,
eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(exprChannel_type,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(ine_type,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(ineM_type,type,
ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(ine_exprChannelSet_type,type,
ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(ine_ex1303305700Single_type,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(notSpe1586871396tsExpr_type,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(out_exprChannelSet_type,type,
out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
thf(out_ex985543062Single_type,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(specKeys_type,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(specKeysSecrets_type,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(specSecrets_type,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(secrecy_dE_type,type,
secrecy_dE: nat > secrecy_Expression ).
thf(secrecy_idE_type,type,
secrecy_idE: secrecy_specID > secrecy_Expression ).
thf(secrecy_kE_type,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(secrecy_sE_type,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(secrec1016742679ession_type,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(secrecy_kKS_type,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(secrecy_sKS_type,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(collect_Secrecy_KS_type,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(collect_Secrecy_Keys_type,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(collec625564175chanID_type,type,
collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
thf(insert751661162chanID_type,type,
insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
thf(insert1671894227specID_type,type,
insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
thf(is_sin1096471309y_Keys_type,type,
is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
thf(is_sin581274182chanID_type,type,
is_sin581274182chanID: set_Secrecy_chanID > $o ).
thf(is_sin1501507247specID_type,type,
is_sin1501507247specID: set_Secrecy_specID > $o ).
thf(the_el2054381829chanID_type,type,
the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
thf(the_el827131246specID_type,type,
the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
thf(correctCompositionIn_type,type,
correctCompositionIn: secrecy_specID > $o ).
thf(correc965049635ionLoc_type,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(correc990227761ionOut_type,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(inStream_type,type,
inStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(ins_type,type,
ins: secrecy_specID > set_Secrecy_chanID ).
thf(loc_type,type,
loc: secrecy_specID > set_Secrecy_chanID ).
thf(locStream_type,type,
locStream: secrecy_specID > set_Secrecy_chanID > $o ).
thf(out_type,type,
out: secrecy_specID > set_Secrecy_chanID ).
thf(subcomponents_type,type,
subcomponents: secrecy_specID > set_Secrecy_specID ).
thf(member_Secrecy_KS_type,type,
member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
thf(member_Secrecy_Keys_type,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(member2138796287ecrets_type,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(member1967978193chanID_type,type,
member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
thf(member740727610specID_type,type,
member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
thf(p_type,type,
p: secrecy_specID ).
thf(pq_type,type,
pq: secrecy_specID ).
thf(q_type,type,
q: secrecy_specID ).
thf(key_type,type,
key: secrecy_Keys ).
thf(183,axiom,
! [A: set_Secrecy_chanID] :
( ( ? [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
= ( A != bot_bo443197316chanID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ex__in__conv) ).
thf(892,plain,
! [A: set_Secrecy_chanID] :
( ( ? [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
= ( A != bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_241_Un__iff) ).
thf(809,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)],[166]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',fact_192_know_Osimps_I2_J) ).
thf(1105,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)],[239]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_106_mk__disjoint__insert) ).
thf(347,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)],[27]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',fact_285_Un__left__commute) ).
thf(962,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)],[205]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_171_TBtheorem4a__notP2) ).
thf(1179,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)],[260]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',fact_332_not__know__s__not__eout) ).
thf(666,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)],[125]) ).
thf(68,axiom,
! [A: set_Secrecy_chanID] :
( ( is_sin581274182chanID @ A )
=> ~ ! [B: secrecy_chanID] :
( A
!= ( insert751661162chanID @ B @ bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_is__singletonE) ).
thf(481,plain,
! [A: set_Secrecy_chanID] :
( ( is_sin581274182chanID @ A )
=> ~ ! [B: secrecy_chanID] :
( A
!= ( insert751661162chanID @ B @ bot_bo443197316chanID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',fact_236_UnCI) ).
thf(909,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)],[189]) ).
thf(23,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( ~ ( member1967978193chanID @ A @ B )
=> ( A = C ) )
=> ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_insertCI) ).
thf(333,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)],[23]) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',fact_223_correctCompositionKS__exprChannel__s__Q) ).
thf(1031,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)],[220]) ).
thf(3,axiom,
! [A: secrecy_chanID] :
( ( the_el2054381829chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_the__elem__eq) ).
thf(276,plain,
! [A: secrecy_chanID] :
( ( the_el2054381829chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_sup__bot__right) ).
thf(308,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(231,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_not__know__s__not__ine) ).
thf(1073,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)],[231]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',fact_225_LocalSecretsComposition__neg) ).
thf(1142,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)],[252]) ).
thf(179,axiom,
! [A: secrecy_chanID > $o] :
( ( bot_bo443197316chanID
= ( collec625564175chanID @ A ) )
= ( ! [B: secrecy_chanID] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_empty__Collect__eq) ).
thf(878,plain,
! [A: secrecy_chanID > $o] :
( ( bot_bo443197316chanID
= ( collec625564175chanID @ A ) )
= ( ! [B: secrecy_chanID] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',fact_176_ine__exprChannelSet__def) ).
thf(597,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)],[106]) ).
thf(254,axiom,
! [A: secrecy_Keys,B: nat] :
( ( secrecy_kE @ A )
!= ( secrecy_dE @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Expression_Odistinct_I3_J) ).
thf(1158,plain,
! [A: secrecy_Keys,B: nat] :
( ( secrecy_kE @ A )
!= ( secrecy_dE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',fact_213_know__composition2) ).
thf(762,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)],[152]) ).
thf(90,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_UnI2) ).
thf(550,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)],[90]) ).
thf(256,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Expression_Oinject_I1_J) ).
thf(1164,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(65,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_UnI1) ).
thf(472,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)],[65]) ).
thf(149,axiom,
! [A: set_Secrecy_chanID] :
( ( A != bot_bo443197316chanID )
=> ( ! [B: secrecy_chanID,C: secrecy_chanID] :
( ( member1967978193chanID @ B @ A )
=> ( ( member1967978193chanID @ C @ A )
=> ( B = C ) ) )
=> ( is_sin581274182chanID @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_is__singletonI_H) ).
thf(747,plain,
! [A: set_Secrecy_chanID] :
( ( A != bot_bo443197316chanID )
=> ( ! [B: secrecy_chanID,C: secrecy_chanID] :
( ( member1967978193chanID @ B @ A )
=> ( ( member1967978193chanID @ C @ A )
=> ( B = C ) ) )
=> ( is_sin581274182chanID @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',fact_219_correctCompositionKS__exprChannel__k__Q) ).
thf(1222,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)],[270]) ).
thf(44,axiom,
! [A: set_Secrecy_specID,B: secrecy_specID] :
( ( A = bot_bo1785112429specID )
=> ~ ( member740727610specID @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_equals0D) ).
thf(404,plain,
! [A: set_Secrecy_specID,B: secrecy_specID] :
( ( A = bot_bo1785112429specID )
=> ~ ( member740727610specID @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(185,axiom,
! [A: secrecy_specID] :
( ( correc965049635ionLoc @ A )
=> ( ( ( subcomponents @ A )
= bot_bo1785112429specID )
=> ( ( loc @ A )
= bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_subcomponents__loc) ).
thf(898,plain,
! [A: secrecy_specID] :
( ( correc965049635ionLoc @ A )
=> ( ( ( subcomponents @ A )
= bot_bo1785112429specID )
=> ( ( loc @ A )
= bot_bo443197316chanID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(215,axiom,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
? [B: secrecy_specID] :
( A
= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_is__singleton__def) ).
thf(1001,plain,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
? [B: secrecy_specID] :
( A
= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(224,axiom,
~ ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(1046,plain,
~ ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(12,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ B )
!= bot_bo443197316chanID ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_insert__not__empty) ).
thf(301,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ B )
!= bot_bo443197316chanID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_128_Set_Oset__insert) ).
thf(565,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)],[96]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',fact_178_LocalSecretsComposition__neg1) ).
thf(1228,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)],[271]) ).
thf(142,axiom,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ( secrecy_sE @ A )
!= ( secrecy_idE @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Expression_Odistinct_I9_J) ).
thf(724,plain,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ( secrecy_sE @ A )
!= ( secrecy_idE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(140,axiom,
! [A: secrecy_specID,B: secrecy_specID] :
( ( ( secrecy_idE @ A )
= ( secrecy_idE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Expression_Oinject_I4_J) ).
thf(719,plain,
! [A: secrecy_specID,B: secrecy_specID] :
( ( ( secrecy_idE @ A )
= ( secrecy_idE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_107_mk__disjoint__insert) ).
thf(372,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)],[35]) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',fact_291_Un__singleton__iff) ).
thf(802,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)],[163]) ).
thf(249,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Expression_Odistinct_I1_J) ).
thf(1132,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(61,axiom,
! [A: secrecy_Keys] :
~ ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_empty__iff) ).
thf(460,plain,
! [A: secrecy_Keys] :
~ ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',fact_331_eout__know__s) ).
thf(619,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)],[113]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',fact_168_TBtheorem4b__notPQ) ).
thf(838,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)],[171]) ).
thf(30,axiom,
! [A: set_Secrecy_Keys] :
( ! [B: secrecy_Keys] :
~ ( member_Secrecy_Keys @ B @ A )
=> ( A = bot_bo701486667y_Keys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_equals0I) ).
thf(357,plain,
! [A: set_Secrecy_Keys] :
( ! [B: secrecy_Keys] :
~ ( member_Secrecy_Keys @ B @ A )
=> ( A = bot_bo701486667y_Keys ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(262,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/sandbox2/benchmark/theBenchmark.p',fact_53_LocalSecretsComposition__ine1__k) ).
thf(1191,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)],[262]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',fact_172_ine__exprChannelSet__Single) ).
thf(770,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)],[154]) ).
thf(180,axiom,
( sup_su1301156759ecy_KS
= ( ^ [A: set_Secrecy_KS,B: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_Un__commute) ).
thf(881,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)],[180]) ).
thf(242,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/sandbox2/benchmark/theBenchmark.p',fact_183_LocalSecretsComposition__ine1__s) ).
thf(1115,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)],[242]) ).
thf(8,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( bot_bo1785112429specID
= ( sup_su1712599557specID @ A @ B ) )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_sup__bot_Oneutr__eq__iff) ).
thf(289,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)],[8]) ).
thf(57,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( ( insert751661162chanID @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_insert__absorb) ).
thf(448,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( ( insert751661162chanID @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',fact_249_Un__insert__left) ).
thf(316,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)],[17]) ).
thf(49,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( bot_bo443197316chanID
= ( sup_su370684444chanID @ A @ B ) )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_bot__eq__sup__iff) ).
thf(421,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)],[49]) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',fact_346_TBtheorem45a__P) ).
thf(870,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)],[176]) ).
thf(207,axiom,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_UnI2) ).
thf(969,plain,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',fact_201_correctCompositionKS__exprChannel__s__Qex) ).
thf(606,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)],[110]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',fact_276_ball__Un) ).
thf(475,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)],[66]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',fact_164_correctCompositionInLoc__exprChannel) ).
thf(591,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)],[105]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',fact_129_Set_Oset__insert) ).
thf(376,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)],[36]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',fact_317_ineM__Un1) ).
thf(485,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)],[69]) ).
thf(250,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/sandbox2/benchmark/theBenchmark.p',fact_341_eout__know__k) ).
thf(1136,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)],[250]) ).
thf(170,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/sandbox2/benchmark/theBenchmark.p',fact_54_TBtheorem4b__P) ).
thf(834,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)],[170]) ).
thf(218,axiom,
! [A: set_Secrecy_Keys] :
( ( collect_Secrecy_Keys
@ ^ [B: secrecy_Keys] : ( member_Secrecy_Keys @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(1020,plain,
! [A: set_Secrecy_Keys] :
( ( collect_Secrecy_Keys
@ ^ [B: secrecy_Keys] : ( member_Secrecy_Keys @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_292_Un__singleton__iff) ).
thf(574,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)],[99]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',fact_26_TBtheorem3b) ).
thf(766,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)],[153]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_277_Un__assoc) ).
thf(687,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)],[133]) ).
thf(117,axiom,
( insert1671894227specID
= ( ^ [A: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_insert__is__Un) ).
thf(634,plain,
( insert1671894227specID
= ( ^ [A: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_318_notSpecKeysSecretsExpr__def) ).
thf(1119,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)],[243]) ).
thf(42,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= bot_bo1785112429specID )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Un__empty) ).
thf(396,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)],[42]) ).
thf(214,axiom,
! [A: set_Secrecy_KS] :
( ( collect_Secrecy_KS
@ ^ [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(998,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)],[214]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',fact_237_UnCI) ).
thf(292,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)],[9]) ).
thf(37,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Un__empty__left) ).
thf(380,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',fact_344_TBtheore54b__P) ).
thf(678,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)],[130]) ).
thf(194,axiom,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_UnI1) ).
thf(925,plain,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(33,axiom,
! [A: secrecy_chanID,B: secrecy_chanID > $o] :
( ( member1967978193chanID @ A @ ( collec625564175chanID @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mem__Collect__eq) ).
thf(366,plain,
! [A: secrecy_chanID,B: secrecy_chanID > $o] :
( ( member1967978193chanID @ A @ ( collec625564175chanID @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(85,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_sup__bot_Oleft__neutral) ).
thf(534,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',fact_167_TBtheorem4a__notP1) ).
thf(1067,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)],[229]) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',fact_57_TBtheorem4a__PQ) ).
thf(1057,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)],[228]) ).
thf(202,axiom,
! [A: nat,B: nat] :
( ( ( secrecy_dE @ A )
= ( secrecy_dE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Expression_Oinject_I3_J) ).
thf(952,plain,
! [A: nat,B: nat] :
( ( ( secrecy_dE @ A )
= ( secrecy_dE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',fact_174_ine__nonempty__exprChannelSet) ).
thf(1123,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)],[245]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',fact_328_out__exprChannelSingle__Set) ).
thf(561,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)],[94]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_209_is__singletonI_H) ).
thf(424,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)],[50]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',fact_220_correctCompositionKS__exprChannel__k__Pex) ).
thf(1238,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)],[272]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',fact_55_TBtheorem4b__PQ) ).
thf(693,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)],[135]) ).
thf(116,axiom,
! [A: nat,B: secrecy_specID] :
( ( secrecy_dE @ A )
!= ( secrecy_idE @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Expression_Odistinct_I11_J) ).
thf(630,plain,
! [A: nat,B: secrecy_specID] :
( ( secrecy_dE @ A )
!= ( secrecy_idE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(31,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ~ ( eoutM @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_not__eout__eoutM) ).
thf(361,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)],[31]) ).
thf(21,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_insertI1) ).
thf(329,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',fact_34_TBtheorem3a) ).
thf(1210,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)],[267]) ).
thf(233,axiom,
~ ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I1_J) ).
thf(1079,plain,
~ ( knowle945212990e_know @ p @ ( secrecy_kKS @ key ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_211_know__composition) ).
thf(710,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)],[138]) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',fact_224_correctCompositionKS__exprChannel__s__Pex) ).
thf(852,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)],[173]) ).
thf(52,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_UnI1) ).
thf(435,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)],[52]) ).
thf(102,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
=> ( ( A != B )
=> ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_insertE) ).
thf(583,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)],[102]) ).
thf(81,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ ( insert751661162chanID @ A @ B ) )
= ( insert751661162chanID @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_insert__absorb2) ).
thf(522,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ ( insert751661162chanID @ A @ B ) )
= ( insert751661162chanID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fact_188_KS_Oinduct) ).
thf(682,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)],[131]) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',fact_6_know_Osimps_I1_J) ).
thf(1195,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)],[263]) ).
thf(80,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
= ( sup_su370684444chanID @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_Un__left__absorb) ).
thf(519,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)],[80]) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',fact_56_TBtheorem4a__P) ).
thf(1089,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)],[236]) ).
thf(177,axiom,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ B @ C ) )
=> ( ~ ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_UnE) ).
thf(874,plain,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ B @ C ) )
=> ( ~ ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',fact_335_TBtheorem2b) ).
thf(615,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)],[112]) ).
thf(244,axiom,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I3_J) ).
thf(1121,plain,
( ( subcomponents @ pq )
= ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',fact_330_TBtheorem5b__notPQ) ).
thf(1006,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)],[217]) ).
thf(158,axiom,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_KS2Expression_Osimps_I2_J) ).
thf(783,plain,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(70,axiom,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( insert751661162chanID @ B @ ( insert751661162chanID @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_insert__commute) ).
thf(488,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)],[70]) ).
thf(86,axiom,
! [A: secrecy_Keys] :
~ ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_emptyE) ).
thf(537,plain,
! [A: secrecy_Keys] :
~ ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(268,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/sandbox2/benchmark/theBenchmark.p',fact_33_LocalSecretsComposition__exprChannel__s) ).
thf(1214,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)],[268]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',fact_325_TBtheorem5a__notP1) ).
thf(1039,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)],[222]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',fact_153_doubleton__eq__iff) ).
thf(547,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)],[89]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',fact_203_correctCompositionKS__neg1) ).
thf(706,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)],[137]) ).
thf(186,axiom,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( ~ ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ C ) )
=> ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_UnCI) ).
thf(901,plain,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( ~ ( member_Secrecy_Keys @ A @ B )
=> ( member_Secrecy_Keys @ A @ C ) )
=> ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(232,axiom,
! [A: secrecy_Keys,B: secrecy_specID] :
( ( secrecy_kE @ A )
!= ( secrecy_idE @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Expression_Odistinct_I5_J) ).
thf(1075,plain,
! [A: secrecy_Keys,B: secrecy_specID] :
( ( secrecy_kE @ A )
!= ( secrecy_idE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(114,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_KS_Odistinct_I1_J) ).
thf(622,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(41,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Un__empty__right) ).
thf(393,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_169_TBtheorem4b__notP2) ).
thf(647,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)],[121]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',fact_352_TBtheorem5a__PQ) ).
thf(985,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)],[212]) ).
thf(248,axiom,
correctCompositionIn @ pq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I4_J) ).
thf(1131,plain,
correctCompositionIn @ pq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_274_bex__Un) ).
thf(457,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)],[60]) ).
thf(97,axiom,
( sup_su370684444chanID
= ( ^ [A: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( sup_su370684444chanID @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_Un__commute) ).
thf(569,plain,
( sup_su370684444chanID
= ( ^ [A: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( sup_su370684444chanID @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(157,axiom,
! [A: set_Secrecy_specID] :
( ( is_sin1501507247specID @ A )
=> ~ ! [B: secrecy_specID] :
( A
!= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_is__singletonE) ).
thf(779,plain,
! [A: set_Secrecy_specID] :
( ( is_sin1501507247specID @ A )
=> ~ ! [B: secrecy_specID] :
( A
!= ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(75,axiom,
( is_sin581274182chanID
= ( ^ [A: set_Secrecy_chanID] :
? [B: secrecy_chanID] :
( A
= ( insert751661162chanID @ B @ bot_bo443197316chanID ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_is__singleton__def) ).
thf(503,plain,
( is_sin581274182chanID
= ( ^ [A: set_Secrecy_chanID] :
? [B: secrecy_chanID] :
( A
= ( insert751661162chanID @ B @ bot_bo443197316chanID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(164,axiom,
! [A: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_is__singletonI) ).
thf(805,plain,
! [A: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(77,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( ~ ( member740727610specID @ A @ B )
=> ( A = C ) )
=> ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_insertCI) ).
thf(508,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)],[77]) ).
thf(15,axiom,
( insert751661162chanID
= ( ^ [A: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_insert__is__Un) ).
thf(311,plain,
( insert751661162chanID
= ( ^ [A: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(227,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( exprChannel @ C @ B )
=> ~ ( member1967978193chanID @ C @ ( ins @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_ine__ins__neg1) ).
thf(1054,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)],[227]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',fact_51_LocalSecretsComposition__neg1__k) ).
thf(1167,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)],[257]) ).
thf(261,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/sandbox2/benchmark/theBenchmark.p',fact_218_correctCompositionKS__exprChannel__k__P) ).
thf(1185,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)],[261]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_177_ine__exprChannelSingle__def) ).
thf(586,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)],[103]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',fact_221_correctCompositionKS__exprChannel__k__Qex) ).
thf(1202,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)],[265]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',fact_324_correctCompositionKS__subcomp3) ).
thf(792,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)],[160]) ).
thf(93,axiom,
! [A: set_Secrecy_Keys] :
( ( ! [B: secrecy_Keys] :
~ ( member_Secrecy_Keys @ B @ A ) )
= ( A = bot_bo701486667y_Keys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_all__not__in__conv) ).
thf(558,plain,
! [A: set_Secrecy_Keys] :
( ( ! [B: secrecy_Keys] :
~ ( member_Secrecy_Keys @ B @ A ) )
= ( A = bot_bo701486667y_Keys ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_339_eoutKnowCorrect__L1k) ).
thf(1071,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)],[230]) ).
thf(188,axiom,
! [A: secrecy_specID] :
( ( the_el827131246specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_the__elem__eq) ).
thf(906,plain,
! [A: secrecy_specID] :
( ( the_el827131246specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',fact_289_singleton__Un__iff) ).
thf(298,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)],[11]) ).
thf(46,axiom,
! [A: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_is__singletonI) ).
thf(412,plain,
! [A: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',fact_202_correctCompositionKS__PQ) ).
thf(965,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)],[206]) ).
thf(78,axiom,
! [A: set_Secrecy_Keys] :
( ( ? [B: secrecy_Keys] : ( member_Secrecy_Keys @ B @ A ) )
= ( A != bot_bo701486667y_Keys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ex__in__conv) ).
thf(513,plain,
! [A: set_Secrecy_Keys] :
( ( ? [B: secrecy_Keys] : ( member_Secrecy_Keys @ B @ A ) )
= ( A != bot_bo701486667y_Keys ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',fact_338_eout__know__nonKS__k) ).
thf(1103,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)],[238]) ).
thf(4,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( eoutM @ A @ B @ C )
=> ( eout @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_eoutM__eout) ).
thf(279,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)],[4]) ).
thf(55,axiom,
( is_sin581274182chanID
= ( ^ [A: set_Secrecy_chanID] :
( A
= ( insert751661162chanID @ ( the_el2054381829chanID @ A ) @ bot_bo443197316chanID ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_is__singleton__the__elem) ).
thf(444,plain,
( is_sin581274182chanID
= ( ^ [A: set_Secrecy_chanID] :
( A
= ( insert751661162chanID @ ( the_el2054381829chanID @ A ) @ bot_bo443197316chanID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_271_UnI2) ).
thf(601,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)],[108]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',fact_21_ineM__L1) ).
thf(772,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)],[155]) ).
thf(7,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( bot_bo443197316chanID
= ( sup_su370684444chanID @ A @ B ) )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_sup__bot_Oneutr__eq__iff) ).
thf(286,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)],[7]) ).
thf(100,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( ( insert1671894227specID @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_insert__absorb) ).
thf(577,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( ( insert1671894227specID @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(204,axiom,
! [A: secrecy_KS] :
( ! [B: secrecy_Keys] :
( A
!= ( secrecy_kKS @ B ) )
=> ~ ! [B: secrecy_Secrets] :
( A
!= ( secrecy_sKS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_KS_Oexhaust) ).
thf(958,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)],[204]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_262_UnE) ).
thf(281,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)],[5]) ).
thf(187,axiom,
( inStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( ins @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_inStream__def) ).
thf(904,plain,
( inStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( ins @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(209,axiom,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_singletonD) ).
thf(975,plain,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(251,axiom,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_KS2Expression_Osimps_I1_J) ).
thf(1139,plain,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(16,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Un__empty__right) ).
thf(313,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(73,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= bot_bo443197316chanID )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_sup__bot_Oeq__neutr__iff) ).
thf(498,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)],[73]) ).
thf(63,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
( ( member740727610specID @ A @ B )
=> ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_insertI2) ).
thf(466,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)],[63]) ).
thf(87,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Un__empty__left) ).
thf(540,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(109,axiom,
( locStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( loc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_locStream__def) ).
thf(604,plain,
( locStream
= ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( loc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1,conjecture,
~ ( ine @ pq @ ( secrecy_kE @ key ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ~ ( ine @ pq @ ( secrecy_kE @ key ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(274,plain,
~ ~ ( ine @ pq @ ( secrecy_kE @ key ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',fact_193_LocalSecretsComposition__neg1__s) ).
thf(1048,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)],[225]) ).
thf(58,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_sup__bot_Oright__neutral) ).
thf(451,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(146,axiom,
! [A: secrecy_specID,B: secrecy_specID] :
( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
= ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_singleton__inject) ).
thf(737,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)],[146]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',fact_200_LocalSecretsComposition__neg__loc__k) ).
thf(1043,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)],[223]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',fact_261_UnE) ).
thf(599,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)],[107]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',fact_12_LocalSecretsComposition__exprChannel__k) ).
thf(1175,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)],[259]) ).
thf(39,axiom,
! [A: set_Secrecy_specID] :
( ( ? [B: secrecy_specID] : ( member740727610specID @ B @ A ) )
= ( A != bot_bo1785112429specID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ex__in__conv) ).
thf(387,plain,
! [A: set_Secrecy_specID] :
( ( ? [B: secrecy_specID] : ( member740727610specID @ B @ A ) )
= ( A != bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',fact_147_correctCompositionIn__L1) ).
thf(758,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)],[151]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',fact_320_correctCompositionKS__subcomp1) ).
thf(848,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)],[172]) ).
thf(184,axiom,
! [A: secrecy_KS,B: secrecy_KS > $o] :
( ( member_Secrecy_KS @ A @ ( collect_Secrecy_KS @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mem__Collect__eq) ).
thf(895,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)],[184]) ).
thf(199,axiom,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_emptyE) ).
thf(943,plain,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',fact_288_singleton__Un__iff) ).
thf(668,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)],[126]) ).
thf(241,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ~ ( ineM @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_not__ine__ineM) ).
thf(1112,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)],[241]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',fact_350_out__exprChannelSingle__def) ).
thf(345,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)],[26]) ).
thf(174,axiom,
( bot_bo1012329985anID_o
= ( ^ [A: secrecy_chanID] : ( member1967978193chanID @ A @ bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_bot__empty__eq) ).
thf(858,plain,
( bot_bo1012329985anID_o
= ( ^ [A: secrecy_chanID] : ( member1967978193chanID @ A @ bot_bo443197316chanID ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(162,axiom,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ B @ C ) )
= ( ( member_Secrecy_Keys @ A @ B )
| ( member_Secrecy_Keys @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_Un__iff) ).
thf(799,plain,
! [A: secrecy_Keys,B: set_Secrecy_Keys,C: set_Secrecy_Keys] :
( ( member_Secrecy_Keys @ A @ ( sup_su552545507y_Keys @ B @ C ) )
= ( ( member_Secrecy_Keys @ A @ B )
| ( member_Secrecy_Keys @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(255,axiom,
( ine
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member1967978193chanID @ C @ ( ins @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_ine__def) ).
thf(1162,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)],[255]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_351_correctCompositionOut__prop1) ).
thf(626,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)],[115]) ).
thf(191,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_KS_Oinject_I2_J) ).
thf(915,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',fact_227_LocalSecretsComposition__neg__k) ).
thf(1198,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)],[264]) ).
thf(43,axiom,
! [A: set_Secrecy_Keys,B: secrecy_Keys] :
( ( A = bot_bo701486667y_Keys )
=> ~ ( member_Secrecy_Keys @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_equals0D) ).
thf(399,plain,
! [A: set_Secrecy_Keys,B: secrecy_Keys] :
( ( A = bot_bo701486667y_Keys )
=> ~ ( member_Secrecy_Keys @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(118,axiom,
! [A: secrecy_Secrets,B: nat] :
( ( secrecy_sE @ A )
!= ( secrecy_dE @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Expression_Odistinct_I7_J) ).
thf(636,plain,
! [A: secrecy_Secrets,B: nat] :
( ( secrecy_sE @ A )
!= ( secrecy_dE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',fact_337_TBtheorem5b__notP1) ).
thf(883,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)],[181]) ).
thf(95,axiom,
( bot_bo443197316chanID
= ( collec625564175chanID @ bot_bo1012329985anID_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_bot__set__def) ).
thf(563,plain,
( bot_bo443197316chanID
= ( collec625564175chanID @ bot_bo1012329985anID_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',fact_319_TBtheorem5a__empty) ).
thf(653,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)],[122]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',fact_199_LocalSecretsComposition__neg__loc__s) ).
thf(922,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)],[193]) ).
thf(190,axiom,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_singleton__iff) ).
thf(912,plain,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',fact_343_eoutKnowCorrect__L1s) ).
thf(685,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)],[132]) ).
thf(258,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/sandbox2/benchmark/theBenchmark.p',fact_175_ine__empty__exprChannelSet) ).
thf(1171,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)],[258]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_286_Un__left__commute) ).
thf(505,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)],[76]) ).
thf(53,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_sup__bot_Oright__neutral) ).
thf(438,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',fact_23_ineM__def) ).
thf(722,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)],[141]) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',fact_340_not__know__k__not__eout) ).
thf(1208,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)],[266]) ).
thf(84,axiom,
! [A: set_Secrecy_chanID] :
( ( collec625564175chanID
@ ^ [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__mem__eq) ).
thf(531,plain,
! [A: set_Secrecy_chanID] :
( ( collec625564175chanID
@ ^ [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(161,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ B )
!= bot_bo1785112429specID ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_insert__not__empty) ).
thf(795,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ B )
!= bot_bo1785112429specID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(124,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_KS_Oinject_I1_J) ).
thf(663,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',fact_336_TBtheorem5b__notP2) ).
thf(812,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)],[167]) ).
thf(234,axiom,
! [A: secrecy_Expression] :
( ! [B: secrecy_Keys] :
( A
!= ( secrecy_kE @ B ) )
=> ( ! [B: secrecy_Secrets] :
( A
!= ( secrecy_sE @ B ) )
=> ( ! [B: nat] :
( A
!= ( secrecy_dE @ B ) )
=> ~ ! [B: secrecy_specID] :
( A
!= ( secrecy_idE @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Expression_Oexhaust) ).
thf(1081,plain,
! [A: secrecy_Expression] :
( ! [B: secrecy_Keys] :
( A
!= ( secrecy_kE @ B ) )
=> ( ! [B: secrecy_Secrets] :
( A
!= ( secrecy_sE @ B ) )
=> ( ! [B: nat] :
( A
!= ( secrecy_dE @ B ) )
=> ~ ! [B: secrecy_specID] :
( A
!= ( secrecy_idE @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(79,axiom,
! [A: set_Secrecy_specID] :
( ( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A ) )
= ( A = bot_bo1785112429specID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_all__not__in__conv) ).
thf(516,plain,
! [A: set_Secrecy_specID] :
( ( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A ) )
= ( A = bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',fact_205_correctCompositionKS__negQ) ).
thf(939,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)],[198]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_248_Un__insert__right) ).
thf(342,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)],[25]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_251_Un__insert__left) ).
thf(553,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)],[91]) ).
thf(82,axiom,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_empty__iff) ).
thf(525,plain,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',fact_283_Un__left__absorb) ).
thf(1003,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)],[216]) ).
thf(101,axiom,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_emptyE) ).
thf(580,plain,
! [A: secrecy_specID] :
~ ( member740727610specID @ A @ bot_bo1785112429specID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(134,axiom,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ ( insert1671894227specID @ A @ B ) )
= ( insert1671894227specID @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__absorb2) ).
thf(690,plain,
! [A: secrecy_specID,B: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ ( insert1671894227specID @ A @ B ) )
= ( insert1671894227specID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',fact_31_correctCompositionIn__prop1) ).
thf(640,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)],[119]) ).
thf(10,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_sup__bot__right) ).
thf(295,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(182,axiom,
! [A: set_Secrecy_chanID,B: secrecy_chanID] :
( ( A = bot_bo443197316chanID )
=> ~ ( member1967978193chanID @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_equals0D) ).
thf(887,plain,
! [A: set_Secrecy_chanID,B: secrecy_chanID] :
( ( A = bot_bo443197316chanID )
=> ~ ( member1967978193chanID @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',fact_124_insert__ident) ).
thf(414,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)],[47]) ).
thf(45,axiom,
! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
( ( ( sup_su370684444chanID @ A @ B )
= bot_bo443197316chanID )
= ( ( A = bot_bo443197316chanID )
& ( B = bot_bo443197316chanID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Un__empty) ).
thf(409,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)],[45]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',fact_152_doubleton__eq__iff) ).
thf(673,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)],[128]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',fact_329_out__exprChannelSet__Single) ).
thf(331,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)],[22]) ).
thf(54,axiom,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
= ( ( A = B )
| ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_insert__iff) ).
thf(441,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)],[54]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_242_Un__iff) ).
thf(463,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)],[62]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',fact_114_insert__eq__iff) ).
thf(338,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)],[24]) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',fact_194_LocalSecretsComposition__ine2__s) ).
thf(1085,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)],[235]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',fact_35_TBtheorem1a) ).
thf(1218,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)],[269]) ).
thf(148,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Expression_Oinject_I2_J) ).
thf(744,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(136,axiom,
! [A: secrecy_Keys,B: secrecy_Keys > $o] :
( ( member_Secrecy_Keys @ A @ ( collect_Secrecy_Keys @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(703,plain,
! [A: secrecy_Keys,B: secrecy_Keys > $o] :
( ( member_Secrecy_Keys @ A @ ( collect_Secrecy_Keys @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(219,axiom,
! [A: set_Secrecy_Keys] :
( ( A != bot_bo701486667y_Keys )
=> ( ! [B: secrecy_Keys,C: secrecy_Keys] :
( ( member_Secrecy_Keys @ B @ A )
=> ( ( member_Secrecy_Keys @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1096471309y_Keys @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_is__singletonI_H) ).
thf(1023,plain,
! [A: set_Secrecy_Keys] :
( ( A != bot_bo701486667y_Keys )
=> ( ! [B: secrecy_Keys,C: secrecy_Keys] :
( ( member_Secrecy_Keys @ B @ A )
=> ( ( member_Secrecy_Keys @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1096471309y_Keys @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(226,axiom,
! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
( ( ineM @ A @ B @ C )
=> ( ine @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ineM__ine) ).
thf(1052,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)],[226]) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',fact_25_TBtheorem1b) ).
thf(978,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)],[210]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_354_adv__not__know2) ).
thf(612,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)],[111]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',fact_342_eout__know__nonKS__s) ).
thf(876,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)],[178]) ).
thf(56,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_insertI1) ).
thf(446,plain,
! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(98,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_sup__bot_Oleft__neutral) ).
thf(571,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',fact_348_eoutM__def) ).
thf(556,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)],[92]) ).
thf(196,axiom,
! [A: set_Secrecy_chanID] :
( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A )
=> ( A = bot_bo443197316chanID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_equals0I) ).
thf(931,plain,
! [A: set_Secrecy_chanID] :
( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A )
=> ( A = bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',fact_173_ine__exprChannelSingle__Set) ).
thf(671,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)],[127]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',fact_233_UnCI) ).
thf(495,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)],[72]) ).
thf(246,axiom,
! [A: secrecy_Expression > $o,B: secrecy_Expression] :
( ! [C: secrecy_Keys] : ( A @ ( secrecy_kE @ C ) )
=> ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sE @ C ) )
=> ( ! [C: nat] : ( A @ ( secrecy_dE @ C ) )
=> ( ! [C: secrecy_specID] : ( A @ ( secrecy_idE @ C ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Expression_Oinduct) ).
thf(1126,plain,
! [A: secrecy_Expression > $o,B: secrecy_Expression] :
( ! [C: secrecy_Keys] : ( A @ ( secrecy_kE @ C ) )
=> ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sE @ C ) )
=> ( ! [C: nat] : ( A @ ( secrecy_dE @ C ) )
=> ( ! [C: secrecy_specID] : ( A @ ( secrecy_idE @ C ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',fact_52_LocalSecretsComposition__ine2__k) ).
thf(1108,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)],[240]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_275_ball__Un) ).
thf(588,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)],[104]) ).
thf(18,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( ( A = B )
| ( member740727610specID @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_insert__iff) ).
thf(319,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)],[18]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_212_know__composition1) ).
thf(946,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)],[200]) ).
thf(28,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_insertI2) ).
thf(351,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)],[28]) ).
thf(40,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( ( sup_su1712599557specID @ A @ B )
= bot_bo1785112429specID )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_sup__bot_Oeq__neutr__iff) ).
thf(390,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)],[40]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',fact_226_LocalSecretsComposition__neg__s) ).
thf(1244,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)],[273]) ).
thf(213,axiom,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_singletonD) ).
thf(995,plain,
! [A: secrecy_specID,B: secrecy_specID] :
( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',fact_322_TBtheorem2a) ).
thf(731,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)],[144]) ).
thf(48,axiom,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_sup__bot__left) ).
thf(418,plain,
! [A: set_Secrecy_specID] :
( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_222_correctCompositionKS__exprChannel__s__P) ).
thf(786,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)],[159]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_278_Un__assoc) ).
thf(478,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)],[67]) ).
thf(38,axiom,
! [A: set_Secrecy_specID] :
( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A )
=> ( A = bot_bo1785112429specID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_equals0I) ).
thf(383,plain,
! [A: set_Secrecy_specID] :
( ! [B: secrecy_specID] :
~ ( member740727610specID @ B @ A )
=> ( A = bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(139,axiom,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_empty__iff) ).
thf(716,plain,
! [A: secrecy_chanID] :
~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(51,axiom,
! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ B )
=> ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_UnI2) ).
thf(432,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)],[51]) ).
thf(201,axiom,
! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_singletonI) ).
thf(950,plain,
! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(168,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/sandbox2/benchmark/theBenchmark.p',fact_345_TBtheorem5b__PQ) ).
thf(818,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)],[168]) ).
thf(145,axiom,
( eout
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member1967978193chanID @ C @ ( out @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_eout__def) ).
thf(735,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)],[145]) ).
thf(13,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_Un__absorb) ).
thf(305,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_sup__bot__left) ).
thf(326,plain,
! [A: set_Secrecy_chanID] :
( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',fact_166_TBtheorem4b__notP1) ).
thf(918,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)],[192]) ).
thf(165,axiom,
! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_singletonI) ).
thf(807,plain,
! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',fact_326_TBtheorem5a__notP2) ).
thf(828,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)],[169]) ).
thf(203,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/sandbox2/benchmark/theBenchmark.p',fact_273_bex__Un) ).
thf(955,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)],[203]) ).
thf(6,axiom,
! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
=> ( ( A != B )
=> ( member1967978193chanID @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_insertE) ).
thf(283,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)],[6]) ).
thf(195,axiom,
! [A: secrecy_chanID > $o] :
( ( ( collec625564175chanID @ A )
= bot_bo443197316chanID )
= ( ! [B: secrecy_chanID] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Collect__empty__eq) ).
thf(928,plain,
! [A: secrecy_chanID > $o] :
( ( ( collec625564175chanID @ A )
= bot_bo443197316chanID )
= ( ! [B: secrecy_chanID] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',fact_170_TBtheorem4a__notPQ) ).
thf(1093,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)],[237]) ).
thf(247,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_not__know__k__not__ine) ).
thf(1129,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)],[247]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_84_TBtheorem4a__empty) ).
thf(1152,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)],[253]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',fact_327_TBtheorem5a__notPQ) ).
thf(860,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)],[175]) ).
thf(83,axiom,
! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
( ( bot_bo1785112429specID
= ( sup_su1712599557specID @ A @ B ) )
= ( ( A = bot_bo1785112429specID )
& ( B = bot_bo1785112429specID ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_bot__eq__sup__iff) ).
thf(528,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)],[83]) ).
thf(120,axiom,
! [A: set_Secrecy_chanID] :
( ( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A ) )
= ( A = bot_bo443197316chanID ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_all__not__in__conv) ).
thf(644,plain,
! [A: set_Secrecy_chanID] :
( ( ! [B: secrecy_chanID] :
~ ( member1967978193chanID @ B @ A ) )
= ( A = bot_bo443197316chanID ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(211,axiom,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_Un__absorb) ).
thf(982,plain,
! [A: set_Secrecy_KS] :
( ( sup_su1301156759ecy_KS @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_349_out__exprChannelSet__def) ).
thf(501,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)],[74]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_238_Un__iff) ).
thf(369,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)],[34]) ).
thf(143,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ C ) )
= ( insert1671894227specID @ B @ ( insert1671894227specID @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_insert__commute) ).
thf(728,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)],[143]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',fact_204_correctCompositionKS__negP) ).
thf(740,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)],[147]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_123_insert__ident) ).
thf(322,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(64,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/sandbox2/benchmark/theBenchmark.p',fact_246_Un__insert__right) ).
thf(469,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)],[64]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_323_correctCompositionKS__subcomp4) ).
thf(354,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)],[29]) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',fact_24_TBlemma3b) ).
thf(935,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)],[197]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',fact_28_correctCompositionIn__L2) ).
thf(659,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)],[123]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_321_correctCompositionKS__subcomp2) ).
thf(543,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)],[88]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',fact_113_insert__eq__iff) ).
thf(491,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)],[71]) ).
thf(59,axiom,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
= ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_singleton__inject) ).
thf(454,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)],[59]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',fact_258_UnE) ).
thf(364,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)],[32]) ).
thf(208,axiom,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_singleton__iff) ).
thf(972,plain,
! [A: secrecy_chanID,B: secrecy_chanID] :
( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(221,axiom,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
( A
= ( insert1671894227specID @ ( the_el827131246specID @ A ) @ bot_bo1785112429specID ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_is__singleton__the__elem) ).
thf(1037,plain,
( is_sin1501507247specID
= ( ^ [A: set_Secrecy_specID] :
( A
= ( insert1671894227specID @ ( the_el827131246specID @ A ) @ bot_bo1785112429specID ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',fact_32_LocalSecretsComposition1) ).
thf(775,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)],[156]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_266_UnI1) ).
thf(755,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)],[150]) ).
thf(129,axiom,
( bot_bo2072920570Keys_o
= ( ^ [A: secrecy_Keys] : ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_bot__empty__eq) ).
thf(676,plain,
( bot_bo2072920570Keys_o
= ( ^ [A: secrecy_Keys] : ( member_Secrecy_Keys @ A @ bot_bo701486667y_Keys ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1311,plain,
$false,
inference(cvc4,[status(thm)],[892,809,1105,347,962,1179,666,481,909,333,1031,276,308,1073,1142,878,597,1158,762,550,1164,472,747,1222,404,898,1001,1046,301,565,1228,724,719,372,802,1132,460,619,838,357,1191,770,881,1115,289,448,316,421,870,969,606,475,591,376,485,1136,834,1020,574,766,687,634,1119,396,998,292,380,678,925,366,534,1067,1057,952,1123,561,424,1238,693,630,361,329,1210,1079,710,852,435,583,522,682,1195,519,1089,874,615,1121,1006,783,488,537,1214,1039,547,706,901,1075,622,393,647,985,1131,457,569,779,503,805,508,311,1054,1167,1185,586,1202,792,558,1071,906,298,412,965,513,1103,279,444,601,772,286,577,958,281,904,975,1139,313,498,466,540,604,274,1048,451,737,1043,599,1175,387,758,848,895,943,668,1112,345,858,799,1162,626,915,1198,399,636,883,563,653,922,912,685,1171,505,438,722,1208,531,795,663,812,1081,516,939,342,553,525,1003,580,690,640,295,887,414,409,673,331,441,463,338,1085,1218,744,703,1023,1052,978,612,876,446,571,556,931,671,495,1126,1108,588,319,946,351,390,1244,995,731,418,786,478,383,716,432,950,818,735,305,326,918,807,828,955,283,928,1093,1129,1152,860,528,644,982,501,369,728,740,322,469,354,935,659,543,491,454,364,972,1037,775,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP088^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n004.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 6 14:33:54 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.14 % [INFO] Parsing done (255ms).
% 1.61/1.15 % [INFO] Running in sequential loop mode.
% 2.72/1.35 % [INFO] eprover registered as external prover.
% 2.72/1.35 % [INFO] cvc4 registered as external prover.
% 2.72/1.36 % [INFO] Scanning for conjecture ...
% 3.02/1.45 % [INFO] Found a conjecture and 355 axioms. Running axiom selection ...
% 3.48/1.56 % [INFO] Axiom selection finished. Selected 271 axioms (removed 84 axioms).
% 3.95/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 4.28/1.77 % [INFO] Type checking passed.
% 4.28/1.77 % [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 ...
% 25.39/6.53 % External prover 'cvc4' found a proof!
% 25.39/6.53 % [INFO] Killing All external provers ...
% 25.39/6.53 % Time passed: 5984ms (effective reasoning time: 5377ms)
% 25.39/6.53 % 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)>
% 25.39/6.54 % Axioms used in derivation (271): fact_303_sup__bot_Oleft__neutral, fact_54_TBtheorem4b__P, fact_124_insert__ident, fact_30_Expression_Oexhaust, fact_342_eout__know__nonKS__s, fact_223_correctCompositionKS__exprChannel__s__Q, fact_233_UnCI, fact_56_TBtheorem4a__P, fact_207_is__singletonI_H, fact_144_insertE, fact_76_all__not__in__conv, fact_283_Un__left__absorb, fact_64_insert__iff, fact_28_correctCompositionIn__L2, fact_104_emptyE, fact_328_out__exprChannelSingle__Set, fact_9_KS2Expression_Osimps_I1_J, fact_198_is__singletonI, fact_323_correctCompositionKS__subcomp4, fact_39_singletonI, fact_190_KS2Expression_Osimps_I2_J, fact_229_bot__empty__eq, fact_138_insertI1, fact_41_mem__Collect__eq, fact_344_TBtheore54b__P, fact_60_insertCI, fact_284_Un__left__absorb, fact_170_TBtheorem4a__notPQ, fact_98_equals0D, fact_113_insert__eq__iff, fact_118_insert__absorb, fact_276_ball__Un, fact_248_Un__insert__right, fact_5_not__know__k__not__ine, fact_291_Un__singleton__iff, fact_175_ine__empty__exprChannelSet, fact_193_LocalSecretsComposition__neg1__s, fact_337_TBtheorem5b__notP1, fact_189_KS_Odistinct_I1_J, fact_89_ex__in__conv, fact_17_Expression_Oinject_I3_J, fact_237_UnCI, fact_271_UnI2, fact_171_TBtheorem4a__notP2, fact_317_ineM__Un1, fact_21_ineM__L1, fact_326_TBtheorem5a__notP2, fact_316_bot__eq__sup__iff, fact_86_ex__in__conv, fact_298_sup__bot_Oright__neutral, fact_254_Un__empty__right, fact_297_sup__bot_Oright__neutral, fact_31_correctCompositionIn__prop1, fact_278_Un__assoc, fact_238_Un__iff, fact_199_LocalSecretsComposition__neg__loc__s, fact_259_UnE, fact_236_UnCI, fact_164_correctCompositionInLoc__exprChannel, fact_352_TBtheorem5a__PQ, fact_334_not__eout__eoutM, fact_211_know__composition, fact_205_correctCompositionKS__negQ, fact_318_notSpecKeysSecretsExpr__def, fact_94_equals0I, fact_96_equals0D, fact_217_is__singleton__def, fact_0_assms_I4_J, fact_183_LocalSecretsComposition__ine1__s, fact_279_Un__absorb, fact_52_LocalSecretsComposition__ine2__k, fact_148_singleton__inject, fact_322_TBtheorem2a, fact_119_insert__absorb, fact_123_insert__ident, fact_7_Expression_Odistinct_I5_J, fact_288_singleton__Un__iff, fact_262_UnE, fact_251_Un__insert__left, fact_65_insert__iff, fact_29_Expression_Oinduct, fact_46_Collect__mem__eq, fact_349_out__exprChannelSet__def, fact_182_the__elem__eq, fact_239_Un__iff, fact_244_Un__empty, fact_281_Un__commute, fact_133_insertI2, fact_285_Un__left__commute, fact_82_insert__absorb2, fact_24_TBlemma3b, fact_167_TBtheorem4a__notP1, fact_275_ball__Un, fact_213_know__composition2, fact_40_singletonI, fact_222_correctCompositionKS__exprChannel__s__P, fact_110_insert__commute, fact_263_UnI1, fact_12_LocalSecretsComposition__exprChannel__k, fact_227_LocalSecretsComposition__neg__k, fact_306_sup__bot_Oeq__neutr__iff, fact_324_correctCompositionKS__subcomp3, fact_8_Expression_Odistinct_I3_J, fact_3_assms_I3_J, fact_286_Un__left__commute, fact_294_insert__is__Un, fact_172_ine__exprChannelSet__Single, fact_300_sup__bot_Oneutr__eq__iff, fact_218_correctCompositionKS__exprChannel__k__P, fact_295_insert__is__Un, fact_267_UnI1, fact_320_correctCompositionKS__subcomp1, fact_153_doubleton__eq__iff, fact_340_not__know__k__not__eout, fact_346_TBtheorem45a__P, fact_345_TBtheorem5b__PQ, fact_301_sup__bot_Oneutr__eq__iff, fact_341_eout__know__k, fact_150_insert__not__empty, fact_321_correctCompositionKS__subcomp2, fact_202_correctCompositionKS__PQ, fact_309_sup__bot__left, fact_179_locStream__def, fact_103_emptyE, fact_261_UnE, fact_18_Expression_Odistinct_I11_J, fact_73_all__not__in__conv, fact_6_know_Osimps_I1_J, fact_195_is__singleton__the__elem, fact_35_TBtheorem1a, fact_258_UnE, fact_273_bex__Un, fact_14_KS_Oinject_I1_J, fact_220_correctCompositionKS__exprChannel__k__Pex, fact_180_inStream__def, fact_187_KS_Oexhaust, fact_88_ex__in__conv, fact_83_insert__absorb2, fact_191_not__know__s__not__ine, fact_163_singletonD, fact_188_KS_Oinduct, fact_312_sup__bot__right, fact_11_not__ine__ineM, fact_107_mk__disjoint__insert, fact_91_equals0I, fact_277_Un__assoc, fact_329_out__exprChannelSet__Single, fact_173_ine__exprChannelSingle__Set, fact_69_empty__Collect__eq, fact_269_UnI2, fact_81_empty__iff, fact_33_LocalSecretsComposition__exprChannel__s, fact_266_UnI1, fact_219_correctCompositionKS__exprChannel__k__Q, fact_177_ine__exprChannelSingle__def, fact_333_eoutM__eout, fact_234_UnCI, fact_338_eout__know__nonKS__k, fact_143_insertE, fact_55_TBtheorem4b__PQ, fact_1_assms_I2_J, fact_216_is__singleton__def, fact_157_singleton__iff, fact_78_empty__iff, fact_93_equals0I, fact_307_sup__bot_Oeq__neutr__iff, fact_174_ine__nonempty__exprChannelSet, fact_272_UnI2, fact_169_TBtheorem4b__notP2, fact_241_Un__iff, fact_268_UnI2, fact_212_know__composition1, fact_336_TBtheorem5b__notP2, fact_280_Un__absorb, fact_84_TBtheorem4a__empty, fact_99_equals0D, fact_186_bot__set__def, fact_75_all__not__in__conv, fact_347_eout__def, fact_15_Expression_Oinject_I2_J, fact_23_ineM__def, fact_351_correctCompositionOut__prop1, fact_274_bex__Un, fact_196_is__singleton__the__elem, fact_203_correctCompositionKS__neg1, fact_134_insertI2, fact_168_TBtheorem4b__notPQ, fact_158_singleton__iff, fact_313_sup__bot__right, fact_319_TBtheorem5a__empty, fact_101_emptyE, fact_214_is__singletonE, fact_16_Expression_Oinject_I4_J, fact_4_Expression_Oinject_I1_J, fact_209_is__singletonI_H, fact_245_Un__empty, fact_339_eoutKnowCorrect__L1k, fact_226_LocalSecretsComposition__neg__s, fact_224_correctCompositionKS__exprChannel__s__Pex, fact_256_Un__empty__left, fact_49_Collect__mem__eq, fact_128_Set_Oset__insert, fact_19_Expression_Odistinct_I9_J, fact_47_Collect__mem__eq, fact_129_Set_Oset__insert, fact_331_eout__know__s, fact_335_TBtheorem2b, fact_354_adv__not__know2, fact_106_mk__disjoint__insert, fact_325_TBtheorem5a__notP1, fact_139_insertI1, fact_194_LocalSecretsComposition__ine2__s, fact_162_singletonD, fact_327_TBtheorem5a__notPQ, fact_197_is__singletonI, fact_221_correctCompositionKS__exprChannel__k__Qex, fact_192_know_Osimps_I2_J, fact_249_Un__insert__left, fact_152_doubleton__eq__iff, fact_348_eoutM__def, fact_147_correctCompositionIn__L1, fact_13_Expression_Odistinct_I1_J, fact_204_correctCompositionKS__negP, fact_210_is__singletonI_H, fact_80_empty__iff, fact_151_insert__not__empty, fact_242_Un__iff, fact_350_out__exprChannelSingle__def, fact_201_correctCompositionKS__exprChannel__s__Qex, fact_34_TBtheorem3a, fact_166_TBtheorem4b__notP1, fact_114_insert__eq__iff, fact_111_insert__commute, fact_253_Un__empty__right, fact_264_UnI1, fact_149_singleton__inject, fact_257_Un__empty__left, fact_2_assms_I1_J, fact_32_LocalSecretsComposition1, fact_25_TBtheorem1b, fact_332_not__know__s__not__eout, fact_71_Collect__empty__eq, fact_42_mem__Collect__eq, fact_27_ine__ins__neg1, fact_304_sup__bot_Oleft__neutral, fact_289_singleton__Un__iff, fact_176_ine__exprChannelSet__def, fact_22_ine__def, fact_343_eoutKnowCorrect__L1s, fact_165_subcomponents__loc, fact_26_TBtheorem3b, fact_51_LocalSecretsComposition__neg1__k, fact_10_ineM__ine, fact_215_is__singletonE, fact_178_LocalSecretsComposition__neg1, fact_200_LocalSecretsComposition__neg__loc__k, fact_315_bot__eq__sup__iff, fact_184_KS_Oinject_I2_J, fact_20_Expression_Odistinct_I7_J, fact_310_sup__bot__left, fact_181_the__elem__eq, fact_59_insertCI, fact_330_TBtheorem5b__notPQ, fact_292_Un__singleton__iff, fact_53_LocalSecretsComposition__ine1__k, fact_225_LocalSecretsComposition__neg, fact_44_mem__Collect__eq, fact_246_Un__insert__right, fact_232_bot__empty__eq, fact_282_Un__commute, fact_57_TBtheorem4a__PQ
% 25.39/6.54 % No. of inferences in proof: 546
% 25.39/6.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5984 ms resp. 5377 ms w/o parsing
% 25.86/6.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.86/6.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------