%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP091^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:43 AM UTC 2026
% Result : Theorem 44.62s 25.76s
% Output : Refutation 45.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 260
% Syntax : Number of formulae : 522 ( 182 unt; 0 typ; 0 def)
% Number of atoms : 2464 ( 534 equ; 8 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 8834 ( 437 ~; 72 |; 180 &;7085 @)
% ( 0 <=>;1060 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 94 ( 94 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 9 con; 0-4 aty)
% Number of variables : 1786 ( 90 ^;1638 !; 58 ?;1786 :)
% Comments :
%------------------------------------------------------------------------------
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(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(bounde1808546759up_bot_decl,type,
bounde1808546759up_bot:
!>[TA: $tType] : $o ).
thf(localSecrets_decl,type,
localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
thf(knowle1667810483orrect_decl,type,
knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
thf(knowle1437066798e_know_decl,type,
knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(mem_decl,type,
mem:
!>[TA: $tType] : ( TA > ( list @ TA ) > $o ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(correctCompositionKS_decl,type,
correctCompositionKS: secrecy_specID > $o ).
thf(eout_decl,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(eoutM_decl,type,
eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
thf(exprChannel_decl,type,
exprChannel: secrecy_chanID > secrecy_Expression > $o ).
thf(ine_decl,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(ineM_decl,type,
ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
thf(ine_exprChannelSet_decl,type,
ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
thf(ine_ex1303305700Single_decl,type,
ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(notSpe1586871396tsExpr_decl,type,
notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
thf(out_exprChannelSet_decl,type,
out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
thf(out_ex985543062Single_decl,type,
out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
thf(specKeys_decl,type,
specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
thf(specKeysSecrets_decl,type,
specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
thf(specSecrets_decl,type,
specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
thf(secrecy_kE_decl,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(secrecy_sE_decl,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(secrec1016742679ession_decl,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(secrecy_case_KS_decl,type,
secrecy_case_KS:
!>[TA: $tType] : ( ( secrecy_Keys > TA ) > ( secrecy_Secrets > TA ) > secrecy_KS > TA ) ).
thf(secrecy_kKS_decl,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(secrecy_rec_KS_decl,type,
secrecy_rec_KS:
!>[TA: $tType] : ( ( secrecy_Keys > TA ) > ( secrecy_Secrets > TA ) > secrecy_KS > TA ) ).
thf(secrecy_sKS_decl,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_decl,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_decl,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(correctCompositionIn_decl,type,
correctCompositionIn: secrecy_specID > $o ).
thf(correc965049635ionLoc_decl,type,
correc965049635ionLoc: secrecy_specID > $o ).
thf(correc990227761ionOut_decl,type,
correc990227761ionOut: secrecy_specID > $o ).
thf(inStream_decl,type,
inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
thf(ins_decl,type,
ins: secrecy_specID > ( set @ secrecy_chanID ) ).
thf(loc_decl,type,
loc: secrecy_specID > ( set @ secrecy_chanID ) ).
thf(locStream_decl,type,
locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
thf(out_decl,type,
out: secrecy_specID > ( set @ secrecy_chanID ) ).
thf(outStream_decl,type,
outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
thf(subcomponents_decl,type,
subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_decl,type,
p: secrecy_specID ).
thf(pq_decl,type,
pq: secrecy_specID ).
thf(q_decl,type,
q: secrecy_specID ).
thf(m_decl,type,
m: secrecy_KS ).
thf(secret_decl,type,
secret: secrecy_Secrets ).
thf(188,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( out @ B ) )
| ( member @ secrecy_chanID @ D @ ( out @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_correctCompositionOut__prop1) ).
thf(892,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( out @ B ) )
| ( member @ secrecy_chanID @ D @ ( out @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(172,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 )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ( G
= ( sup_sup @ ( set @ secrecy_chanID ) @ D @ F ) )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ D )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ F )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_TBtheorem5b__notPQ) ).
thf(809,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 )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ( G
= ( sup_sup @ ( set @ secrecy_chanID ) @ D @ F ) )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ D )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ F )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_singleton__insert__inj__eq) ).
thf(628,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(73,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_13) ).
thf(481,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(71,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_17) ).
thf(479,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(238,axiom,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ A @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( member @ secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_LocalSecretsComposition1) ).
thf(1105,plain,
! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ A @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( member @ secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(184,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_emptyE) ).
thf(873,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_bex__Un) ).
thf(861,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(186,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ F @ ( out @ A ) )
| ( member @ secrecy_chanID @ F @ ( out @ D ) ) )
& ( member @ secrecy_chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ( eoutM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_TBtheorem5b__PQ) ).
thf(878,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ F @ ( out @ A ) )
| ( member @ secrecy_chanID @ F @ ( out @ D ) ) )
& ( member @ secrecy_chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ( eoutM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(83,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Un__insert__right) ).
thf(511,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(118,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_subset__insertI) ).
thf(614,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_le__funI) ).
thf(269,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_insert__not__empty) ).
thf(385,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(247,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 ) )
=> ( ( ( knowle1437066798e_know @ B @ A )
| ( knowle1437066798e_know @ C @ A ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_know__composition) ).
thf(1137,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 ) )
=> ( ( ( knowle1437066798e_know @ B @ A )
| ( knowle1437066798e_know @ C @ A ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(90,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_equalityD2) ).
thf(533,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(97,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Un__commute) ).
thf(550,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(146,axiom,
( out_ex985543062Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member @ secrecy_chanID @ B @ ( out @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID,E: nat] :
( ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_out__exprChannelSingle__def) ).
thf(715,plain,
( out_ex985543062Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member @ secrecy_chanID @ B @ ( out @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(235,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_subset__eq) ).
thf(1095,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(260,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Keys @ C @ ( specKeys @ B ) )
=> ( member @ secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_correctCompositionKS__subcomp3) ).
thf(1196,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Keys @ C @ ( specKeys @ B ) )
=> ( member @ secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_subset__singleton__iff) ).
thf(417,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_10) ).
thf(301,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_subset__antisym) ).
thf(436,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(148,axiom,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_KS2Expression_Osimps_I2_J) ).
thf(719,plain,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(81,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Expression_Odistinct_I1_J) ).
thf(504,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(120,axiom,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_KS_Osimps_I5_J) ).
thf(619,plain,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(30,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_sup__bot_Oright__neutral) ).
thf(357,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
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 ) )
=> ( ( knowle1437066798e_know @ C @ A )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_know__composition2) ).
thf(949,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 ) )
=> ( ( knowle1437066798e_know @ C @ A )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(93,axiom,
bounde1808546759up_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12) ).
thf(542,plain,
bounde1808546759up_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(194,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( out_ex985543062Single @ A @ F @ C )
& ( member @ secrecy_chanID @ F @ B )
& ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_TBtheorem5b__notP1) ).
thf(917,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ E )
=> ( ? [F: secrecy_chanID] :
( ( out_ex985543062Single @ A @ F @ C )
& ( member @ secrecy_chanID @ F @ B )
& ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(143,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_all__not__in__conv) ).
thf(702,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(127,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Collect__empty__eq__bot) ).
thf(638,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(204,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_correctCompositionKS__exprChannel__s__Q) ).
thf(969,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_bot__fun__def) ).
thf(325,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_eq__refl) ).
thf(289,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: set @ secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ~ ( ineM @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_not__ine__ineM) ).
thf(448,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)],[61]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_singleton__inject) ).
thf(443,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(37,axiom,
( inStream
= ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( ins @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_inStream__def) ).
thf(376,plain,
( inStream
= ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( ins @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insert__absorb2) ).
thf(514,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(106,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_empty__Collect__eq) ).
thf(574,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(222,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
= ( ( ine @ A @ ( secrecy_sE @ B ) )
| ( member @ secrecy_KS @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_know_Osimps_I2_J) ).
thf(1040,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle1437066798e_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)],[222]) ).
thf(239,axiom,
( ine
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member @ secrecy_chanID @ C @ ( ins @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_ine__def) ).
thf(1109,plain,
( ine
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member @ secrecy_chanID @ C @ ( ins @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(75,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_sup__bot__right) ).
thf(485,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(176,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ! [E: secrecy_Keys] :
( ( D
= ( secrecy_kKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
& ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
=> ( ! [E: secrecy_Secrets] :
( ( D
= ( secrecy_sKS @ E ) )
=> ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
& ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
=> ( ~ ( member @ secrecy_KS @ D @ ( localSecrets @ B ) )
=> ( ~ ( member @ secrecy_KS @ D @ ( localSecrets @ C ) )
=> ~ ( member @ secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_LocalSecretsComposition__neg1) ).
thf(834,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[176]) ).
thf(191,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_singleton__iff) ).
thf(905,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(72,axiom,
correc965049635ionLoc @ pq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_cCompLoc) ).
thf(480,plain,
correc965049635ionLoc @ pq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(45,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(397,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(153,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 )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ D )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ F )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_TBtheorem4b__notPQ) ).
thf(734,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 )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ D )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ( ! [H: secrecy_chanID] :
( ( member @ secrecy_chanID @ H @ F )
=> ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
=> ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_ord__le__eq__trans) ).
thf(293,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(182,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_subset__iff) ).
thf(866,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(162,axiom,
~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_a22) ).
thf(774,plain,
~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_ex__in__conv) ).
thf(988,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Un__assoc) ).
thf(527,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(229,axiom,
! [A: secrecy_KS] :
( ! [B: secrecy_Keys] :
( A
!= ( secrecy_kKS @ B ) )
=> ~ ! [B: secrecy_Secrets] :
( A
!= ( secrecy_sKS @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_KS_Oexhaust) ).
thf(1072,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)],[229]) ).
thf(63,axiom,
! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle1437066798e_know @ A @ B )
=> ( ~ ( knowle1437066798e_know @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ D )
=> ( ( correctCompositionIn @ D )
=> ~ ( knowle1437066798e_know @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_know__composition__neg1) ).
thf(453,plain,
! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle1437066798e_know @ A @ B )
=> ( ~ ( knowle1437066798e_know @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ D )
=> ( ( correctCompositionIn @ D )
=> ~ ( knowle1437066798e_know @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(39,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_sup__bot_Oleft__neutral) ).
thf(380,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(57,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Un__left__absorb) ).
thf(439,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(135,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ( ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
| ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_correctCompositionKS__PQ) ).
thf(678,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[135]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Un__empty) ).
thf(546,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(261,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_correctCompositionKS__exprChannel__k__Q) ).
thf(1199,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(158,axiom,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_KS_Osimps_I8_J) ).
thf(761,plain,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(33,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_empty__subsetI) ).
thf(366,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(225,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
| ( member @ secrecy_chanID @ F @ ( ins @ D ) ) )
& ( member @ secrecy_chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ( ineM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_TBtheorem4b__PQ) ).
thf(1047,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
| ( member @ secrecy_chanID @ F @ ( ins @ D ) ) )
& ( member @ secrecy_chanID @ F @ B )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ( ineM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(171,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ D )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ~ ( eout @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_TBtheorem5a__notPQ) ).
thf(798,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( out_exprChannelSet @ B @ D @ E )
=> ( ( out_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ D )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ~ ( eout @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(252,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member @ secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_LocalSecretsComposition__neg) ).
thf(1163,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member @ secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(26,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_le__cases3) ).
thf(334,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(202,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_correctCompositionKS__exprChannel__k__Qex) ).
thf(957,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(234,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ B ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ C ) )
=> ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_LocalSecretsComposition__neg1__k) ).
thf(1091,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[234]) ).
thf(215,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ A )
=> ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
=> ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ B ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ C ) )
=> ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_LocalSecretsComposition__neg1__s) ).
thf(1021,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[215]) ).
thf(27,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_11) ).
thf(349,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(253,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_equals0I) ).
thf(1174,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(113,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_KS_Oinject_I1_J) ).
thf(598,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(43,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_subset__insertI2) ).
thf(392,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(297,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(48,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_sup__eq__bot__iff) ).
thf(407,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(168,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_insertI2) ).
thf(788,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_insert__eq__iff) ).
thf(729,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(68,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ( loc @ D )
= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_TBtheorem4a__empty) ).
thf(467,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ( loc @ D )
= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(219,axiom,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_KS_Osimps_I6_J) ).
thf(1032,plain,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(122,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Un__empty__left) ).
thf(625,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(132,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
=> ( ( exprChannel @ D @ E )
=> ( ! [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
=> ~ ( exprChannel @ F @ E ) )
=> ( member @ secrecy_chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_correctCompositionInLoc__exprChannel) ).
thf(665,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
=> ( ( exprChannel @ D @ E )
=> ( ! [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
=> ~ ( exprChannel @ F @ E ) )
=> ( member @ secrecy_chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(175,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
| ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_correctCompositionIn__L2) ).
thf(830,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
| ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_singletonD) ).
thf(889,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(66,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Collect__mono__iff) ).
thf(461,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(231,axiom,
( ine_exprChannelSet
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ B )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member @ secrecy_chanID @ D @ B )
& ( member @ secrecy_chanID @ D @ ( ins @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ine__exprChannelSet__def) ).
thf(1079,plain,
( ine_exprChannelSet
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ B )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member @ secrecy_chanID @ D @ B )
& ( member @ secrecy_chanID @ D @ ( ins @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(136,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insertE) ).
thf(682,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(10,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_le__cases) ).
thf(285,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_insertI1) ).
thf(1089,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ord__eq__le__subst) ).
thf(317,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(240,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_insert__absorb) ).
thf(1111,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(150,axiom,
! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
=> ( ~ ( knowle1437066798e_know @ C @ ( secrecy_sKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_know__composition__neg__ine__s) ).
thf(725,plain,
! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
=> ( ~ ( knowle1437066798e_know @ C @ ( secrecy_sKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(47,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eout @ C @ B )
| ( eout @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_TBtheorem2a) ).
thf(403,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eout @ C @ B )
| ( eout @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(211,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Keys @ C @ ( specKeys @ A ) )
=> ? [D: secrecy_specID] :
( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
& ( member @ secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_correctCompositionKS__subcomp1) ).
thf(1006,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Keys @ C @ ( specKeys @ A ) )
=> ? [D: secrecy_specID] :
( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
& ( member @ secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(42,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_equalityD1) ).
thf(388,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(183,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( out @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
& ( member @ secrecy_chanID @ F @ B ) )
=> ( eoutM @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_TBtheore54b__P) ).
thf(869,plain,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( out @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
& ( member @ secrecy_chanID @ F @ B ) )
=> ( eoutM @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(52,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_subset__singletonD) ).
thf(420,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(242,axiom,
( out_exprChannelSet
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ B )
=> ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member @ secrecy_chanID @ D @ B )
& ( member @ secrecy_chanID @ D @ ( out @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_out__exprChannelSet__def) ).
thf(1118,plain,
( out_exprChannelSet
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ! [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ B )
=> ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
& ( exprChannel @ D @ C ) ) )
& ! [D: secrecy_chanID] :
( ( ~ ( member @ secrecy_chanID @ D @ B )
& ( member @ secrecy_chanID @ D @ ( out @ A ) ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(328,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(217,axiom,
( eoutM
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ ( out @ A ) )
& ( member @ secrecy_chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_eoutM__def) ).
thf(1028,plain,
( eoutM
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ ( out @ A ) )
& ( member @ secrecy_chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(76,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_insert__mono) ).
thf(488,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(255,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_not__know__s__not__ine) ).
thf(1182,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(91,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B
!= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ( ine @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_ine__nonempty__exprChannelSet) ).
thf(537,plain,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B
!= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ( ine @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(70,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Collect__empty__eq) ).
thf(476,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(249,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
=> ( ( eout @ A @ ( secrecy_kE @ B ) )
=> ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_eoutKnowCorrect__L1k) ).
thf(1155,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
=> ( ( eout @ A @ ( secrecy_kE @ B ) )
=> ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(121,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_set__eq__subset) ).
thf(622,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(241,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ~ ( member @ secrecy_chanID @ D @ ( loc @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
=> ( member @ secrecy_chanID @ D @ ( ins @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_correctCompositionIn__L1) ).
thf(1114,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ~ ( member @ secrecy_chanID @ D @ ( loc @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
=> ( member @ secrecy_chanID @ D @ ( ins @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(259,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ( member @ secrecy_chanID @ F @ B )
=> ( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
=> ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_TBlemma3b) ).
thf(1192,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ( member @ secrecy_chanID @ F @ B )
=> ( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
=> ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(64,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
=> ( ine_ex1303305700Single @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_ine__exprChannelSet__Single) ).
thf(457,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
=> ( ine_ex1303305700Single @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(35,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_is__singletonI) ).
thf(371,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_bot__apply) ).
thf(266,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(82,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_is__singleton__def) ).
thf(508,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(195,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 )
= ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( out_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
=> ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_TBtheorem5b__notP2) ).
thf(921,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 )
= ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( out_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
=> ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(220,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(1035,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(100,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ineM @ D @ B @ C )
| ( ineM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_TBtheorem1b) ).
thf(558,plain,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ineM @ D @ B @ C )
| ( ineM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(89,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Expression_Oinject_I1_J) ).
thf(530,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(201,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
| ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_correctCompositionIn__prop1) ).
thf(953,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
=> ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
| ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(170,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_LocalSecretsComposition__neg__s) ).
thf(794,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(125,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
=> ( out_ex985543062Single @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_out__exprChannelSet__Single) ).
thf(633,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
=> ( out_ex985543062Single @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(31,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Expression_Oinject_I2_J) ).
thf(360,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_equalityE) ).
thf(425,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(173,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
= ( ( ine @ A @ ( secrecy_kE @ B ) )
| ( member @ secrecy_KS @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_know_Osimps_I1_J) ).
thf(824,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle1437066798e_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)],[173]) ).
thf(3,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_order__refl) ).
thf(264,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(178,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_subsetD) ).
thf(856,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(154,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_correctCompositionKS__negQ) ).
thf(745,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(8,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_ord__eq__le__trans) ).
thf(279,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(114,axiom,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_KS_Osimps_I7_J) ).
thf(601,plain,
! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(101,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ( ineM @ A @ B @ C )
=> ( ine @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_ineM__ine) ).
thf(562,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)],[101]) ).
thf(53,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(423,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(140,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_singletonI) ).
thf(694,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(152,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__iff) ).
thf(732,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(161,axiom,
( m
= ( secrecy_sKS @ secret ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_a2) ).
thf(772,plain,
( m
= ( secrecy_sKS @ secret ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Un__iff) ).
thf(875,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(107,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine @ C @ B )
| ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_TBtheorem1a) ).
thf(577,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine @ C @ B )
| ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(145,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_subsetI) ).
thf(711,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(128,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_correctCompositionKS__exprChannel__k__Pex) ).
thf(641,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(19,axiom,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7) ).
thf(313,plain,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(117,axiom,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_KS2Expression_Osimps_I1_J) ).
thf(611,plain,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(79,axiom,
! [A: secrecy_specID] :
( ( correc965049635ionLoc @ A )
=> ( ( ( subcomponents @ A )
= ( bot_bot @ ( set @ secrecy_specID ) ) )
=> ( ( loc @ A )
= ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_subcomponents__loc) ).
thf(498,plain,
! [A: secrecy_specID] :
( ( correc965049635ionLoc @ A )
=> ( ( ( subcomponents @ A )
= ( bot_bot @ ( set @ secrecy_specID ) ) )
=> ( ( loc @ A )
= ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(226,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 ) )
=> ( ( knowle1437066798e_know @ B @ A )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_know__composition1) ).
thf(1058,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 ) )
=> ( ( knowle1437066798e_know @ B @ A )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( correctCompositionKS @ D )
=> ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(92,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ( eoutM @ A @ B @ C )
=> ( eout @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_eoutM__eout) ).
thf(540,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)],[92]) ).
thf(133,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_insert__subset) ).
thf(672,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(190,axiom,
! [A: secrecy_KS > $o,B: secrecy_KS] :
( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
=> ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_KS_Oinduct) ).
thf(900,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)],[190]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_UnE) ).
thf(784,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(212,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_ball__Un) ).
thf(1011,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(248,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ D )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ~ ( ine @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_TBtheorem4a__notPQ) ).
thf(1144,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ A )
=> ( ( ine_exprChannelSet @ B @ D @ E )
=> ( ( ine_exprChannelSet @ C @ F @ E )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ D )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
=> ~ ( ine @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(223,axiom,
( ( subcomponents @ pq )
= ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_subPQ) ).
thf(1043,plain,
( ( subcomponents @ pq )
= ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(6,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_linear) ).
thf(271,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(159,axiom,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ D @ ( secrecy_kE @ A ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ C @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_LocalSecretsComposition__ine1__k) ).
thf(764,plain,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[159]) ).
thf(115,axiom,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
=> ( ~ ( knowle1437066798e_know @ C @ ( secrecy_kKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_know__composition__neg__ine__k) ).
thf(604,plain,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
=> ( ~ ( knowle1437066798e_know @ C @ ( secrecy_kKS @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(62,axiom,
( outStream
= ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( out @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_outStream__def) ).
thf(451,plain,
( outStream
= ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( out @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(103,axiom,
correctCompositionIn @ pq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_cCompI) ).
thf(567,plain,
correctCompositionIn @ pq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(119,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_insert__is__Un) ).
thf(616,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(303,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(244,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 )
= ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ine_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
=> ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_TBtheorem4b__notP2) ).
thf(1122,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 )
= ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ( ine_exprChannelSet @ E @ F @ C )
=> ( ! [G: secrecy_chanID] :
( ( member @ secrecy_chanID @ G @ F )
=> ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
=> ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(124,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_subset__trans) ).
thf(631,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(179,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_KS_Oinject_I2_J) ).
thf(858,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(86,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Collect__mono) ).
thf(520,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(203,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) )
=> ? [D: secrecy_specID] :
( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
& ( member @ secrecy_Secrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_correctCompositionKS__subcomp2) ).
thf(964,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) )
=> ? [D: secrecy_specID] :
( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
& ( member @ secrecy_Secrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(193,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_in__mono) ).
thf(915,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(254,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 ) )
=> ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
& ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_LocalSecretsComposition__exprChannel__s) ).
thf(1177,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 ) )
=> ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
& ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(24,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_8) ).
thf(330,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(137,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_subset__insert) ).
thf(685,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(206,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 ) )
=> ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
& ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_LocalSecretsComposition__exprChannel__k) ).
thf(983,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 ) )
=> ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
& ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(164,axiom,
member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_sg5) ).
thf(780,plain,
member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(116,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_sup__bot__left) ).
thf(608,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(44,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: set @ secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ~ ( eoutM @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_not__eout__eoutM) ).
thf(394,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)],[44]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_le__funD) ).
thf(299,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(160,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ~ ( eout @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( out_ex985543062Single @ A @ E @ B )
& ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ~ ( eout @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_TBtheorem5a__notP1) ).
thf(768,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ~ ( eout @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( out_ex985543062Single @ A @ E @ B )
& ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ~ ( eout @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(174,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_bot__empty__eq) ).
thf(827,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(230,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
= ( ( eout @ A @ ( secrecy_kE @ B ) )
= ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_eout__know__k) ).
thf(1076,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
= ( ( eout @ A @ ( secrecy_kE @ B ) )
= ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(149,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 ) )
=> ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_LocalSecretsComposition__neg__loc__s) ).
thf(722,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 ) )
=> ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(199,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mk__disjoint__insert) ).
thf(944,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_UnI1) ).
thf(663,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(129,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
=> ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) )
=> ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_correctCompositionKS__neg1) ).
thf(648,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[129]) ).
thf(198,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Set_Oset__insert) ).
thf(939,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(214,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( exprChannel @ C @ B )
=> ~ ( member @ secrecy_chanID @ C @ ( ins @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_ine__ins__neg1) ).
thf(1018,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( exprChannel @ C @ B )
=> ~ ( member @ secrecy_chanID @ C @ ( ins @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(157,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ( ine_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ E )
=> ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
=> ~ ( ine @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_TBtheorem4a__notP2) ).
thf(754,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
( ~ ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ( ine_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ E )
=> ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
=> ~ ( ine @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(98,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ~ ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_TBtheorem3a) ).
thf(553,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ~ ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ~ ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(77,axiom,
knowle1437066798e_know @ pq @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_knowPQ) ).
thf(490,plain,
knowle1437066798e_know @ pq @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_insert__ident) ).
thf(675,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(232,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_is__singletonI_H) ).
thf(1081,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(155,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
= ( ( eout @ A @ ( secrecy_sE @ B ) )
= ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_eout__know__s) ).
thf(749,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
= ( ( eout @ A @ ( secrecy_sE @ B ) )
= ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(163,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_UnCI) ).
thf(776,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(99,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_14) ).
thf(557,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(139,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ? [E: secrecy_chanID] :
( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
=> ( ine @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_TBtheorem4a__P) ).
thf(690,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ C )
=> ( ? [E: secrecy_chanID] :
( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
=> ( ine @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(216,axiom,
! [A: secrecy_chanID,B: set @ secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
( ( member @ secrecy_chanID @ A @ B )
=> ( ( member @ secrecy_chanID @ A @ ( ins @ C ) )
=> ( ( exprChannel @ A @ D )
=> ( ineM @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_ineM__L1) ).
thf(1025,plain,
! [A: secrecy_chanID,B: set @ secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
( ( member @ secrecy_chanID @ A @ B )
=> ( ( member @ secrecy_chanID @ A @ ( ins @ C ) )
=> ( ( exprChannel @ A @ D )
=> ( ineM @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(144,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insertCI) ).
thf(705,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(50,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Un__subset__iff) ).
thf(414,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(236,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(1098,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(147,axiom,
( ineM
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
& ( member @ secrecy_chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ineM__def) ).
thf(717,plain,
( ineM
= ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
? [D: secrecy_chanID] :
( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
& ( member @ secrecy_chanID @ D @ B )
& ( exprChannel @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(258,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ F @ C )
& ( member @ secrecy_chanID @ F @ B )
& ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_TBtheorem4b__notP1) ).
thf(1188,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ( ? [F: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ F @ C )
& ( member @ secrecy_chanID @ F @ B )
& ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(257,axiom,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
=> ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_not__know__s__not__eout) ).
thf(1186,plain,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
=> ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(221,axiom,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ~ ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_not__know__k__not__eout) ).
thf(1038,plain,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ~ ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
=> ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(109,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: set @ secrecy_chanID] :
( ( ineM @ A @ B @ C )
=> ( ineM @ A @ ( sup_sup @ ( set @ secrecy_chanID ) @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_ineM__Un1) ).
thf(585,plain,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: set @ secrecy_chanID] :
( ( ineM @ A @ B @ C )
=> ( ineM @ A @ ( sup_sup @ ( set @ secrecy_chanID ) @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(181,axiom,
( ine_ex1303305700Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member @ secrecy_chanID @ B @ ( ins @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID,E: nat] :
( ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ine__exprChannelSingle__def) ).
thf(864,plain,
( ine_ex1303305700Single
= ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( member @ secrecy_chanID @ B @ ( ins @ A ) )
& ( exprChannel @ B @ C )
& ! [D: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
& ( D != B ) )
=> ~ ( exprChannel @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(112,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_subset__empty) ).
thf(595,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(208,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_equals0D) ).
thf(991,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(60,axiom,
( locStream
= ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( loc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_locStream__def) ).
thf(446,plain,
( locStream
= ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( loc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(105,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_doubleton__eq__iff) ).
thf(571,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(177,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ E @ ( out @ A ) )
| ( member @ secrecy_chanID @ E @ ( out @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ( eout @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_TBtheorem5a__PQ) ).
thf(845,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ E @ ( out @ A ) )
| ( member @ secrecy_chanID @ E @ ( out @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ( eout @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(32,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_sup__bot_Oneutr__eq__iff) ).
thf(363,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_bot__set__def) ).
thf(482,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(250,axiom,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ C @ ( secrecy_kE @ A ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ D @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_LocalSecretsComposition__ine2__k) ).
thf(1157,plain,
! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[250]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Un__insert__left) ).
thf(368,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(205,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_correctCompositionKS__exprChannel__s__P) ).
thf(976,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(138,axiom,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ( eout @ B @ ( secrecy_kE @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
=> ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_eout__know__nonKS__k) ).
thf(688,plain,
! [A: secrecy_Keys,B: secrecy_specID] :
( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
=> ( ( eout @ B @ ( secrecy_kE @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
=> ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(87,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Un__singleton__iff) ).
thf(524,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(108,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eoutM @ D @ B @ C )
| ( eoutM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_TBtheorem2b) ).
thf(581,plain,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( eoutM @ A @ B @ C )
=> ( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ A )
=> ( ( eoutM @ D @ B @ C )
| ( eoutM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(85,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_Un__left__commute) ).
thf(517,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(189,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ? [E: secrecy_chanID] :
( ( member @ secrecy_chanID @ E @ ( out @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
=> ( eout @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_TBtheorem45a__P) ).
thf(896,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ? [E: secrecy_chanID] :
( ( member @ secrecy_chanID @ E @ ( out @ A ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
=> ( eout @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(227,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 ) )
=> ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_LocalSecretsComposition__neg__loc__k) ).
thf(1062,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 ) )
=> ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(237,axiom,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ D @ ( secrecy_sE @ A ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ C @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_LocalSecretsComposition__ine1__s) ).
thf(1101,plain,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[237]) ).
thf(167,axiom,
~ ( knowle1437066798e_know @ q @ m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_not__knowQm) ).
thf(786,plain,
~ ( knowle1437066798e_know @ q @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(165,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ A ) @ ( ins @ B ) )
=> ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ C ) )
=> ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_adv__not__know2) ).
thf(781,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ A ) @ ( ins @ B ) )
=> ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ C ) )
=> ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(209,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_LocalSecretsComposition__neg__k) ).
thf(995,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
=> ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(110,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B
= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ~ ( ine @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_ine__empty__exprChannelSet) ).
thf(588,plain,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
( ( ine_exprChannelSet @ A @ B @ C )
=> ( ( B
= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ~ ( ine @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(142,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ B ) )
=> ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_correctCompositionKS__subcomp4) ).
thf(699,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
( ( correctCompositionKS @ A )
=> ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
=> ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ B ) )
=> ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(130,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
| ( member @ secrecy_chanID @ E @ ( ins @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ( ine @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_TBtheorem4a__PQ) ).
thf(652,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( ine @ A @ B )
| ( ine @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
| ( member @ secrecy_chanID @ E @ ( ins @ C ) ) )
& ( exprChannel @ E @ B )
& ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ( ine @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_le__fun__def) ).
thf(351,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(218,axiom,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
=> ( ( eout @ B @ ( secrecy_sE @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
=> ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_eout__know__nonKS__s) ).
thf(1030,plain,
! [A: secrecy_Secrets,B: secrecy_specID] :
( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
=> ( ( eout @ B @ ( secrecy_sE @ A ) )
=> ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
=> ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_singleton__insert__inj__eq_H) ).
thf(568,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(38,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__refl) ).
thf(378,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_singleton__Un__iff) ).
thf(433,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(40,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_ex985543062Single @ A @ B @ C )
=> ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_out__exprChannelSingle__Set) ).
thf(383,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( out_ex985543062Single @ A @ B @ C )
=> ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(96,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_16) ).
thf(549,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(224,axiom,
( notSpe1586871396tsExpr
= ( ^ [A: secrecy_specID,B: list @ secrecy_Expression] :
( ! [C: secrecy_Keys] :
( ( mem @ secrecy_Expression @ ( secrecy_kE @ C ) @ B )
=> ~ ( member @ secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
& ! [C: secrecy_Secrets] :
( ( mem @ secrecy_Expression @ ( secrecy_sE @ C ) @ B )
=> ~ ( member @ secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_notSpecKeysSecretsExpr__def) ).
thf(1045,plain,
( notSpe1586871396tsExpr
= ( ^ [A: secrecy_specID,B: list @ secrecy_Expression] :
( ! [C: secrecy_Keys] :
( ( mem @ secrecy_Expression @ ( secrecy_kE @ C ) @ B )
=> ~ ( member @ secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
& ! [C: secrecy_Secrets] :
( ( mem @ secrecy_Expression @ ( secrecy_sE @ C ) @ B )
=> ~ ( member @ secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(251,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
=> ( ( eout @ A @ ( secrecy_sE @ B ) )
=> ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_eoutKnowCorrect__L1s) ).
thf(1161,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
=> ( ( eout @ A @ ( secrecy_sE @ B ) )
=> ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
| ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1808546759up_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__sup__bot) ).
thf(287,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1808546759up_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(246,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_correctCompositionKS__negP) ).
thf(1133,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
=> ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(210,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_correctCompositionKS__exprChannel__k__P) ).
thf(999,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
& ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(156,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_UnI2) ).
thf(752,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(315,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(49,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_TBtheorem3b) ).
thf(410,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 )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ E )
=> ~ ( ineM @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1,conjecture,
~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(262,plain,
~ ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(169,axiom,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc965049635ionLoc @ B )
=> ( ~ ( ine @ C @ ( secrecy_sE @ A ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
=> ( ine @ D @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_LocalSecretsComposition__ine2__s) ).
thf(790,plain,
! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
=> ( ( ( subcomponents @ B )
= ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( 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)],[169]) ).
thf(7,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_linorder__wlog) ).
thf(273,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Set_Ois__empty__def) ).
thf(373,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(102,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_is__singletonE) ).
thf(564,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_ord__le__eq__subst) ).
thf(305,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(69,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_not__know__k__not__ine) ).
thf(474,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
=> ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(46,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_the__elem__eq) ).
thf(400,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Un__empty__right) ).
thf(635,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(228,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_correctCompositionKS__exprChannel__s__Qex) ).
thf(1065,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(141,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_insert__iff) ).
thf(696,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(9,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_order__trans) ).
thf(283,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(196,axiom,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_correctCompositionKS__exprChannel__s__Pex) ).
thf(928,plain,
! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
( ( ( subcomponents @ A )
= ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionKS @ A )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
=> ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
=> ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
=> ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
=> ( ( correctCompositionIn @ A )
=> ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
& ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_insert__commute) ).
thf(464,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(65,axiom,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_ex1303305700Single @ A @ B @ C )
=> ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_ine__exprChannelSingle__Set) ).
thf(459,plain,
! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
( ( ine_ex1303305700Single @ A @ B @ C )
=> ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(192,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ( out_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ E )
=> ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
=> ~ ( eout @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_TBtheorem5a__notP2) ).
thf(908,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
( ~ ( eout @ A @ B )
=> ( ( ( subcomponents @ C )
= ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ C )
=> ( ( out_exprChannelSet @ D @ E @ B )
=> ( ! [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ E )
=> ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
=> ~ ( eout @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(58,axiom,
bounded_lattice @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(442,plain,
bounded_lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(243,axiom,
( eout
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member @ secrecy_chanID @ C @ ( out @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_eout__def) ).
thf(1120,plain,
( eout
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
? [C: secrecy_chanID] :
( ( member @ secrecy_chanID @ C @ ( out @ A ) )
& ( exprChannel @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(80,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_bot__eq__sup__iff) ).
thf(501,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_le__funE) ).
thf(332,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(245,axiom,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
& ( member @ secrecy_chanID @ F @ B ) )
=> ( ineM @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_TBtheorem4b__P) ).
thf(1129,plain,
! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
( ( ineM @ A @ B @ C )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [F: secrecy_chanID] :
( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
& ( exprChannel @ F @ C )
& ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
& ( member @ secrecy_chanID @ F @ B ) )
=> ( ineM @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(29,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_sup__bot_Oeq__neutr__iff) ).
thf(354,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(197,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ E @ B )
& ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ~ ( ine @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_TBtheorem4a__notP1) ).
thf(935,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ine @ A @ B )
=> ( ~ ( ine @ C @ B )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correctCompositionIn @ D )
=> ( ? [E: secrecy_chanID] :
( ( ine_ex1303305700Single @ A @ E @ B )
& ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
=> ~ ( ine @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(256,axiom,
~ ( ine @ q @ ( secrecy_sE @ secret ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_sg6a) ).
thf(1184,plain,
~ ( ine @ q @ ( secrecy_sE @ secret ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(94,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_is__singleton__the__elem) ).
thf(543,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(78,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( ( loc @ D )
= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ( eout @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_TBtheorem5a__empty) ).
thf(491,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
( ( ( eout @ A @ B )
| ( eout @ C @ B ) )
=> ( ( ( subcomponents @ D )
= ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
=> ( ( correc990227761ionOut @ D )
=> ( ( ( loc @ D )
= ( bot_bot @ ( set @ secrecy_chanID ) ) )
=> ( eout @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(111,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Un__absorb) ).
thf(592,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(213,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_KS_Odistinct_I1_J) ).
thf(1014,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1206,plain,
$false,
inference(e,[status(thm)],[892,809,628,481,479,1105,873,861,878,511,614,269,385,1137,533,550,715,1095,1196,417,301,436,719,504,619,357,949,542,917,702,638,969,325,289,448,443,376,514,574,1040,1109,485,834,905,480,397,734,293,866,774,988,527,1072,453,380,439,678,546,1199,761,366,1047,798,1163,334,957,1091,1021,349,1174,598,392,297,407,788,729,467,1032,625,665,830,889,461,1079,682,285,1089,317,1111,725,403,1006,388,869,420,1118,328,1028,488,1182,537,476,1155,622,1114,1192,457,371,266,508,921,1035,558,530,953,794,633,360,425,824,264,856,745,279,601,562,423,694,732,772,875,577,711,641,313,611,498,1058,540,672,900,784,1011,1144,1043,271,764,604,451,567,616,303,1122,631,858,520,964,915,1177,330,685,983,780,608,394,299,768,827,1076,722,944,663,648,939,1018,754,553,490,675,1081,749,776,557,690,1025,705,414,1098,717,1188,1186,1038,585,864,595,991,446,571,845,363,482,1157,368,976,688,524,581,517,896,1062,1101,786,781,995,588,699,652,351,1030,568,378,433,383,549,1045,1161,287,1133,999,752,315,410,262,790,273,373,564,305,474,400,635,1065,696,283,928,464,459,908,442,1120,501,332,1129,354,935,1184,543,491,592,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP091^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n018.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:54:26 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.99/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.93/1.18 % [INFO] Parsing done (374ms).
% 2.21/1.20 % [INFO] Running in sequential loop mode.
% 3.36/1.60 % [INFO] eprover registered as external prover.
% 3.36/1.60 % [INFO] Scanning for conjecture ...
% 3.62/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 280 axioms. Running axiom selection ...
% 4.34/1.90 % [INFO] Axiom selection finished. Selected 259 axioms (removed 21 axioms).
% 5.15/2.24 % [INFO] Problem is higher-order (TPTP THF).
% 5.15/2.28 % [INFO] Type checking passed.
% 5.15/2.28 % [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 ...
% 44.62/25.75 % External prover 'e' found a proof!
% 44.62/25.75 % [INFO] Killing All external provers ...
% 44.62/25.75 % Time passed: 25404ms (effective reasoning time: 24543ms)
% 44.62/25.75 % 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)>
% 44.62/25.76 % Axioms used in derivation (259): fact_185_TBtheorem5b__notP1, tcon_fun___Orderings_Obot, fact_212_subset__singletonD, tcon_Set_Oset___Orderings_Oord_10, fact_69_KS2Expression_Osimps_I1_J, fact_136_LocalSecretsComposition__neg__k, fact_249_subset__trans, fact_226_le__cases, fact_6_cCompLoc, fact_161_sup__bot_Oeq__neutr__iff, fact_70_bot__set__def, fact_12_cCompI, tcon_HOL_Obool___Orderings_Oord_16, fact_8_KS_Osimps_I8_J, fact_201_outStream__def, fact_119_correctCompositionKS__exprChannel__s__Qex, fact_188_not__know__k__not__eout, fact_24_LocalSecretsComposition__ine2__s, tcon_HOL_Obool___Orderings_Olinorder_14, fact_36_empty__iff, fact_133_correctCompositionKS__exprChannel__k__Qex, fact_139_Un__iff, fact_61_bot__apply, fact_132_correctCompositionKS__exprChannel__k__Pex, fact_81_TBtheorem3b, tcon_Set_Oset___Orderings_Opreorder_8, fact_130_correctCompositionKS__exprChannel__k__P, fact_205_subset__antisym, fact_253_subset__insert, fact_14_KS_Oinduct, fact_146_bex__Un, fact_202_adv__not__know2, fact_59_LocalSecretsComposition__neg1, fact_31_insert__iff, fact_206_subset__empty, fact_184_TBtheorem5b__notP2, fact_10_know_Osimps_I2_J, fact_169_correctCompositionKS__subcomp2, fact_166_ineM__Un1, fact_23_LocalSecretsComposition__ine1__s, fact_141_Un__insert__right, fact_17_KS_Osimps_I7_J, fact_224_linear, tcon_fun___Orderings_Oord, fact_28_singletonI, fact_173_TBtheorem5a__notP1, fact_149_Un__absorb, fact_67_KS2Expression_Osimps_I2_J, fact_228_le__cases3, fact_151_Un__left__absorb, fact_217_le__fun__def, fact_108_correctCompositionInLoc__exprChannel, fact_51_insertI2, fact_84_correctCompositionIn__prop1, fact_171_correctCompositionKS__subcomp4, fact_236_linorder__wlog, fact_37_ex__in__conv, fact_153_Un__empty__left, fact_41_mk__disjoint__insert, fact_193_TBtheorem5b__PQ, fact_243_subset__eq, fact_126_correctCompositionKS__negQ, tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, fact_246_subset__iff, fact_80_TBtheorem1b, fact_197_out__exprChannelSet__def, tcon_fun___Lattices_Obounded__semilattice__sup__bot, fact_116_bot__empty__eq, fact_200_TBtheorem5a__PQ, fact_245_equalityD2, fact_251_Collect__mono__iff, fact_29_LocalSecretsComposition1, fact_152_Un__left__commute, fact_16_Expression_Oinject_I2_J, fact_121_correctCompositionKS__exprChannel__s__Q, fact_155_singleton__Un__iff, fact_50_Set_Oset__insert, fact_118_LocalSecretsComposition__neg__loc__k, fact_125_correctCompositionKS__negP, fact_46_Collect__mem__eq, fact_179_eout__know__s, fact_44_insert__absorb, fact_53_insertE, fact_34_Collect__empty__eq, fact_191_eoutKnowCorrect__L1s, fact_88_TBtheorem4b__notP1, fact_244_equalityD1, fact_162_sup__bot__left, fact_94_TBtheorem4a__notP2, fact_89_correctCompositionIn__L1, fact_145_UnI2, fact_56_doubleton__eq__iff, fact_180_not__know__s__not__eout, fact_76_is__singletonE, fact_98_ine__ins__neg1, fact_158_sup__bot_Oright__neutral, fact_18_KS_Osimps_I5_J, fact_213_subset__singleton__iff, fact_42_insert__commute, fact_5_sg6a, fact_199_correctCompositionOut__prop1, fact_111_TBtheorem4a__PQ, tcon_fun___Lattices_Obounded__lattice_2, fact_113_locStream__def, fact_190_eout__know__nonKS__s, fact_115_Collect__empty__eq__bot, fact_214_le__funD, fact_0_not__knowQm, fact_128_know__composition1, fact_140_Un__empty, fact_99_ineM__def, fact_210_singleton__insert__inj__eq_H, fact_90_subcomponents__loc, tcon_Set_Oset___Orderings_Obot_11, fact_79_TBtheorem4a__empty, fact_55_insert__not__empty, fact_255_subset__insertI2, fact_25_LocalSecretsComposition__neg1__s, fact_163_sup__bot__right, fact_192_TBtheore54b__P, fact_19_know__composition__neg1, fact_183_TBtheorem2b, fact_20_know__composition__neg__ine__s, fact_250_set__eq__subset, fact_77_is__singleton__def, fact_105_ine__empty__exprChannelSet, fact_102_LocalSecretsComposition__exprChannel__s, fact_112_TBtheorem4b__P, fact_168_correctCompositionKS__subcomp1, fact_177_out__exprChannelSet__Single, fact_72_is__singleton__the__elem, fact_78_know_Osimps_I1_J, fact_109_TBlemma3b, fact_181_not__eout__eoutM, fact_21_not__know__s__not__ine, fact_208_insert__subset, fact_247_subset__refl, fact_91_TBtheorem4b__notPQ, fact_248_Collect__mono, fact_64_LocalSecretsComposition__ine1__k, fact_252_insert__mono, fact_58_singletonD, fact_45_mem__Collect__eq, fact_66_is__singletonI, fact_54_singleton__inject, fact_215_le__funE, fact_172_correctCompositionKS__subcomp3, fact_86_not__ine__ineM, fact_194_TBtheorem45a__P, fact_123_correctCompositionKS__PQ, fact_231_ord__eq__le__trans, fact_170_TBtheorem2a, fact_4_KS_Oinject_I2_J, fact_85_TBtheorem4a__notP1, fact_138_UnCI, fact_30_insertCI, fact_187_eoutKnowCorrect__L1k, fact_241_subsetD, fact_142_Un__insert__left, fact_3_sg5, fact_49_insert__ident, fact_65_know__composition__neg__ine__k, fact_204_subsetI, fact_221_ord__le__eq__subst, fact_40_emptyE, fact_143_UnE, fact_9_KS_Osimps_I6_J, fact_240_in__mono, fact_176_out__exprChannelSingle__Set, fact_32_insert__absorb2, fact_101_ine__exprChannelSingle__def, fact_82_Set_Ois__empty__def, fact_22_KS_Oexhaust, fact_73_is__singletonI_H, fact_43_insert__eq__iff, fact_189_eout__know__k, fact_87_ineM__ine, fact_47_Collect__cong, fact_93_TBtheorem4a__notPQ, fact_39_equals0D, fact_254_subset__insertI, fact_165_sup__eq__bot__iff, fact_13_KS_Odistinct_I1_J, tcon_Set_Oset___Lattices_Obounded__lattice_1, fact_150_Un__commute, fact_234_order__trans, fact_120_correctCompositionKS__exprChannel__s__Pex, fact_26_TBtheorem1a, fact_122_correctCompositionKS__exprChannel__s__P, fact_33_empty__Collect__eq, fact_62_LocalSecretsComposition__neg1__k, fact_52_insertI1, fact_167_TBtheorem5a__empty, tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12, fact_110_TBtheorem4a__P, fact_83_correctCompositionIn__L2, fact_175_TBtheorem5a__notP2, fact_27_TBtheorem3a, fact_186_eout__know__nonKS__k, fact_203_order__refl, fact_100_ineM__L1, fact_164_bot__eq__sup__iff, fact_92_TBtheorem4b__notP2, tcon_fun___Orderings_Opreorder, fact_2_knowPQ, fact_95_TBtheorem4b__PQ, fact_207_empty__subsetI, fact_106_ine__exprChannelSingle__Set, fact_174_TBtheorem5a__notPQ, fact_57_singleton__iff, fact_211_singleton__insert__inj__eq, fact_147_ball__Un, fact_216_le__funI, fact_35_all__not__in__conv, fact_117_LocalSecretsComposition__neg__loc__s, fact_159_sup__bot_Oneutr__eq__iff, fact_71_Expression_Odistinct_I1_J, fact_63_LocalSecretsComposition__ine2__k, fact_1_a2, fact_137_notSpecKeysSecretsExpr__def, fact_104_ine__nonempty__exprChannelSet, fact_144_UnI1, fact_196_eoutM__def, fact_195_eout__def, fact_225_eq__refl, fact_75_not__know__k__not__ine, fact_60_the__elem__eq, fact_7_a22, fact_160_sup__bot_Oleft__neutral, fact_209_Un__subset__iff, fact_242_equalityE, fact_97_ine__def, fact_131_correctCompositionKS__exprChannel__k__Q, fact_232_ord__le__eq__trans, tcon_HOL_Obool___Lattices_Obounded__lattice, fact_135_LocalSecretsComposition__neg__s, tcon_HOL_Obool___Orderings_Opreorder_13, fact_154_Un__empty__right, fact_220_ord__eq__le__subst, fact_178_TBtheorem5b__notPQ, fact_38_equals0I, fact_103_LocalSecretsComposition__exprChannel__k, tcon_HOL_Obool___Orderings_Obot_17, fact_107_ine__exprChannelSet__Single, fact_68_Expression_Oinject_I1_J, fact_96_ine__exprChannelSet__def, fact_127_know__composition, fact_156_Un__singleton__iff, fact_157_insert__is__Un, fact_198_out__exprChannelSingle__def, fact_114_inStream__def, fact_11_subPQ, fact_134_LocalSecretsComposition__neg, fact_148_Un__assoc, fact_124_correctCompositionKS__neg1, fact_182_eoutM__eout, fact_129_know__composition2, fact_15_KS_Oinject_I1_J, fact_74_bot__fun__def
% 44.62/25.76 % No. of inferences in proof: 522
% 44.62/25.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 25404 ms resp. 24543 ms w/o parsing
% 45.95/26.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.95/26.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------