TSTP Solution File: ITP085^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP085^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:22:45 EDT 2024
% Result : Theorem 22.03s 7.49s
% Output : Refutation 22.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 259
% Syntax : Number of formulae : 450 ( 218 unt; 70 typ; 0 def)
% Number of atoms : 990 ( 674 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 3359 ( 198 ~; 76 |; 120 &;2589 @)
% ( 0 <=>; 376 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 308 ( 308 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 4 con; 0-3 aty)
% Number of variables : 1110 ( 26 ^1018 !; 66 ?;1110 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_l425507653ession_type,type,
list_l425507653ession: $tType ).
thf(set_li185139947ession_type,type,
set_li185139947ession: $tType ).
thf(set_li2007071804ecrets_type,type,
set_li2007071804ecrets: $tType ).
thf(set_li849033543y_Keys_type,type,
set_li849033543y_Keys: $tType ).
thf(list_list_Secrecy_KS_type,type,
list_list_Secrecy_KS: $tType ).
thf(set_list_Secrecy_KS_type,type,
set_list_Secrecy_KS: $tType ).
thf(list_S529945141ession_type,type,
list_S529945141ession: $tType ).
thf(set_Se1942955227ession_type,type,
set_Se1942955227ession: $tType ).
thf(list_Secrecy_Secrets_type,type,
list_Secrecy_Secrets: $tType ).
thf(set_Secrecy_Secrets_type,type,
set_Secrecy_Secrets: $tType ).
thf(list_Secrecy_Keys_type,type,
list_Secrecy_Keys: $tType ).
thf(set_Secrecy_Keys_type,type,
set_Secrecy_Keys: $tType ).
thf(list_Secrecy_KS_type,type,
list_Secrecy_KS: $tType ).
thf(set_Secrecy_KS_type,type,
set_Secrecy_KS: $tType ).
thf(secrecy_Expression_type,type,
secrecy_Expression: $tType ).
thf(secrecy_Secrets_type,type,
secrecy_Secrets: $tType ).
thf(secrecy_specID_type,type,
secrecy_specID: $tType ).
thf(secrecy_Keys_type,type,
secrecy_Keys: $tType ).
thf(secrecy_KS_type,type,
secrecy_KS: $tType ).
thf(localSecrets_type,type,
localSecrets: secrecy_specID > set_Secrecy_KS ).
thf(knowle233900195orrect_type,type,
knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
thf(knowle1268625169orrect_type,type,
knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
thf(knowle945212990e_know_type,type,
knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
thf(knowle731562421_knows_type,type,
knowle731562421_knows: secrecy_specID > list_S529945141ession > $o ).
thf(mem_Se1967555118ession_type,type,
mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
thf(append2089414218ession_type,type,
append2089414218ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(bind_S815874003ession_type,type,
bind_S815874003ession: list_S529945141ession > ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession ).
thf(butlas171474643ession_type,type,
butlas171474643ession: list_S529945141ession > list_S529945141ession ).
thf(distin1076152135ession_type,type,
distin1076152135ession: list_S529945141ession > $o ).
thf(insert1173886601ession_type,type,
insert1173886601ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
thf(last_S1532390982ession_type,type,
last_S1532390982ession: list_S529945141ession > secrecy_Expression ).
thf(cons_S112077679ession_type,type,
cons_S112077679ession: secrecy_Expression > list_S529945141ession > list_S529945141ession ).
thf(nil_Se901661471ession_type,type,
nil_Se901661471ession: list_S529945141ession ).
thf(hd_Sec357328890ession_type,type,
hd_Sec357328890ession: list_S529945141ession > secrecy_Expression ).
thf(tl_Sec1905266422ession_type,type,
tl_Sec1905266422ession: list_S529945141ession > list_S529945141ession ).
thf(list_e1486860828ession_type,type,
list_e1486860828ession: ( secrecy_Expression > $o ) > list_S529945141ession > $o ).
thf(listre84909707ession_type,type,
listre84909707ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
thf(map_ta1624757057ession_type,type,
map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(maps_S599402637ession_type,type,
maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
thf(member2020590922ession_type,type,
member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
thf(lexord1123423577ession_type,type,
lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
thf(remdup484344169ession_type,type,
remdup484344169ession: list_S529945141ession > list_S529945141ession ).
thf(rev_Se1073238207ession_type,type,
rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
thf(rotate1237234450ession_type,type,
rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
thf(splice1390717708ession_type,type,
splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
thf(succes1388047762ession_type,type,
succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
thf(decr_type,type,
decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(enc_type,type,
enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(encrDecrKeys_type,type,
encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
thf(ext_type,type,
ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(sign_type,type,
sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
thf(eout_type,type,
eout: secrecy_specID > secrecy_Expression > $o ).
thf(ine_type,type,
ine: secrecy_specID > secrecy_Expression > $o ).
thf(notSpe1586871396tsExpr_type,type,
notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
thf(specKeys_type,type,
specKeys: secrecy_specID > set_Secrecy_Keys ).
thf(specKeysSecrets_type,type,
specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
thf(specSecrets_type,type,
specSecrets: secrecy_specID > set_Secrecy_Secrets ).
thf(secrecy_kE_type,type,
secrecy_kE: secrecy_Keys > secrecy_Expression ).
thf(secrecy_sE_type,type,
secrecy_sE: secrecy_Secrets > secrecy_Expression ).
thf(secrec1016742679ession_type,type,
secrec1016742679ession: secrecy_KS > secrecy_Expression ).
thf(secrecy_kKS_type,type,
secrecy_kKS: secrecy_Keys > secrecy_KS ).
thf(secrecy_sKS_type,type,
secrecy_sKS: secrecy_Secrets > secrecy_KS ).
thf(collect_Secrecy_KS_type,type,
collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
thf(collect_Secrecy_Keys_type,type,
collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
thf(collec836099393ecrets_type,type,
collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
thf(member_Secrecy_KS2_type,type,
member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
thf(member_Secrecy_Keys_type,type,
member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
thf(member2138796287ecrets_type,type,
member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
thf(a_type,type,
a: secrecy_specID ).
thf(m_type,type,
m: secrecy_Secrets ).
thf(142,axiom,
! [A: secrecy_specID,B: secrecy_Expression] :
( ( knowle1268625169orrect @ A @ B )
=> ( ( eout @ A @ B )
=> ( ? [C: secrecy_Keys] :
( ( B
= ( secrecy_kE @ C ) )
& ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) )
| ? [C: secrecy_Secrets] :
( ( B
= ( secrecy_sE @ C ) )
& ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) )
| ( knowle731562421_knows @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_eoutKnowsECorrect__L1) ).
thf(760,plain,
! [A: secrecy_specID,B: secrecy_Expression] :
( ( knowle1268625169orrect @ A @ B )
=> ( ( eout @ A @ B )
=> ( ? [C: secrecy_Keys] :
( ( B
= ( secrecy_kE @ C ) )
& ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) )
| ? [C: secrecy_Secrets] :
( ( B
= ( secrecy_sE @ C ) )
& ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) )
| ( knowle731562421_knows @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(171,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ B ) ) @ nil_Se901661471ession ) )
= ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_know1k) ).
thf(941,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ B ) ) @ nil_Se901661471ession ) )
= ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(101,axiom,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ B )
= ( append2089414218ession @ C @ D ) )
= ( ( ( C = nil_Se901661471ession )
& ( ( cons_S112077679ession @ A @ B )
= D ) )
| ? [E: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ E )
= C )
& ( B
= ( append2089414218ession @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Cons__eq__append__conv) ).
thf(555,plain,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ B )
= ( append2089414218ession @ C @ D ) )
= ( ( ( C = nil_Se901661471ession )
& ( ( cons_S112077679ession @ A @ B )
= D ) )
| ? [E: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ E )
= C )
& ( B
= ( append2089414218ession @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(120,axiom,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_last__ConsR) ).
thf(666,plain,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(85,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( append2089414218ession @ ( append2089414218ession @ A @ B ) @ C )
= ( append2089414218ession @ A @ ( append2089414218ession @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_append__assoc) ).
thf(481,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( append2089414218ession @ ( append2089414218ession @ A @ B ) @ C )
= ( append2089414218ession @ A @ ( append2089414218ession @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(48,axiom,
! [A: list_S529945141ession] :
( ( splice1390717708ession @ nil_Se901661471ession @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_splice_Osimps_I1_J) ).
thf(352,plain,
! [A: list_S529945141ession] :
( ( splice1390717708ession @ nil_Se901661471ession @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(65,axiom,
! [A: secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession] :
( ( ( A = B )
=> ( ( remdup484344169ession @ ( cons_S112077679ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( remdup484344169ession @ ( cons_S112077679ession @ A @ C ) ) ) )
& ( ( A != B )
=> ( ( remdup484344169ession @ ( cons_S112077679ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( cons_S112077679ession @ A @ ( remdup484344169ession @ ( cons_S112077679ession @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_remdups__adj_Osimps_I3_J) ).
thf(408,plain,
! [A: secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession] :
( ( ( A = B )
=> ( ( remdup484344169ession @ ( cons_S112077679ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( remdup484344169ession @ ( cons_S112077679ession @ A @ C ) ) ) )
& ( ( A != B )
=> ( ( remdup484344169ession @ ( cons_S112077679ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( cons_S112077679ession @ A @ ( remdup484344169ession @ ( cons_S112077679ession @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(135,axiom,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession,D: secrecy_Expression] :
( ( ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
= ( append2089414218ession @ C @ ( cons_S112077679ession @ D @ nil_Se901661471ession ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_append1__eq__conv) ).
thf(730,plain,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession,D: secrecy_Expression] :
( ( ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
= ( append2089414218ession @ C @ ( cons_S112077679ession @ D @ nil_Se901661471ession ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(73,axiom,
! [A: secrecy_Expression,B: list_S529945141ession,C: secrecy_Expression > list_S529945141ession] :
( ( bind_S815874003ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( append2089414218ession @ ( C @ A ) @ ( bind_S815874003ession @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_bind__simps_I2_J) ).
thf(440,plain,
! [A: secrecy_Expression,B: list_S529945141ession,C: secrecy_Expression > list_S529945141ession] :
( ( bind_S815874003ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( append2089414218ession @ ( C @ A ) @ ( bind_S815874003ession @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(123,axiom,
! [A: secrecy_Expression] :
~ ( member2020590922ession @ nil_Se901661471ession @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_member__rec_I2_J) ).
thf(677,plain,
! [A: secrecy_Expression] :
~ ( member2020590922ession @ nil_Se901661471ession @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(58,axiom,
! [A: list_S529945141ession] :
( ( append2089414218ession @ nil_Se901661471ession @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_append_Oleft__neutral) ).
thf(384,plain,
! [A: list_S529945141ession] :
( ( append2089414218ession @ nil_Se901661471ession @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(82,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= B )
= ( A = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_append__self__conv2) ).
thf(472,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= B )
= ( A = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(162,axiom,
! [A: secrecy_Expression,B: list_S529945141ession,C: secrecy_Expression,D: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ B )
= ( cons_S112077679ession @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_list_Oinject) ).
thf(913,plain,
! [A: secrecy_Expression,B: list_S529945141ession,C: secrecy_Expression,D: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ B )
= ( cons_S112077679ession @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(121,axiom,
! [A: secrecy_Keys,B: secrecy_Keys,C: list_S529945141ession] :
( ( encrDecrKeys @ A @ B )
=> ( ( ext @ A @ ( sign @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_ExtSign) ).
thf(670,plain,
! [A: secrecy_Keys,B: secrecy_Keys,C: list_S529945141ession] :
( ( encrDecrKeys @ A @ B )
=> ( ( ext @ A @ ( sign @ B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(183,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
= ( ( eout @ A @ ( secrecy_sE @ B ) )
= ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_eout__know__s) ).
thf(973,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
= ( ( eout @ A @ ( secrecy_sE @ B ) )
= ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(27,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( distin1076152135ession @ ( append2089414218ession @ A @ B ) )
=> ( distin1076152135ession @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_distinct__adj__appendD1) ).
thf(288,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( distin1076152135ession @ ( append2089414218ession @ A @ B ) )
=> ( distin1076152135ession @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(31,axiom,
! [A: list_S529945141ession] :
( ( ( rev_Se1073238207ession @ A )
= nil_Se901661471ession )
= ( A = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_rev__is__Nil__conv) ).
thf(301,plain,
! [A: list_S529945141ession] :
( ( ( rev_Se1073238207ession @ A )
= nil_Se901661471ession )
= ( A = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(60,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession,E: list_S529945141ession] :
( ( A @ B @ C )
=> ( ( listre84909707ession @ A @ D @ E )
=> ( listre84909707ession @ A @ ( cons_S112077679ession @ B @ D ) @ ( cons_S112077679ession @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_listrelp_OCons) ).
thf(389,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession,E: list_S529945141ession] :
( ( A @ B @ C )
=> ( ( listre84909707ession @ A @ D @ E )
=> ( listre84909707ession @ A @ ( cons_S112077679ession @ B @ D ) @ ( cons_S112077679ession @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(133,axiom,
! [A: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,B: secrecy_Expression > secrecy_Expression > $o,C: list_S529945141ession] :
( ! [D: secrecy_Expression > secrecy_Expression > $o] : ( A @ D @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression > secrecy_Expression > $o,E: secrecy_Expression,F: list_S529945141ession] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_S112077679ession @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_sorted__wrt_Oinduct) ).
thf(724,plain,
! [A: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,B: secrecy_Expression > secrecy_Expression > $o,C: list_S529945141ession] :
( ! [D: secrecy_Expression > secrecy_Expression > $o] : ( A @ D @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression > secrecy_Expression > $o,E: secrecy_Expression,F: list_S529945141ession] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_S112077679ession @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(45,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( distin1076152135ession @ ( append2089414218ession @ A @ B ) )
=> ( distin1076152135ession @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_distinct__adj__appendD2) ).
thf(344,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( distin1076152135ession @ ( append2089414218ession @ A @ B ) )
=> ( distin1076152135ession @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(50,axiom,
! [A: list_S529945141ession] :
( ( append2089414218ession @ nil_Se901661471ession @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_append__Nil) ).
thf(357,plain,
! [A: list_S529945141ession] :
( ( append2089414218ession @ nil_Se901661471ession @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(159,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: list_S529945141ession] :
~ ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ C ) @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ord_Olexordp__eq__simps_I3_J) ).
thf(902,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: list_S529945141ession] :
~ ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ C ) @ nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(155,axiom,
( ( rotate1237234450ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_rotate1_Osimps_I1_J) ).
thf(853,plain,
( ( rotate1237234450ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(182,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_KS_Odistinct_I1_J) ).
thf(969,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kKS @ A )
!= ( secrecy_sKS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(66,axiom,
! [A: secrecy_Expression > list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( maps_S599402637ession @ A @ ( cons_S112077679ession @ B @ C ) )
= ( append2089414218ession @ ( A @ B ) @ ( maps_S599402637ession @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_maps__simps_I1_J) ).
thf(416,plain,
! [A: secrecy_Expression > list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( maps_S599402637ession @ A @ ( cons_S112077679ession @ B @ C ) )
= ( append2089414218ession @ ( A @ B ) @ ( maps_S599402637ession @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(39,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( rotate1237234450ession @ ( cons_S112077679ession @ A @ B ) )
= ( append2089414218ession @ B @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_rotate1_Osimps_I2_J) ).
thf(325,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( rotate1237234450ession @ ( cons_S112077679ession @ A @ B ) )
= ( append2089414218ession @ B @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(36,axiom,
! [A: list_S529945141ession] :
( ( splice1390717708ession @ A @ nil_Se901661471ession )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_splice__Nil2) ).
thf(316,plain,
! [A: list_S529945141ession] :
( ( splice1390717708ession @ A @ nil_Se901661471ession )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(89,axiom,
! [A: secrecy_Expression] : ( distin1076152135ession @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_distinct__adj__singleton) ).
thf(492,plain,
! [A: secrecy_Expression] : ( distin1076152135ession @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(106,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets > $o] :
( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_mem__Collect__eq) ).
thf(591,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets > $o] :
( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(74,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( distin1076152135ession @ ( cons_S112077679ession @ A @ B ) )
=> ( distin1076152135ession @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_distinct__adj__ConsD) ).
thf(443,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( distin1076152135ession @ ( cons_S112077679ession @ A @ B ) )
=> ( distin1076152135ession @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(115,axiom,
! [A: list_S529945141ession > list_S529945141ession > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ! [D: list_S529945141ession] : ( A @ nil_Se901661471ession @ D )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession,F: list_S529945141ession] :
( ( A @ F @ E )
=> ( A @ ( cons_S112077679ession @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_splice_Oinduct) ).
thf(646,plain,
! [A: list_S529945141ession > list_S529945141ession > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ! [D: list_S529945141ession] : ( A @ nil_Se901661471ession @ D )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession,F: list_S529945141ession] :
( ( A @ F @ E )
=> ( A @ ( cons_S112077679ession @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(180,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
=> ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_sE @ B ) @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_know2knows__s) ).
thf(966,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
=> ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_sE @ B ) @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(160,axiom,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_last__ConsL) ).
thf(905,plain,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(83,axiom,
! [A: list_S529945141ession] :
( ( ( remdup484344169ession @ A )
= nil_Se901661471ession )
= ( A = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_remdups__adj__Nil__iff) ).
thf(475,plain,
! [A: list_S529945141ession] :
( ( ( remdup484344169ession @ A )
= nil_Se901661471ession )
= ( A = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(164,axiom,
! [A: secrecy_specID,B: secrecy_Keys,C: list_S529945141ession] :
( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
& ( knowle731562421_knows @ A @ C ) )
=> ( knowle731562421_knows @ A @ ( sign @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_knows7) ).
thf(924,plain,
! [A: secrecy_specID,B: secrecy_Keys,C: list_S529945141ession] :
( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
& ( knowle731562421_knows @ A @ C ) )
=> ( knowle731562421_knows @ A @ ( sign @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(25,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= C )
=> ( ( D
= ( append2089414218ession @ B @ E ) )
=> ( ( append2089414218ession @ A @ D )
= ( append2089414218ession @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_append__eq__appendI) ).
thf(280,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= C )
=> ( ( D
= ( append2089414218ession @ B @ E ) )
=> ( ( append2089414218ession @ A @ D )
= ( append2089414218ession @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(111,axiom,
! [A: secrecy_Expression > list_S529945141ession] :
( ( maps_S599402637ession @ A @ nil_Se901661471ession )
= nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_maps__simps_I2_J) ).
thf(634,plain,
! [A: secrecy_Expression > list_S529945141ession] :
( ( maps_S599402637ession @ A @ nil_Se901661471ession )
= nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(9,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
= ( B = nil_Se901661471ession ) )
=> ( ( ( A != nil_Se901661471ession )
=> ( ( B != nil_Se901661471ession )
=> ( ( ( hd_Sec357328890ession @ A )
= ( hd_Sec357328890ession @ B ) )
& ( ( tl_Sec1905266422ession @ A )
= ( tl_Sec1905266422ession @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_list_Oexpand) ).
thf(221,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
= ( B = nil_Se901661471ession ) )
=> ( ( ( A != nil_Se901661471ession )
=> ( ( B != nil_Se901661471ession )
=> ( ( ( hd_Sec357328890ession @ A )
= ( hd_Sec357328890ession @ B ) )
& ( ( tl_Sec1905266422ession @ A )
= ( tl_Sec1905266422ession @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(176,axiom,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID] :
( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
| ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) ) )
=> ( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
| ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_know2knowsPQ__k) ).
thf(956,plain,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID] :
( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
| ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) ) )
=> ( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
| ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(189,axiom,
! [A: secrecy_specID,B: secrecy_Keys,C: list_S529945141ession] :
( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
& ( knowle731562421_knows @ A @ C ) )
=> ( knowle731562421_knows @ A @ ( enc @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_knows6) ).
thf(988,plain,
! [A: secrecy_specID,B: secrecy_Keys,C: list_S529945141ession] :
( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
& ( knowle731562421_knows @ A @ C ) )
=> ( knowle731562421_knows @ A @ ( enc @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(154,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ! [B: secrecy_Expression] :
( A
!= ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
=> ~ ! [B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession] :
( A
!= ( cons_S112077679ession @ B @ ( cons_S112077679ession @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_remdups__adj_Ocases) ).
thf(849,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ! [B: secrecy_Expression] :
( A
!= ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
=> ~ ! [B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession] :
( A
!= ( cons_S112077679ession @ B @ ( cons_S112077679ession @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(33,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession] :
( ( succes1388047762ession @ A @ ( cons_S112077679ession @ B @ ( cons_S112077679ession @ C @ D ) ) )
= ( ( A @ B @ C )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_successively_Osimps_I3_J) ).
thf(307,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession] :
( ( succes1388047762ession @ A @ ( cons_S112077679ession @ B @ ( cons_S112077679ession @ C @ D ) ) )
= ( ( A @ B @ C )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(11,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ ( tl_Sec1905266422ession @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_list_Ocollapse) ).
thf(233,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ ( tl_Sec1905266422ession @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession,E: list_S529945141ession] :
( ( A @ B @ C )
=> ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ D ) @ ( cons_S112077679ession @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ord_Olexordp__eq_OCons) ).
thf(248,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession,E: list_S529945141ession] :
( ( A @ B @ C )
=> ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ D ) @ ( cons_S112077679ession @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(57,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( tl_Sec1905266422ession @ ( append2089414218ession @ A @ B ) )
= ( append2089414218ession @ ( tl_Sec1905266422ession @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_tl__append2) ).
thf(380,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( tl_Sec1905266422ession @ ( append2089414218ession @ A @ B ) )
= ( append2089414218ession @ ( tl_Sec1905266422ession @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(94,axiom,
! [A: set_Secrecy_Secrets] :
( ( collec836099393ecrets
@ ^ [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Collect__mem__eq) ).
thf(512,plain,
! [A: set_Secrecy_Secrets] :
( ( collec836099393ecrets
@ ^ [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(118,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Expression_Oinject_I1_J) ).
thf(661,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kE @ A )
= ( secrecy_kE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(53,axiom,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ B )
= C )
=> ( ( D
= ( append2089414218ession @ B @ E ) )
=> ( ( cons_S112077679ession @ A @ D )
= ( append2089414218ession @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Cons__eq__appendI) ).
thf(366,plain,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ B )
= C )
=> ( ( D
= ( append2089414218ession @ B @ E ) )
=> ( ( cons_S112077679ession @ A @ D )
= ( append2089414218ession @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(161,axiom,
! [A: set_Secrecy_KS] :
( ( collect_Secrecy_KS
@ ^ [B: secrecy_KS] : ( member_Secrecy_KS2 @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Collect__mem__eq) ).
thf(910,plain,
! [A: set_Secrecy_KS] :
( ( collect_Secrecy_KS
@ ^ [B: secrecy_KS] : ( member_Secrecy_KS2 @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(175,axiom,
! [A: secrecy_KS] :
( ! [B: secrecy_Keys] :
( A
!= ( secrecy_kKS @ B ) )
=> ~ ! [B: secrecy_Secrets] :
( A
!= ( secrecy_sKS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_KS_Oexhaust) ).
thf(952,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)],[175]) ).
thf(47,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( succes1388047762ession @ A @ ( append2089414218ession @ B @ C ) )
= ( ( succes1388047762ession @ A @ B )
& ( succes1388047762ession @ A @ C )
& ( ( B = nil_Se901661471ession )
| ( C = nil_Se901661471ession )
| ( A @ ( last_S1532390982ession @ B ) @ ( hd_Sec357328890ession @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_successively__append__iff) ).
thf(349,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( succes1388047762ession @ A @ ( append2089414218ession @ B @ C ) )
= ( ( succes1388047762ession @ A @ B )
& ( succes1388047762ession @ A @ C )
& ( ( B = nil_Se901661471ession )
| ( C = nil_Se901661471ession )
| ( A @ ( last_S1532390982ession @ B ) @ ( hd_Sec357328890ession @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(103,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( remdup484344169ession @ A )
= B )
=> ( ( ( A = nil_Se901661471ession )
=> ( B != nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression] :
( ( A
= ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( B
!= ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) )
=> ~ ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) )
=> ~ ( ( ( C = D )
=> ( B
= ( remdup484344169ession @ ( cons_S112077679ession @ C @ E ) ) ) )
& ( ( C != D )
=> ( B
= ( cons_S112077679ession @ C @ ( remdup484344169ession @ ( cons_S112077679ession @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_remdups__adj_Oelims) ).
thf(561,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( remdup484344169ession @ A )
= B )
=> ( ( ( A = nil_Se901661471ession )
=> ( B != nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression] :
( ( A
= ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( B
!= ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) )
=> ~ ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) )
=> ~ ( ( ( C = D )
=> ( B
= ( remdup484344169ession @ ( cons_S112077679ession @ C @ E ) ) ) )
& ( ( C != D )
=> ( B
= ( cons_S112077679ession @ C @ ( remdup484344169ession @ ( cons_S112077679ession @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(61,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( append2089414218ession @ B @ A ) )
= ( butlas171474643ession @ B ) ) )
& ( ( A != nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( append2089414218ession @ B @ A ) )
= ( append2089414218ession @ B @ ( butlas171474643ession @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_butlast__append) ).
thf(392,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( append2089414218ession @ B @ A ) )
= ( butlas171474643ession @ B ) ) )
& ( ( A != nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( append2089414218ession @ B @ A ) )
= ( append2089414218ession @ B @ ( butlas171474643ession @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(69,axiom,
! [A: secrecy_specID,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( knowle731562421_knows @ A @ B )
& ( knowle731562421_knows @ A @ C ) )
=> ( knowle731562421_knows @ A @ ( append2089414218ession @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_knows3) ).
thf(424,plain,
! [A: secrecy_specID,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( knowle731562421_knows @ A @ B )
& ( knowle731562421_knows @ A @ C ) )
=> ( knowle731562421_knows @ A @ ( append2089414218ession @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(71,axiom,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( butlas171474643ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_butlast__snoc) ).
thf(429,plain,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( butlas171474643ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(3,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
? [C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( A
= ( append2089414218ession @ C @ D ) )
& ( B
= ( append2089414218ession @ C @ E ) )
& ( ( D = nil_Se901661471ession )
| ( E = nil_Se901661471ession )
| ( ( hd_Sec357328890ession @ D )
!= ( hd_Sec357328890ession @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_longest__common__prefix) ).
thf(192,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
? [C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( A
= ( append2089414218ession @ C @ D ) )
& ( B
= ( append2089414218ession @ C @ E ) )
& ( ( D = nil_Se901661471ession )
| ( E = nil_Se901661471ession )
| ( ( hd_Sec357328890ession @ D )
!= ( hd_Sec357328890ession @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(126,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( cons_S112077679ession @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_not__Cons__self2) ).
thf(693,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( cons_S112077679ession @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(86,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A
= ( append2089414218ession @ B @ A ) )
= ( B = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_self__append__conv2) ).
thf(484,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A
= ( append2089414218ession @ B @ A ) )
= ( B = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(131,axiom,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( A @ D )
=> ( A @ ( append2089414218ession @ D @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_rev__induct) ).
thf(710,plain,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( A @ D )
=> ( A @ ( append2089414218ession @ D @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(26,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( append2089414218ession @ ( append2089414218ession @ A @ B ) @ C )
= ( append2089414218ession @ A @ ( append2089414218ession @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_append_Oassoc) ).
thf(285,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( append2089414218ession @ ( append2089414218ession @ A @ B ) @ C )
= ( append2089414218ession @ A @ ( append2089414218ession @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(163,axiom,
! [A: list_S529945141ession,B: list_S529945141ession > $o] :
( ( A != nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( B @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( D != nil_Se901661471ession )
=> ( ( B @ D )
=> ( B @ ( append2089414218ession @ D @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_rev__nonempty__induct) ).
thf(916,plain,
! [A: list_S529945141ession,B: list_S529945141ession > $o] :
( ( A != nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( B @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( D != nil_Se901661471ession )
=> ( ( B @ D )
=> ( B @ ( append2089414218ession @ D @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(80,axiom,
( ( tl_Sec1905266422ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_list_Osel_I2_J) ).
thf(467,plain,
( ( tl_Sec1905266422ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(104,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: secrecy_Expression,D: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( cons_S112077679ession @ C @ D ) )
= ( ( ( A = nil_Se901661471ession )
& ( B
= ( cons_S112077679ession @ C @ D ) ) )
| ? [E: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ C @ E ) )
& ( ( append2089414218ession @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_append__eq__Cons__conv) ).
thf(583,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: secrecy_Expression,D: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( cons_S112077679ession @ C @ D ) )
= ( ( ( A = nil_Se901661471ession )
& ( B
= ( cons_S112077679ession @ C @ D ) ) )
| ? [E: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ C @ E ) )
& ( ( append2089414218ession @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(97,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession > list_S529945141ession > $o] :
( ( listre84909707ession @ A @ B @ C )
=> ( ( D @ nil_Se901661471ession @ nil_Se901661471ession )
=> ( ! [E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ( A @ E @ F )
=> ( ( listre84909707ession @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_S112077679ession @ E @ G ) @ ( cons_S112077679ession @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_listrelp_Oinducts) ).
thf(522,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession > list_S529945141ession > $o] :
( ( listre84909707ession @ A @ B @ C )
=> ( ( D @ nil_Se901661471ession @ nil_Se901661471ession )
=> ( ! [E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ( A @ E @ F )
=> ( ( listre84909707ession @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_S112077679ession @ E @ G ) @ ( cons_S112077679ession @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(127,axiom,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Expression_Odistinct_I1_J) ).
thf(697,plain,
! [A: secrecy_Keys,B: secrecy_Secrets] :
( ( secrecy_kE @ A )
!= ( secrecy_sE @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(116,axiom,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= B ) )
& ( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_last_Osimps) ).
thf(650,plain,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= B ) )
& ( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( cons_S112077679ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(186,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_KS_Oinject_I2_J) ).
thf(980,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sKS @ A )
= ( secrecy_sKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(63,axiom,
( ( butlas171474643ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_butlast_Osimps_I1_J) ).
thf(403,plain,
( ( butlas171474643ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(43,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] : ( lexord1123423577ession @ A @ B @ ( append2089414218ession @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_ord_Olexordp__eq__pref) ).
thf(339,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] : ( lexord1123423577ession @ A @ B @ ( append2089414218ession @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(168,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
= ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_knows1k) ).
thf(933,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
= ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(112,axiom,
! [A: secrecy_Expression] :
~ ( mem_Se1967555118ession @ A @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_mem_Osimps_I1_J) ).
thf(637,plain,
! [A: secrecy_Expression] :
~ ( mem_Se1967555118ession @ A @ nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(100,axiom,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( ( A = nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( cons_S112077679ession @ B @ A ) )
= nil_Se901661471ession ) )
& ( ( A != nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( cons_S112077679ession @ B @ A ) )
= ( cons_S112077679ession @ B @ ( butlas171474643ession @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_butlast_Osimps_I2_J) ).
thf(547,plain,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( ( A = nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( cons_S112077679ession @ B @ A ) )
= nil_Se901661471ession ) )
& ( ( A != nil_Se901661471ession )
=> ( ( butlas171474643ession @ ( cons_S112077679ession @ B @ A ) )
= ( cons_S112077679ession @ B @ ( butlas171474643ession @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(40,axiom,
! [A: secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession] :
( ( distin1076152135ession @ ( cons_S112077679ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( ( A != B )
& ( distin1076152135ession @ ( cons_S112077679ession @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_distinct__adj__Cons__Cons) ).
thf(328,plain,
! [A: secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession] :
( ( distin1076152135ession @ ( cons_S112077679ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( ( A != B )
& ( distin1076152135ession @ ( cons_S112077679ession @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(19,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( nil_Se901661471ession
= ( append2089414218ession @ A @ B ) )
= ( ( A = nil_Se901661471ession )
& ( B = nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Nil__is__append__conv) ).
thf(256,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( nil_Se901661471ession
= ( append2089414218ession @ A @ B ) )
= ( ( A = nil_Se901661471ession )
& ( B = nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(188,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
= ( ( ine @ A @ ( secrecy_sE @ B ) )
| ( member_Secrecy_KS2 @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_know_Osimps_I2_J) ).
thf(985,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
= ( ( ine @ A @ ( secrecy_sE @ B ) )
| ( member_Secrecy_KS2 @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(128,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
= ( ? [B: secrecy_Expression,C: list_S529945141ession] :
( A
= ( cons_S112077679ession @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_neq__Nil__conv) ).
thf(701,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
= ( ? [B: secrecy_Expression,C: list_S529945141ession] :
( A
= ( cons_S112077679ession @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(95,axiom,
( knowle1268625169orrect
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
( ( eout @ A @ B )
= ( ? [C: secrecy_Keys] :
( ( B
= ( secrecy_kE @ C ) )
& ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) )
| ? [C: secrecy_Secrets] :
( ( B
= ( secrecy_sE @ C ) )
& ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) )
| ( knowle731562421_knows @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_eoutKnowsECorrect__def) ).
thf(515,plain,
( knowle1268625169orrect
= ( ^ [A: secrecy_specID,B: secrecy_Expression] :
( ( eout @ A @ B )
= ( ? [C: secrecy_Keys] :
( ( B
= ( secrecy_kE @ C ) )
& ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) )
| ? [C: secrecy_Secrets] :
( ( B
= ( secrecy_sE @ C ) )
& ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) )
| ( knowle731562421_knows @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(54,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( splice1390717708ession @ A @ B )
= nil_Se901661471ession )
= ( ( A = nil_Se901661471ession )
& ( B = nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_split__Nil__iff) ).
thf(371,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( splice1390717708ession @ A @ B )
= nil_Se901661471ession )
= ( ( A = nil_Se901661471ession )
& ( B = nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(170,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ B ) ) @ nil_Se901661471ession ) )
= ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_know1s) ).
thf(938,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ B ) ) @ nil_Se901661471ession ) )
= ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(51,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( append2089414218ession @ C @ D ) )
= ( ? [E: list_S529945141ession] :
( ( ( A
= ( append2089414218ession @ C @ E ) )
& ( ( append2089414218ession @ E @ B )
= D ) )
| ( ( ( append2089414218ession @ A @ E )
= C )
& ( B
= ( append2089414218ession @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_append__eq__append__conv2) ).
thf(360,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( append2089414218ession @ C @ D ) )
= ( ? [E: list_S529945141ession] :
( ( ( A
= ( append2089414218ession @ C @ E ) )
& ( ( append2089414218ession @ E @ B )
= D ) )
| ( ( ( append2089414218ession @ A @ E )
= C )
& ( B
= ( append2089414218ession @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(93,axiom,
! [A: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,B: secrecy_Expression > secrecy_Expression,C: list_S529945141ession,D: list_S529945141ession] :
( ! [E: secrecy_Expression > secrecy_Expression,F: list_S529945141ession] : ( A @ E @ nil_Se901661471ession @ F )
=> ( ! [E: secrecy_Expression > secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ( A @ E @ G @ ( cons_S112077679ession @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_S112077679ession @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_map__tailrec__rev_Oinduct) ).
thf(508,plain,
! [A: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,B: secrecy_Expression > secrecy_Expression,C: list_S529945141ession,D: list_S529945141ession] :
( ! [E: secrecy_Expression > secrecy_Expression,F: list_S529945141ession] : ( A @ E @ nil_Se901661471ession @ F )
=> ( ! [E: secrecy_Expression > secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ( A @ E @ G @ ( cons_S112077679ession @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_S112077679ession @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(102,axiom,
! [A: secrecy_Expression > list_S529945141ession] :
( ( bind_S815874003ession @ nil_Se901661471ession @ A )
= nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_bind__simps_I1_J) ).
thf(558,plain,
! [A: secrecy_Expression > list_S529945141ession] :
( ( bind_S815874003ession @ nil_Se901661471ession @ A )
= nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(122,axiom,
! [A: list_S529945141ession] :
( ( ( tl_Sec1905266422ession @ A )
= nil_Se901661471ession )
= ( ( A = nil_Se901661471ession )
| ? [B: secrecy_Expression] :
( A
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_tl__Nil) ).
thf(674,plain,
! [A: list_S529945141ession] :
( ( ( tl_Sec1905266422ession @ A )
= nil_Se901661471ession )
= ( ( A = nil_Se901661471ession )
| ? [B: secrecy_Expression] :
( A
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(105,axiom,
! [A: list_S529945141ession > list_S529945141ession > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ! [D: list_S529945141ession] : ( A @ nil_Se901661471ession @ D )
=> ( ! [D: list_S529945141ession] : ( A @ D @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession,F: secrecy_Expression,G: list_S529945141ession] :
( ( A @ E @ ( cons_S112077679ession @ F @ G ) )
=> ( ( A @ ( cons_S112077679ession @ D @ E ) @ G )
=> ( A @ ( cons_S112077679ession @ D @ E ) @ ( cons_S112077679ession @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_shuffles_Oinduct) ).
thf(586,plain,
! [A: list_S529945141ession > list_S529945141ession > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ! [D: list_S529945141ession] : ( A @ nil_Se901661471ession @ D )
=> ( ! [D: list_S529945141ession] : ( A @ D @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession,F: secrecy_Expression,G: list_S529945141ession] :
( ( A @ E @ ( cons_S112077679ession @ F @ G ) )
=> ( ( A @ ( cons_S112077679ession @ D @ E ) @ G )
=> ( A @ ( cons_S112077679ession @ D @ E ) @ ( cons_S112077679ession @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(165,axiom,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_KS2Expression_Osimps_I2_J) ).
thf(926,plain,
! [A: secrecy_Secrets] :
( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
= ( secrecy_sE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(30,axiom,
! [A: list_S529945141ession] :
( ( append2089414218ession @ A @ nil_Se901661471ession )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_append_Oright__neutral) ).
thf(298,plain,
! [A: list_S529945141ession] :
( ( append2089414218ession @ A @ nil_Se901661471ession )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(136,axiom,
! [A: secrecy_Expression > $o] :
~ ( list_e1486860828ession @ A @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_list__ex1__simps_I1_J) ).
thf(733,plain,
! [A: secrecy_Expression > $o] :
~ ( list_e1486860828ession @ A @ nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(150,axiom,
! [A: secrecy_KS,B: secrecy_KS > $o] :
( ( member_Secrecy_KS2 @ A @ ( collect_Secrecy_KS @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mem__Collect__eq) ).
thf(819,plain,
! [A: secrecy_KS,B: secrecy_KS > $o] :
( ( member_Secrecy_KS2 @ A @ ( collect_Secrecy_KS @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(68,axiom,
distin1076152135ession @ nil_Se901661471ession,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_distinct__adj__Nil) ).
thf(423,plain,
distin1076152135ession @ nil_Se901661471ession,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1,conjecture,
knowle945212990e_know @ a @ ( secrecy_sKS @ m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(191,plain,
~ ( knowle945212990e_know @ a @ ( secrecy_sKS @ m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( tl_Sec1905266422ession @ ( cons_S112077679ession @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_list_Osel_I3_J) ).
thf(291,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( tl_Sec1905266422ession @ ( cons_S112077679ession @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
| ( B = nil_Se901661471ession )
| ( ( last_S1532390982ession @ A )
!= ( hd_Sec357328890ession @ B ) ) )
=> ( ( remdup484344169ession @ ( append2089414218ession @ A @ B ) )
= ( append2089414218ession @ ( remdup484344169ession @ A ) @ ( remdup484344169ession @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_remdups__adj__append_H) ).
thf(259,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
| ( B = nil_Se901661471ession )
| ( ( last_S1532390982ession @ A )
!= ( hd_Sec357328890ession @ B ) ) )
=> ( ( remdup484344169ession @ ( append2089414218ession @ A @ B ) )
= ( append2089414218ession @ ( remdup484344169ession @ A ) @ ( remdup484344169ession @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(35,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A
= ( append2089414218ession @ A @ B ) )
= ( B = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_self__append__conv) ).
thf(313,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A
= ( append2089414218ession @ A @ B ) )
= ( B = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(146,axiom,
! [A: list_S529945141ession,B: list_S529945141ession > $o] :
( ( A != nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( B @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( D != nil_Se901661471ession )
=> ( ( B @ D )
=> ( B @ ( cons_S112077679ession @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_list__nonempty__induct) ).
thf(787,plain,
! [A: list_S529945141ession,B: list_S529945141ession > $o] :
( ( A != nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( B @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( D != nil_Se901661471ession )
=> ( ( B @ D )
=> ( B @ ( cons_S112077679ession @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(12,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( rev_Se1073238207ession @ A ) )
= ( hd_Sec357328890ession @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_last__rev) ).
thf(236,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( rev_Se1073238207ession @ A ) )
= ( hd_Sec357328890ession @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(129,axiom,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_KS2Expression_Osimps_I1_J) ).
thf(704,plain,
! [A: secrecy_Keys] :
( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
= ( secrecy_kE @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(173,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
= ( ( eout @ A @ ( secrecy_kE @ B ) )
= ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_eout__know__k) ).
thf(947,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
= ( ( eout @ A @ ( secrecy_kE @ B ) )
= ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(98,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ~ ! [B: list_S529945141ession,C: secrecy_Expression] :
( A
!= ( append2089414218ession @ B @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_rev__exhaust) ).
thf(540,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ~ ! [B: list_S529945141ession,C: secrecy_Expression] :
( A
!= ( append2089414218ession @ B @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(75,axiom,
! [A: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
| ( ( tl_Sec1905266422ession @ A )
!= nil_Se901661471ession ) )
=> ( ( last_S1532390982ession @ ( tl_Sec1905266422ession @ A ) )
= ( last_S1532390982ession @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_last__tl) ).
thf(445,plain,
! [A: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
| ( ( tl_Sec1905266422ession @ A )
!= nil_Se901661471ession ) )
=> ( ( last_S1532390982ession @ ( tl_Sec1905266422ession @ A ) )
= ( last_S1532390982ession @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(169,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
=> ( ( eout @ A @ ( secrecy_kE @ B ) )
=> ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_eoutKnowCorrect__L1k) ).
thf(936,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
=> ( ( eout @ A @ ( secrecy_kE @ B ) )
=> ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(145,axiom,
! [A: secrecy_Expression] :
( ( insert1173886601ession @ A @ nil_Se901661471ession )
= ( cons_S112077679ession @ A @ nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_insert__Nil) ).
thf(784,plain,
! [A: secrecy_Expression] :
( ( insert1173886601ession @ A @ nil_Se901661471ession )
= ( cons_S112077679ession @ A @ nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(67,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_last__appendR) ).
thf(419,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(137,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( nil_Se901661471ession
!= ( cons_S112077679ession @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_list_Odistinct_I1_J) ).
thf(736,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( nil_Se901661471ession
!= ( cons_S112077679ession @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(10,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ ( tl_Sec1905266422ession @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_hd__Cons__tl) ).
thf(230,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ ( tl_Sec1905266422ession @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
? [C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( A
= ( append2089414218ession @ D @ C ) )
& ( B
= ( append2089414218ession @ E @ C ) )
& ( ( D = nil_Se901661471ession )
| ( E = nil_Se901661471ession )
| ( ( last_S1532390982ession @ D )
!= ( last_S1532390982ession @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_longest__common__suffix) ).
thf(451,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
? [C: list_S529945141ession,D: list_S529945141ession,E: list_S529945141ession] :
( ( A
= ( append2089414218ession @ D @ C ) )
& ( B
= ( append2089414218ession @ E @ C ) )
& ( ( D = nil_Se901661471ession )
| ( E = nil_Se901661471ession )
| ( ( last_S1532390982ession @ D )
!= ( last_S1532390982ession @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(15,axiom,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( remdup484344169ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( append2089414218ession @ ( remdup484344169ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_remdups__adj__append) ).
thf(245,plain,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( remdup484344169ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ C ) ) )
= ( append2089414218ession @ ( remdup484344169ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(109,axiom,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( A @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( ( C = D )
=> ( A @ ( cons_S112077679ession @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_S112077679ession @ D @ E ) ) )
=> ( A @ ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_remdups__adj_Oinduct) ).
thf(616,plain,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( A @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( ( C = D )
=> ( A @ ( cons_S112077679ession @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_S112077679ession @ D @ E ) ) )
=> ( A @ ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(22,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] : ( lexord1123423577ession @ A @ nil_Se901661471ession @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_ord_Olexordp__eq__simps_I1_J) ).
thf(271,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] : ( lexord1123423577ession @ A @ nil_Se901661471ession @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(56,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( rev_Se1073238207ession @ ( cons_S112077679ession @ A @ B ) )
= ( append2089414218ession @ ( rev_Se1073238207ession @ B ) @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_rev_Osimps_I2_J) ).
thf(377,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( rev_Se1073238207ession @ ( cons_S112077679ession @ A @ B ) )
= ( append2089414218ession @ ( rev_Se1073238207ession @ B ) @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(190,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
= ( ( ine @ A @ ( secrecy_kE @ B ) )
| ( member_Secrecy_KS2 @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_know_Osimps_I1_J) ).
thf(990,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
= ( ( ine @ A @ ( secrecy_kE @ B ) )
| ( member_Secrecy_KS2 @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(59,axiom,
! [A: secrecy_specID,B: list_S529945141ession,C: list_S529945141ession] :
( ( knowle731562421_knows @ A @ ( append2089414218ession @ B @ C ) )
=> ( knowle731562421_knows @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_knows2a) ).
thf(387,plain,
! [A: secrecy_specID,B: list_S529945141ession,C: list_S529945141ession] :
( ( knowle731562421_knows @ A @ ( append2089414218ession @ B @ C ) )
=> ( knowle731562421_knows @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(90,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] :
( ( succes1388047762ession @ A @ B )
=> ( ( B != nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] :
( B
!= ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ~ ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_successively_Oelims_I2_J) ).
thf(494,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] :
( ( succes1388047762ession @ A @ B )
=> ( ( B != nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] :
( B
!= ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ~ ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(141,axiom,
( lexord1123423577ession
= ( ^ [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ? [D: list_S529945141ession] :
( ( B = nil_Se901661471ession )
& ( C = D ) )
| ? [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession,G: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
& ( C
= ( cons_S112077679ession @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession,G: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
& ( C
= ( cons_S112077679ession @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexord1123423577ession @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_ord_Olexordp__eq_Osimps) ).
thf(758,plain,
( lexord1123423577ession
= ( ^ [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ? [D: list_S529945141ession] :
( ( B = nil_Se901661471ession )
& ( C = D ) )
| ? [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession,G: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
& ( C
= ( cons_S112077679ession @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession,G: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
& ( C
= ( cons_S112077679ession @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexord1123423577ession @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(149,axiom,
! [A: set_Secrecy_Keys] :
( ( collect_Secrecy_Keys
@ ^ [B: secrecy_Keys] : ( member_Secrecy_Keys @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Collect__mem__eq) ).
thf(816,plain,
! [A: set_Secrecy_Keys] :
( ( collect_Secrecy_Keys
@ ^ [B: secrecy_Keys] : ( member_Secrecy_Keys @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(107,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: $o] :
( ( ( succes1388047762ession @ A @ B )
= C )
=> ( ( ( B = nil_Se901661471ession )
=> ~ C )
=> ( ( ? [D: secrecy_Expression] :
( B
= ( cons_S112077679ession @ D @ nil_Se901661471ession ) )
=> ~ C )
=> ~ ! [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ ( cons_S112077679ession @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_successively_Oelims_I1_J) ).
thf(594,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: $o] :
( ( ( succes1388047762ession @ A @ B )
= C )
=> ( ( ( B = nil_Se901661471ession )
=> ~ C )
=> ( ( ? [D: secrecy_Expression] :
( B
= ( cons_S112077679ession @ D @ nil_Se901661471ession ) )
=> ~ C )
=> ~ ! [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ ( cons_S112077679ession @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(8,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( append2089414218ession @ A @ B ) )
= ( hd_Sec357328890ession @ B ) ) )
& ( ( A != nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( append2089414218ession @ A @ B ) )
= ( hd_Sec357328890ession @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_hd__append) ).
thf(213,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( append2089414218ession @ A @ B ) )
= ( hd_Sec357328890ession @ B ) ) )
& ( ( A != nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( append2089414218ession @ A @ B ) )
= ( hd_Sec357328890ession @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( last_S1532390982ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_last__snoc) ).
thf(251,plain,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( last_S1532390982ession @ ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(179,axiom,
! [A: secrecy_Keys > secrecy_Keys > $o,B: secrecy_Keys,C: secrecy_Keys,D: secrecy_specID,E: list_S529945141ession] :
( ( ( A @ B @ C )
& ( knowle945212990e_know @ D @ ( secrecy_kKS @ B ) )
& ( knowle731562421_knows @ D @ ( sign @ C @ E ) ) )
=> ( knowle731562421_knows @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_knows5) ).
thf(964,plain,
! [A: secrecy_Keys > secrecy_Keys > $o,B: secrecy_Keys,C: secrecy_Keys,D: secrecy_specID,E: list_S529945141ession] :
( ( ( A @ B @ C )
& ( knowle945212990e_know @ D @ ( secrecy_kKS @ B ) )
& ( knowle731562421_knows @ D @ ( sign @ C @ E ) ) )
=> ( knowle731562421_knows @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(78,axiom,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
= C )
= ( ( C != nil_Se901661471ession )
& ( ( butlas171474643ession @ C )
= A )
& ( ( last_S1532390982ession @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_snoc__eq__iff__butlast) ).
thf(462,plain,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( ( append2089414218ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
= C )
= ( ( C != nil_Se901661471ession )
& ( ( butlas171474643ession @ C )
= A )
& ( ( last_S1532390982ession @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(187,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
=> ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_knows2know__k) ).
thf(983,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
=> ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(177,axiom,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
=> ( ( eout @ A @ ( secrecy_sE @ B ) )
=> ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_eoutKnowCorrect__L1s) ).
thf(959,plain,
! [A: secrecy_specID,B: secrecy_Secrets] :
( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
=> ( ( eout @ A @ ( secrecy_sE @ B ) )
=> ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
| ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(143,axiom,
! [A: secrecy_Expression > secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession] :
( ( ( map_ta1624757057ession @ A @ B @ C )
= D )
=> ( ( ( B = nil_Se901661471ession )
=> ( D != C ) )
=> ~ ! [E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ E @ F ) )
=> ( D
!= ( map_ta1624757057ession @ A @ F @ ( cons_S112077679ession @ ( A @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_map__tailrec__rev_Oelims) ).
thf(768,plain,
! [A: secrecy_Expression > secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession] :
( ( ( map_ta1624757057ession @ A @ B @ C )
= D )
=> ( ( ( B = nil_Se901661471ession )
=> ( D != C ) )
=> ~ ! [E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ E @ F ) )
=> ( D
!= ( map_ta1624757057ession @ A @ F @ ( cons_S112077679ession @ ( A @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(157,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( lexord1123423577ession @ A @ B @ C )
=> ( ( B != nil_Se901661471ession )
=> ( ! [D: secrecy_Expression] :
( ? [E: list_S529945141ession] :
( B
= ( cons_S112077679ession @ D @ E ) )
=> ! [E: secrecy_Expression] :
( ? [F: list_S529945141ession] :
( C
= ( cons_S112077679ession @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
=> ! [G: list_S529945141ession] :
( ( C
= ( cons_S112077679ession @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexord1123423577ession @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_ord_Olexordp__eq_Ocases) ).
thf(868,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( lexord1123423577ession @ A @ B @ C )
=> ( ( B != nil_Se901661471ession )
=> ( ! [D: secrecy_Expression] :
( ? [E: list_S529945141ession] :
( B
= ( cons_S112077679ession @ D @ E ) )
=> ! [E: secrecy_Expression] :
( ? [F: list_S529945141ession] :
( C
= ( cons_S112077679ession @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
=> ! [G: list_S529945141ession] :
( ( C
= ( cons_S112077679ession @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexord1123423577ession @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(92,axiom,
! [A: list_S529945141ession] :
( ( ( rotate1237234450ession @ A )
= nil_Se901661471ession )
= ( A = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_rotate1__is__Nil__conv) ).
thf(505,plain,
! [A: list_S529945141ession] :
( ( ( rotate1237234450ession @ A )
= nil_Se901661471ession )
= ( A = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(117,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ nil_Se901661471ession )
= ( rev_Se1073238207ession @ B ) )
= ( B
= ( cons_S112077679ession @ A @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_singleton__rev__conv) ).
thf(658,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( ( cons_S112077679ession @ A @ nil_Se901661471ession )
= ( rev_Se1073238207ession @ B ) )
= ( B
= ( cons_S112077679ession @ A @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(88,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o] : ( succes1388047762ession @ A @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_successively_Osimps_I1_J) ).
thf(490,plain,
! [A: secrecy_Expression > secrecy_Expression > $o] : ( succes1388047762ession @ A @ nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(70,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( append2089414218ession @ ( butlas171474643ession @ A ) @ ( cons_S112077679ession @ ( last_S1532390982ession @ A ) @ nil_Se901661471ession ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_append__butlast__last__id) ).
thf(426,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( append2089414218ession @ ( butlas171474643ession @ A ) @ ( cons_S112077679ession @ ( last_S1532390982ession @ A ) @ nil_Se901661471ession ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(172,axiom,
! [A: secrecy_KS > $o,B: secrecy_KS] :
( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
=> ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_KS_Oinduct) ).
thf(944,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)],[172]) ).
thf(55,axiom,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( ( rev_Se1073238207ession @ A )
= ( cons_S112077679ession @ B @ C ) )
= ( A
= ( append2089414218ession @ ( rev_Se1073238207ession @ C ) @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_rev__eq__Cons__iff) ).
thf(374,plain,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( ( rev_Se1073238207ession @ A )
= ( cons_S112077679ession @ B @ C ) )
= ( A
= ( append2089414218ession @ ( rev_Se1073238207ession @ C ) @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(87,axiom,
! [A: list_S529945141ession] :
( ( nil_Se901661471ession
= ( rev_Se1073238207ession @ A ) )
= ( A = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Nil__is__rev__conv) ).
thf(487,plain,
! [A: list_S529945141ession] :
( ( nil_Se901661471ession
= ( rev_Se1073238207ession @ A ) )
= ( A = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(148,axiom,
! [A: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,B: secrecy_Expression > secrecy_Expression > $o,C: list_S529945141ession] :
( ! [D: secrecy_Expression > secrecy_Expression > $o] : ( A @ D @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression > secrecy_Expression > $o,E: secrecy_Expression] : ( A @ D @ ( cons_S112077679ession @ E @ nil_Se901661471ession ) )
=> ( ! [D: secrecy_Expression > secrecy_Expression > $o,E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession] :
( ( A @ D @ ( cons_S112077679ession @ F @ G ) )
=> ( A @ D @ ( cons_S112077679ession @ E @ ( cons_S112077679ession @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_successively_Oinduct) ).
thf(812,plain,
! [A: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,B: secrecy_Expression > secrecy_Expression > $o,C: list_S529945141ession] :
( ! [D: secrecy_Expression > secrecy_Expression > $o] : ( A @ D @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression > secrecy_Expression > $o,E: secrecy_Expression] : ( A @ D @ ( cons_S112077679ession @ E @ nil_Se901661471ession ) )
=> ( ! [D: secrecy_Expression > secrecy_Expression > $o,E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession] :
( ( A @ D @ ( cons_S112077679ession @ F @ G ) )
=> ( A @ D @ ( cons_S112077679ession @ E @ ( cons_S112077679ession @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(49,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] : ( lexord1123423577ession @ A @ nil_Se901661471ession @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_ord_Olexordp__eq_ONil) ).
thf(355,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] : ( lexord1123423577ession @ A @ nil_Se901661471ession @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(181,axiom,
knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms) ).
thf(968,plain,
knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(147,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( listre84909707ession @ A @ B @ C )
=> ( ( ( B = nil_Se901661471ession )
=> ( C != nil_Se901661471ession ) )
=> ~ ! [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
=> ! [G: list_S529945141ession] :
( ( C
= ( cons_S112077679ession @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listre84909707ession @ A @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_listrelp_Ocases) ).
thf(795,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( listre84909707ession @ A @ B @ C )
=> ( ( ( B = nil_Se901661471ession )
=> ( C != nil_Se901661471ession ) )
=> ~ ! [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
=> ! [G: list_S529945141ession] :
( ( C
= ( cons_S112077679ession @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listre84909707ession @ A @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(124,axiom,
! [A: list_S529945141ession > list_S529945141ession > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( A @ nil_Se901661471ession @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession] : ( A @ ( cons_S112077679ession @ D @ E ) @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession] : ( A @ nil_Se901661471ession @ ( cons_S112077679ession @ D @ E ) )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession,F: secrecy_Expression,G: list_S529945141ession] :
( ( A @ E @ G )
=> ( A @ ( cons_S112077679ession @ D @ E ) @ ( cons_S112077679ession @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_list__induct2_H) ).
thf(680,plain,
! [A: list_S529945141ession > list_S529945141ession > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( A @ nil_Se901661471ession @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession] : ( A @ ( cons_S112077679ession @ D @ E ) @ nil_Se901661471ession )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession] : ( A @ nil_Se901661471ession @ ( cons_S112077679ession @ D @ E ) )
=> ( ! [D: secrecy_Expression,E: list_S529945141ession,F: secrecy_Expression,G: list_S529945141ession] :
( ( A @ E @ G )
=> ( A @ ( cons_S112077679ession @ D @ E ) @ ( cons_S112077679ession @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(156,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( splice1390717708ession @ A @ B )
= C )
=> ( ( ( A = nil_Se901661471ession )
=> ( C != B ) )
=> ~ ! [D: secrecy_Expression,E: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ D @ E ) )
=> ( C
!= ( cons_S112077679ession @ D @ ( splice1390717708ession @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_splice_Oelims) ).
thf(855,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( splice1390717708ession @ A @ B )
= C )
=> ( ( ( A = nil_Se901661471ession )
=> ( C != B ) )
=> ~ ! [D: secrecy_Expression,E: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ D @ E ) )
=> ( C
!= ( cons_S112077679ession @ D @ ( splice1390717708ession @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(125,axiom,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Expression_Oinject_I2_J) ).
thf(690,plain,
! [A: secrecy_Secrets,B: secrecy_Secrets] :
( ( ( secrecy_sE @ A )
= ( secrecy_sE @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(113,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ~ ! [B: secrecy_Expression,C: list_S529945141ession] :
( A
!= ( cons_S112077679ession @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_list_Oexhaust) ).
thf(640,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ~ ! [B: secrecy_Expression,C: list_S529945141ession] :
( A
!= ( cons_S112077679ession @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(130,axiom,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_KS_Oinject_I1_J) ).
thf(707,plain,
! [A: secrecy_Keys,B: secrecy_Keys] :
( ( ( secrecy_kKS @ A )
= ( secrecy_kKS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(34,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( rotate1237234450ession @ A )
= ( append2089414218ession @ ( tl_Sec1905266422ession @ A ) @ ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ nil_Se901661471ession ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_rotate1__hd__tl) ).
thf(310,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( rotate1237234450ession @ A )
= ( append2089414218ession @ ( tl_Sec1905266422ession @ A ) @ ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ nil_Se901661471ession ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(41,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_last__appendL) ).
thf(331,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(91,axiom,
! [A: secrecy_Expression > secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession,D: list_S529945141ession] :
( ( map_ta1624757057ession @ A @ ( cons_S112077679ession @ B @ C ) @ D )
= ( map_ta1624757057ession @ A @ C @ ( cons_S112077679ession @ ( A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_map__tailrec__rev_Osimps_I2_J) ).
thf(502,plain,
! [A: secrecy_Expression > secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession,D: list_S529945141ession] :
( ( map_ta1624757057ession @ A @ ( cons_S112077679ession @ B @ C ) @ D )
= ( map_ta1624757057ession @ A @ C @ ( cons_S112077679ession @ ( A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(99,axiom,
! [A: secrecy_Expression,B: list_S529945141ession,C: secrecy_Expression] :
( ( member2020590922ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( ( A = C )
| ( member2020590922ession @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_member__rec_I1_J) ).
thf(544,plain,
! [A: secrecy_Expression,B: list_S529945141ession,C: secrecy_Expression] :
( ( member2020590922ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( ( A = C )
| ( member2020590922ession @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(42,axiom,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession] :
( ( splice1390717708ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( cons_S112077679ession @ A @ ( splice1390717708ession @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_splice_Osimps_I2_J) ).
thf(336,plain,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession] :
( ( splice1390717708ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( cons_S112077679ession @ A @ ( splice1390717708ession @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(108,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: list_S529945141ession] :
( ( notSpe1586871396tsExpr @ A @ ( cons_S112077679ession @ B @ C ) )
=> ( notSpe1586871396tsExpr @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_notSpecKeysSecretsExpr__L1) ).
thf(613,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: list_S529945141ession] :
( ( notSpe1586871396tsExpr @ A @ ( cons_S112077679ession @ B @ C ) )
=> ( notSpe1586871396tsExpr @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(185,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_know2knows__k) ).
thf(978,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(79,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o] : ( listre84909707ession @ A @ nil_Se901661471ession @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_listrelp_ONil) ).
thf(465,plain,
! [A: secrecy_Expression > secrecy_Expression > $o] : ( listre84909707ession @ A @ nil_Se901661471ession @ nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(52,axiom,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession] :
( ( append2089414218ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( cons_S112077679ession @ A @ ( append2089414218ession @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_append__Cons) ).
thf(363,plain,
! [A: secrecy_Expression,B: list_S529945141ession,C: list_S529945141ession] :
( ( append2089414218ession @ ( cons_S112077679ession @ A @ B ) @ C )
= ( cons_S112077679ession @ A @ ( append2089414218ession @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(167,axiom,
( notSpe1586871396tsExpr
= ( ^ [A: secrecy_specID,B: list_S529945141ession] :
( ! [C: secrecy_Keys] :
( ( mem_Se1967555118ession @ ( secrecy_kE @ C ) @ B )
=> ~ ( member_Secrecy_KS2 @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
& ! [C: secrecy_Secrets] :
( ( mem_Se1967555118ession @ ( secrecy_sE @ C ) @ B )
=> ~ ( member_Secrecy_KS2 @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_notSpecKeysSecretsExpr__def) ).
thf(931,plain,
( notSpe1586871396tsExpr
= ( ^ [A: secrecy_specID,B: list_S529945141ession] :
( ! [C: secrecy_Keys] :
( ( mem_Se1967555118ession @ ( secrecy_kE @ C ) @ B )
=> ~ ( member_Secrecy_KS2 @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
& ! [C: secrecy_Secrets] :
( ( mem_Se1967555118ession @ ( secrecy_sE @ C ) @ B )
=> ~ ( member_Secrecy_KS2 @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(5,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( append2089414218ession @ A @ B ) )
= ( hd_Sec357328890ession @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_hd__append2) ).
thf(203,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( append2089414218ession @ A @ B ) )
= ( hd_Sec357328890ession @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(184,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_know2knows__neg__k) ).
thf(976,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
=> ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(178,axiom,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID] :
( ( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
| ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) )
=> ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
| ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_knows2knowPQ__k) ).
thf(961,plain,
! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID] :
( ( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
| ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) ) )
=> ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
| ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(96,axiom,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ B @ C ) )
=> ( A != nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_list_OdiscI) ).
thf(517,plain,
! [A: list_S529945141ession,B: secrecy_Expression,C: list_S529945141ession] :
( ( A
= ( cons_S112077679ession @ B @ C ) )
=> ( A != nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(37,axiom,
! [A: list_S529945141ession] :
( ( append2089414218ession @ A @ nil_Se901661471ession )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_append__Nil2) ).
thf(319,plain,
! [A: list_S529945141ession] :
( ( append2089414218ession @ A @ nil_Se901661471ession )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( rev_Se1073238207ession @ ( append2089414218ession @ A @ B ) )
= ( append2089414218ession @ ( rev_Se1073238207ession @ B ) @ ( rev_Se1073238207ession @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_rev__append) ).
thf(304,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( rev_Se1073238207ession @ ( append2089414218ession @ A @ B ) )
= ( append2089414218ession @ ( rev_Se1073238207ession @ B ) @ ( rev_Se1073238207ession @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(110,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression] : ( succes1388047762ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_successively_Osimps_I2_J) ).
thf(632,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression] : ( succes1388047762ession @ A @ ( cons_S112077679ession @ B @ nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(144,axiom,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( ( rev_Se1073238207ession @ A )
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
= ( A
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_rev__singleton__conv) ).
thf(781,plain,
! [A: list_S529945141ession,B: secrecy_Expression] :
( ( ( rev_Se1073238207ession @ A )
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) )
= ( A
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(6,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( hd_Sec357328890ession @ ( cons_S112077679ession @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_list_Osel_I1_J) ).
thf(207,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( hd_Sec357328890ession @ ( cons_S112077679ession @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(166,axiom,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
=> ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_knows2know__neg__k) ).
thf(929,plain,
! [A: secrecy_specID,B: secrecy_Keys] :
( ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ B ) @ nil_Se901661471ession ) )
=> ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(84,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] :
( ( lexord1123423577ession @ A @ B @ nil_Se901661471ession )
= ( B = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ord_Olexordp__eq__simps_I2_J) ).
thf(478,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] :
( ( lexord1123423577ession @ A @ B @ nil_Se901661471ession )
= ( B = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(158,axiom,
! [A: list_S529945141ession] :
( ( nil_Se901661471ession
= ( tl_Sec1905266422ession @ A ) )
= ( ( A = nil_Se901661471ession )
| ? [B: secrecy_Expression] :
( A
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_Nil__tl) ).
thf(899,plain,
! [A: list_S529945141ession] :
( ( nil_Se901661471ession
= ( tl_Sec1905266422ession @ A ) )
= ( ( A = nil_Se901661471ession )
| ? [B: secrecy_Expression] :
( A
= ( cons_S112077679ession @ B @ nil_Se901661471ession ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(152,axiom,
! [A: secrecy_Expression] :
( ( remdup484344169ession @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) )
= ( cons_S112077679ession @ A @ nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_remdups__adj_Osimps_I2_J) ).
thf(832,plain,
! [A: secrecy_Expression] :
( ( remdup484344169ession @ ( cons_S112077679ession @ A @ nil_Se901661471ession ) )
= ( cons_S112077679ession @ A @ nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(46,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession,E: list_S529945141ession] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexord1123423577ession @ A @ D @ E )
=> ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ D ) @ ( cons_S112077679ession @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_ord_Olexordp__eq_OCons__eq) ).
thf(346,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: secrecy_Expression,D: list_S529945141ession,E: list_S529945141ession] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexord1123423577ession @ A @ D @ E )
=> ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ D ) @ ( cons_S112077679ession @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(139,axiom,
! [A: secrecy_Keys,B: secrecy_Keys > $o] :
( ( member_Secrecy_Keys @ A @ ( collect_Secrecy_Keys @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_mem__Collect__eq) ).
thf(752,plain,
! [A: secrecy_Keys,B: secrecy_Keys > $o] :
( ( member_Secrecy_Keys @ A @ ( collect_Secrecy_Keys @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(72,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ B ) ) )
& ( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_last__append) ).
thf(432,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( A = nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ B ) ) )
& ( ( A != nil_Se901661471ession )
=> ( ( last_S1532390982ession @ ( append2089414218ession @ B @ A ) )
= ( last_S1532390982ession @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(64,axiom,
! [A: secrecy_specID,B: list_S529945141ession,C: list_S529945141ession] :
( ( knowle731562421_knows @ A @ ( append2089414218ession @ B @ C ) )
=> ( knowle731562421_knows @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_knows2b) ).
thf(405,plain,
! [A: secrecy_specID,B: list_S529945141ession,C: list_S529945141ession] :
( ( knowle731562421_knows @ A @ ( append2089414218ession @ B @ C ) )
=> ( knowle731562421_knows @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(23,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A = B )
=> ( A
= ( append2089414218ession @ nil_Se901661471ession @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_eq__Nil__appendI) ).
thf(273,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( A = B )
=> ( A
= ( append2089414218ession @ nil_Se901661471ession @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(174,axiom,
! [A: secrecy_Keys > secrecy_Keys > $o,B: secrecy_Keys,C: secrecy_Keys,D: secrecy_specID,E: list_S529945141ession] :
( ( ( A @ B @ C )
& ( knowle945212990e_know @ D @ ( secrecy_kKS @ C ) )
& ( knowle731562421_knows @ D @ ( enc @ B @ E ) ) )
=> ( knowle731562421_knows @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_knows4) ).
thf(950,plain,
! [A: secrecy_Keys > secrecy_Keys > $o,B: secrecy_Keys,C: secrecy_Keys,D: secrecy_specID,E: list_S529945141ession] :
( ( ( A @ B @ C )
& ( knowle945212990e_know @ D @ ( secrecy_kKS @ C ) )
& ( knowle731562421_knows @ D @ ( enc @ B @ E ) ) )
=> ( knowle731562421_knows @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(153,axiom,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( A @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( A @ E )
=> ( ( A @ ( cons_S112077679ession @ D @ E ) )
=> ( A @ ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_induct__list012) ).
thf(835,plain,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression] : ( A @ ( cons_S112077679ession @ C @ nil_Se901661471ession ) )
=> ( ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( A @ E )
=> ( ( A @ ( cons_S112077679ession @ D @ E ) )
=> ( A @ ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(7,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: list_S529945141ession] :
( ( succes1388047762ession @ A @ ( cons_S112077679ession @ B @ C ) )
= ( ( C = nil_Se901661471ession )
| ( ( A @ B @ ( hd_Sec357328890ession @ C ) )
& ( succes1388047762ession @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_successively__Cons) ).
thf(210,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: list_S529945141ession] :
( ( succes1388047762ession @ A @ ( cons_S112077679ession @ B @ C ) )
= ( ( C = nil_Se901661471ession )
| ( ( A @ B @ ( hd_Sec357328890ession @ C ) )
& ( succes1388047762ession @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] :
( ~ ( succes1388047762ession @ A @ B )
=> ~ ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_successively_Oelims_I3_J) ).
thf(294,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession] :
( ~ ( succes1388047762ession @ A @ B )
=> ~ ! [C: secrecy_Expression,D: secrecy_Expression,E: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ C @ ( cons_S112077679ession @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( succes1388047762ession @ A @ ( cons_S112077679ession @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(44,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( cons_S112077679ession @ A @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ A @ B ) ) ) )
= ( remdup484344169ession @ ( cons_S112077679ession @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_remdups__adj__Cons__alt) ).
thf(341,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( cons_S112077679ession @ A @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ A @ B ) ) ) )
= ( remdup484344169ession @ ( cons_S112077679ession @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(21,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= A )
= ( B = nil_Se901661471ession ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_append__self__conv) ).
thf(268,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= A )
= ( B = nil_Se901661471ession ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(119,axiom,
! [A: secrecy_specID] : ( knowle731562421_knows @ A @ nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_knows__emptyexpression) ).
thf(664,plain,
! [A: secrecy_specID] : ( knowle731562421_knows @ A @ nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(62,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( distin1076152135ession @ ( append2089414218ession @ A @ B ) )
= ( ( distin1076152135ession @ A )
& ( distin1076152135ession @ B )
& ( ( A = nil_Se901661471ession )
| ( B = nil_Se901661471ession )
| ( ( last_S1532390982ession @ A )
!= ( hd_Sec357328890ession @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_distinct__adj__append__iff) ).
thf(400,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( distin1076152135ession @ ( append2089414218ession @ A @ B ) )
= ( ( distin1076152135ession @ A )
& ( distin1076152135ession @ B )
& ( ( A = nil_Se901661471ession )
| ( B = nil_Se901661471ession )
| ( ( last_S1532390982ession @ A )
!= ( hd_Sec357328890ession @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(132,axiom,
! [A: secrecy_Keys,B: secrecy_Keys,C: list_S529945141ession] :
( ( encrDecrKeys @ A @ B )
=> ( ( decr @ B @ ( enc @ A @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_DecrEnc) ).
thf(720,plain,
! [A: secrecy_Keys,B: secrecy_Keys,C: list_S529945141ession] :
( ( encrDecrKeys @ A @ B )
=> ( ( decr @ B @ ( enc @ A @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(13,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( rev_Se1073238207ession @ A ) )
= ( last_S1532390982ession @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_hd__rev) ).
thf(239,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( ( hd_Sec357328890ession @ ( rev_Se1073238207ession @ A ) )
= ( last_S1532390982ession @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( distin1076152135ession @ ( cons_S112077679ession @ A @ B ) )
= ( ( B = nil_Se901661471ession )
| ( ( A
!= ( hd_Sec357328890ession @ B ) )
& ( distin1076152135ession @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_distinct__adj__Cons) ).
thf(242,plain,
! [A: secrecy_Expression,B: list_S529945141ession] :
( ( distin1076152135ession @ ( cons_S112077679ession @ A @ B ) )
= ( ( B = nil_Se901661471ession )
| ( ( A
!= ( hd_Sec357328890ession @ B ) )
& ( distin1076152135ession @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(114,axiom,
( listre84909707ession
= ( ^ [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( B = nil_Se901661471ession )
& ( C = nil_Se901661471ession ) )
| ? [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession,G: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
& ( C
= ( cons_S112077679ession @ E @ G ) )
& ( A @ D @ E )
& ( listre84909707ession @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_listrelp_Osimps) ).
thf(644,plain,
( listre84909707ession
= ( ^ [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( B = nil_Se901661471ession )
& ( C = nil_Se901661471ession ) )
| ? [D: secrecy_Expression,E: secrecy_Expression,F: list_S529945141ession,G: list_S529945141ession] :
( ( B
= ( cons_S112077679ession @ D @ F ) )
& ( C
= ( cons_S112077679ession @ E @ G ) )
& ( A @ D @ E )
& ( listre84909707ession @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(77,axiom,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= nil_Se901661471ession )
= ( ( A = nil_Se901661471ession )
& ( B = nil_Se901661471ession ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_append__is__Nil__conv) ).
thf(459,plain,
! [A: list_S529945141ession,B: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= nil_Se901661471ession )
= ( ( A = nil_Se901661471ession )
& ( B = nil_Se901661471ession ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(151,axiom,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( A @ D )
=> ( A @ ( cons_S112077679ession @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_list_Oinducts) ).
thf(822,plain,
! [A: list_S529945141ession > $o,B: list_S529945141ession] :
( ( A @ nil_Se901661471ession )
=> ( ! [C: secrecy_Expression,D: list_S529945141ession] :
( ( A @ D )
=> ( A @ ( cons_S112077679ession @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(4,axiom,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( A
= ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ ( tl_Sec1905266422ession @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_list_Oexhaust__sel) ).
thf(200,plain,
! [A: list_S529945141ession] :
( ( A != nil_Se901661471ession )
=> ( A
= ( cons_S112077679ession @ ( hd_Sec357328890ession @ A ) @ ( tl_Sec1905266422ession @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: list_S529945141ession,D: secrecy_Expression,E: list_S529945141ession] :
( ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ C ) @ ( cons_S112077679ession @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexord1123423577ession @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ord_Olexordp__eq__simps_I4_J) ).
thf(277,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: secrecy_Expression,C: list_S529945141ession,D: secrecy_Expression,E: list_S529945141ession] :
( ( lexord1123423577ession @ A @ ( cons_S112077679ession @ B @ C ) @ ( cons_S112077679ession @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexord1123423577ession @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(134,axiom,
! [A: secrecy_specID,B: secrecy_Expression,C: list_S529945141ession] :
( ( notSpe1586871396tsExpr @ A @ ( cons_S112077679ession @ B @ C ) )
=> ( notSpe1586871396tsExpr @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_notSpecKeysSecretsExpr__L2) ).
thf(728,plain,
! [A: secrecy_specID,B: secrecy_Expression,C: list_S529945141ession] :
( ( notSpe1586871396tsExpr @ A @ ( cons_S112077679ession @ B @ C ) )
=> ( notSpe1586871396tsExpr @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(138,axiom,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession > list_S529945141ession > $o] :
( ( lexord1123423577ession @ A @ B @ C )
=> ( ! [E: list_S529945141ession] : ( D @ nil_Se901661471ession @ E )
=> ( ! [E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ( A @ E @ F )
=> ( D @ ( cons_S112077679ession @ E @ G ) @ ( cons_S112077679ession @ F @ H ) ) )
=> ( ! [E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexord1123423577ession @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_S112077679ession @ E @ G ) @ ( cons_S112077679ession @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_ord_Olexordp__eq_Oinducts) ).
thf(740,plain,
! [A: secrecy_Expression > secrecy_Expression > $o,B: list_S529945141ession,C: list_S529945141ession,D: list_S529945141ession > list_S529945141ession > $o] :
( ( lexord1123423577ession @ A @ B @ C )
=> ( ! [E: list_S529945141ession] : ( D @ nil_Se901661471ession @ E )
=> ( ! [E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ( A @ E @ F )
=> ( D @ ( cons_S112077679ession @ E @ G ) @ ( cons_S112077679ession @ F @ H ) ) )
=> ( ! [E: secrecy_Expression,F: secrecy_Expression,G: list_S529945141ession,H: list_S529945141ession] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexord1123423577ession @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_S112077679ession @ E @ G ) @ ( cons_S112077679ession @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(18,axiom,
( ( rev_Se1073238207ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_rev_Osimps_I1_J) ).
thf(254,plain,
( ( rev_Se1073238207ession @ nil_Se901661471ession )
= nil_Se901661471ession ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( append2089414218ession @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_append__same__eq) ).
thf(322,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( append2089414218ession @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(81,axiom,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( append2089414218ession @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_same__append__eq) ).
thf(469,plain,
! [A: list_S529945141ession,B: list_S529945141ession,C: list_S529945141ession] :
( ( ( append2089414218ession @ A @ B )
= ( append2089414218ession @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(140,axiom,
! [A: secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession] :
( ( mem_Se1967555118ession @ A @ ( cons_S112077679ession @ B @ C ) )
= ( ( A = B )
| ( mem_Se1967555118ession @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mem_Osimps_I2_J) ).
thf(755,plain,
! [A: secrecy_Expression,B: secrecy_Expression,C: list_S529945141ession] :
( ( mem_Se1967555118ession @ A @ ( cons_S112077679ession @ B @ C ) )
= ( ( A = B )
| ( mem_Se1967555118ession @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(993,plain,
$false,
inference(e,[status(thm)],[760,941,555,666,481,352,408,730,440,677,384,472,913,670,973,288,301,389,724,344,357,902,853,969,416,325,316,492,591,443,646,966,905,475,924,280,634,221,956,988,849,307,233,248,380,512,661,366,910,952,349,561,392,424,429,192,693,484,710,285,916,467,583,522,697,650,980,403,339,933,637,547,328,256,985,701,515,371,938,360,508,558,674,586,926,298,733,819,423,191,291,259,313,787,236,704,947,540,445,936,784,419,736,230,451,245,616,271,377,990,387,494,758,816,594,213,251,964,462,983,959,768,868,505,658,490,426,944,374,487,812,355,968,795,680,855,690,640,707,310,331,502,544,336,613,978,465,363,931,203,976,961,517,319,304,632,781,207,929,478,899,832,346,752,432,405,273,950,835,210,294,341,268,664,400,720,239,242,644,459,822,200,277,728,740,254,322,469,755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : ITP085^1 : TPTP v8.2.0. Released v7.5.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n014.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat May 18 17:01:39 EDT 2024
% 0.11/0.31 % CPUTime :
% 1.00/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.84/1.31 % [INFO] Parsing done (372ms).
% 1.84/1.33 % [INFO] Running in sequential loop mode.
% 3.10/1.69 % [INFO] eprover registered as external prover.
% 3.10/1.69 % [INFO] cvc4 registered as external prover.
% 3.10/1.70 % [INFO] Scanning for conjecture ...
% 3.46/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ...
% 3.81/2.00 % [INFO] Axiom selection finished. Selected 188 axioms (removed 164 axioms).
% 4.87/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 4.87/2.25 % [INFO] Type checking passed.
% 4.87/2.25 % [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 ...
% 21.80/7.49 % External prover 'e' found a proof!
% 21.80/7.49 % [INFO] Killing All external provers ...
% 22.03/7.49 % Time passed: 7026ms (effective reasoning time: 6159ms)
% 22.03/7.49 % 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)>
% 22.03/7.49 % Axioms used in derivation (188): fact_40_map__tailrec__rev_Oinduct, fact_175_splice_Osimps_I1_J, fact_348_remdups__adj_Osimps_I2_J, fact_54_Collect__mem__eq, fact_186_rev__induct, fact_155_splice__Nil2, fact_330_successively_Osimps_I1_J, fact_162_Cons__eq__appendI, fact_129_member__rec_I1_J, fact_189_DecrEnc, fact_27_list_Oinducts, fact_307_Nil__tl, fact_350_remdups__adj_Oelims, fact_171_knows3, fact_53_mem__Collect__eq, fact_211_notSpecKeysSecretsExpr__def, fact_126_notSpecKeysSecretsExpr__L1, fact_16_KS_Oinduct, fact_68_know_Osimps_I1_J, fact_174_splice_Osimps_I2_J, fact_44_successively_Oinduct, fact_208_butlast__snoc, fact_223_last__ConsR, fact_1_KS_Oinject_I2_J, fact_111_listrelp_ONil, fact_127_member__rec_I2_J, fact_343_remdups__adj__append, fact_62_know2knows__k, fact_163_append_Oleft__neutral, fact_300_distinct__adj__ConsD, fact_158_append1__eq__conv, fact_291_list_Ocollapse, fact_145_append__self__conv2, fact_263_rev_Osimps_I2_J, fact_284_rotate1__hd__tl, fact_218_butlast_Osimps_I1_J, fact_167_eq__Nil__appendI, fact_64_know2knowsPQ__k, fact_48_sorted__wrt_Oinduct, fact_237_mem_Osimps_I1_J, fact_70_insert__Nil, fact_346_remdups__adj__Cons__alt, fact_303_list_Osel_I3_J, fact_344_remdups__adj__Nil__iff, fact_25_list_Oexhaust, fact_287_distinct__adj__Cons__Cons, fact_19_list_Oinject, fact_165_append__Nil, fact_88_ord_Olexordp__eq__simps_I3_J, fact_10_knows6, fact_169_knows2b, fact_100_listrelp_Osimps, fact_12_Expression_Oinject_I2_J, fact_180_append__eq__Cons__conv, fact_137_append_Oright__neutral, fact_13_know1k, fact_121_ord_Olexordp__eq_Oinducts, fact_3_know1s, fact_339_successively__Cons, fact_55_Collect__mem__eq, fact_15_KS_Oexhaust, fact_214_last__appendL, fact_75_eout__know__k, fact_234_butlast__append, fact_141_Nil__is__append__conv, fact_217_append__butlast__last__id, fact_187_maps__simps_I1_J, fact_221_snoc__eq__iff__butlast, fact_63_knows2know__k, fact_18_knows7, fact_315_distinct__adj__Cons, fact_29_neq__Nil__conv, fact_294_list_Oexpand, fact_73_KS2Expression_Osimps_I1_J, fact_160_append__eq__append__conv2, fact_288_tl__append2, fact_125_listrelp_Ocases, fact_61_knows1k, fact_238_mem_Osimps_I2_J, fact_210_last__snoc, fact_173_notSpecKeysSecretsExpr__L2, fact_251_Nil__is__rev__conv, fact_197_rotate1_Osimps_I1_J, fact_327_successively_Oelims_I1_J, fact_35_splice_Oinduct, fact_278_longest__common__prefix, fact_233_butlast_Osimps_I2_J, fact_298_distinct__adj__Nil, fact_170_knows2a, fact_172_ord_Olexordp__eq__pref, fact_151_append__Nil2, fact_259_rev__singleton__conv, fact_325_successively_Osimps_I2_J, fact_194_rotate1__is__Nil__conv, fact_17_KS_Odistinct_I1_J, fact_106_ord_Olexordp__eq_OCons, fact_96_listrelp_Oinducts, fact_51_mem__Collect__eq, fact_101_ord_Olexordp__eq__simps_I4_J, fact_67_knows2know__neg__k, fact_83_list__ex1__simps_I1_J, fact_255_rev__append, fact_305_tl__Nil, fact_60_shuffles_Oinduct, fact_38_not__Cons__self2, fact_9_knows5, fact_228_longest__common__suffix, fact_282_list_Osel_I1_J, fact_202_maps__simps_I2_J, fact_4_eoutKnowCorrect__L1s, fact_117_ord_Olexordp__eq_Ocases, fact_333_successively_Oelims_I3_J, fact_159_append__eq__appendI, fact_107_ord_Olexordp__eq_OCons__eq, fact_110_listrelp_OCons, fact_329_successively_Oelims_I2_J, fact_42_list__nonempty__induct, fact_272_hd__rev, fact_119_ord_Olexordp__eq_Osimps, fact_270_last__rev, fact_14_knows__emptyexpression, fact_143_self__append__conv2, fact_6_know_Osimps_I2_J, fact_72_Expression_Odistinct_I1_J, fact_136_same__append__eq, fact_301_list_Osel_I2_J, fact_50_remdups__adj_Ocases, fact_2_know2knows__s, fact_250_rev__eq__Cons__iff, fact_134_append__assoc, fact_102_ord_Olexordp__eq__simps_I2_J, fact_74_eoutKnowCorrect__L1k, fact_11_KS_Oinject_I1_J, fact_276_hd__append, fact_230_last__append, fact_351_remdups__adj_Osimps_I3_J, fact_65_knows2knowPQ__k, fact_178_rev__nonempty__induct, fact_182_Cons__eq__append__conv, fact_313_list_Oexhaust__sel, fact_86_map__tailrec__rev_Oelims, fact_135_append__same__eq, fact_293_hd__Cons__tl, fact_147_self__append__conv, fact_184_rev__exhaust, fact_71_Expression_Oinject_I1_J, fact_5_eout__know__s, fact_104_ord_Olexordp__eq__simps_I1_J, fact_66_know2knows__neg__k, fact_108_ord_Olexordp__eq_ONil, fact_212_last__appendR, fact_89_bind__simps_I1_J, fact_227_last_Osimps, fact_8_knows4, fact_297_distinct__adj__appendD2, fact_56_Collect__mem__eq, fact_316_successively__append__iff, fact_340_remdups__adj__append_H, fact_188_ExtSign, fact_260_rev_Osimps_I1_J, fact_37_induct__list012, fact_161_append__Cons, fact_33_list__induct2_H, fact_193_rotate1_Osimps_I2_J, fact_308_last__tl, fact_77_eoutKnowsECorrect__def, fact_46_remdups__adj_Oinduct, fact_7_KS2Expression_Osimps_I2_J, fact_76_eoutKnowsECorrect__L1, fact_139_append__is__Nil__conv, fact_0_assms, fact_153_split__Nil__iff, fact_285_distinct__adj__append__iff, fact_257_singleton__rev__conv, fact_225_last__ConsL, fact_115_map__tailrec__rev_Osimps_I2_J, fact_23_list_OdiscI, fact_274_hd__append2, fact_52_mem__Collect__eq, fact_332_successively_Osimps_I3_J, fact_132_bind__simps_I2_J, fact_149_append__self__conv, fact_253_rev__is__Nil__conv, fact_131_splice_Oelims, fact_311_distinct__adj__singleton, fact_296_distinct__adj__appendD1, fact_21_list_Odistinct_I1_J, fact_133_append_Oassoc
% 22.03/7.49 % No. of inferences in proof: 380
% 22.03/7.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7026 ms resp. 6159 ms w/o parsing
% 22.76/7.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.76/7.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------