TSTP Solution File: ITP085^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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 ... 
%------------------------------------------------------------------------------