TSTP Solution File: ITP091^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP091^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 22:22:49 EDT 2024

% Result   : Theorem 23.38s 6.93s
% Output   : Refutation 24.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  371
% Syntax   : Number of formulae    :  667 ( 284 unt;  77 typ;   0 def)
%            Number of atoms       : 2202 ( 744 equ;   6 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 7033 ( 509   ~;  96   |; 230   &;5178   @)
%                                         (   0 <=>;1020  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Number of types       :   14 (  13 usr)
%            Number of type conns  :  106 ( 106   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   67 (  64 usr;  11 con; 0-3 aty)
%            Number of variables   : 1716 (  82   ^1556   !;  78   ?;1716   :)

% Comments : 
%------------------------------------------------------------------------------
thf(list_S529945141ession_type,type,
    list_S529945141ession: $tType ).

thf(set_Secrecy_Secrets_type,type,
    set_Secrecy_Secrets: $tType ).

thf(set_Secrecy_specID_type,type,
    set_Secrecy_specID: $tType ).

thf(set_Secrecy_chanID_type,type,
    set_Secrecy_chanID: $tType ).

thf(set_Secrecy_Keys_type,type,
    set_Secrecy_Keys: $tType ).

thf(set_Secrecy_KS_type,type,
    set_Secrecy_KS: $tType ).

thf(secrecy_Expression_type,type,
    secrecy_Expression: $tType ).

thf(secrecy_Secrets_type,type,
    secrecy_Secrets: $tType ).

thf(secrecy_specID_type,type,
    secrecy_specID: $tType ).

thf(secrecy_chanID_type,type,
    secrecy_chanID: $tType ).

thf(secrecy_Keys_type,type,
    secrecy_Keys: $tType ).

thf(secrecy_KS_type,type,
    secrecy_KS: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(localSecrets_type,type,
    localSecrets: secrecy_specID > set_Secrecy_KS ).

thf(knowle233900195orrect_type,type,
    knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).

thf(knowle945212990e_know_type,type,
    knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).

thf(sup_su1301156759ecy_KS_type,type,
    sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).

thf(sup_su1029080330ecrets_type,type,
    sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).

thf(sup_su370684444chanID_type,type,
    sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).

thf(sup_su1712599557specID_type,type,
    sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).

thf(mem_Se1967555118ession_type,type,
    mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).

thf(bot_bot_Secrecy_KS_o_type,type,
    bot_bot_Secrecy_KS_o: secrecy_KS > $o ).

thf(bot_bo1909946299rets_o_type,type,
    bot_bo1909946299rets_o: secrecy_Secrets > $o ).

thf(bot_bo1943466239ecy_KS_type,type,
    bot_bo1943466239ecy_KS: set_Secrecy_KS ).

thf(bot_bo1124690338ecrets_type,type,
    bot_bo1124690338ecrets: set_Secrecy_Secrets ).

thf(bot_bo443197316chanID_type,type,
    bot_bo443197316chanID: set_Secrecy_chanID ).

thf(bot_bo1785112429specID_type,type,
    bot_bo1785112429specID: set_Secrecy_specID ).

thf(ord_le1802272080chanID_type,type,
    ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).

thf(correctCompositionKS_type,type,
    correctCompositionKS: secrecy_specID > $o ).

thf(eout_type,type,
    eout: secrecy_specID > secrecy_Expression > $o ).

thf(eoutM_type,type,
    eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).

thf(exprChannel_type,type,
    exprChannel: secrecy_chanID > secrecy_Expression > $o ).

thf(ine_type,type,
    ine: secrecy_specID > secrecy_Expression > $o ).

thf(ineM_type,type,
    ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).

thf(ine_exprChannelSet_type,type,
    ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).

thf(ine_ex1303305700Single_type,type,
    ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).

thf(notSpe1586871396tsExpr_type,type,
    notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).

thf(out_exprChannelSet_type,type,
    out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).

thf(out_ex985543062Single_type,type,
    out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).

thf(specKeys_type,type,
    specKeys: secrecy_specID > set_Secrecy_Keys ).

thf(specKeysSecrets_type,type,
    specKeysSecrets: secrecy_specID > set_Secrecy_KS ).

thf(specSecrets_type,type,
    specSecrets: secrecy_specID > set_Secrecy_Secrets ).

thf(secrecy_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(collec836099393ecrets_type,type,
    collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).

thf(insert_Secrecy_KS_type,type,
    insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).

thf(insert751661162chanID_type,type,
    insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).

thf(insert1671894227specID_type,type,
    insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).

thf(is_emp1849217361specID_type,type,
    is_emp1849217361specID: set_Secrecy_specID > $o ).

thf(is_sin1442426433ecy_KS_type,type,
    is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).

thf(is_sin1002224330ecrets_type,type,
    is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).

thf(is_sin1501507247specID_type,type,
    is_sin1501507247specID: set_Secrecy_specID > $o ).

thf(the_el827131246specID_type,type,
    the_el827131246specID: set_Secrecy_specID > secrecy_specID ).

thf(correctCompositionIn_type,type,
    correctCompositionIn: secrecy_specID > $o ).

thf(correc965049635ionLoc_type,type,
    correc965049635ionLoc: secrecy_specID > $o ).

thf(correc990227761ionOut_type,type,
    correc990227761ionOut: secrecy_specID > $o ).

thf(inStream_type,type,
    inStream: secrecy_specID > set_Secrecy_chanID > $o ).

thf(ins_type,type,
    ins: secrecy_specID > set_Secrecy_chanID ).

thf(loc_type,type,
    loc: secrecy_specID > set_Secrecy_chanID ).

thf(locStream_type,type,
    locStream: secrecy_specID > set_Secrecy_chanID > $o ).

thf(out_type,type,
    out: secrecy_specID > set_Secrecy_chanID ).

thf(outStream_type,type,
    outStream: secrecy_specID > set_Secrecy_chanID > $o ).

thf(subcomponents_type,type,
    subcomponents: secrecy_specID > set_Secrecy_specID ).

thf(member_Secrecy_KS_type,type,
    member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).

thf(member_Secrecy_Keys_type,type,
    member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).

thf(member2138796287ecrets_type,type,
    member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).

thf(member1967978193chanID_type,type,
    member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).

thf(member740727610specID_type,type,
    member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).

thf(p_type,type,
    p: secrecy_specID ).

thf(pq_type,type,
    pq: secrecy_specID ).

thf(q_type,type,
    q: secrecy_specID ).

thf(m_type,type,
    m: secrecy_KS ).

thf(secret_type,type,
    secret: secrecy_Secrets ).

thf(179,axiom,
    correc965049635ionLoc @ pq,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_cCompLoc) ).

thf(892,plain,
    correc965049635ionLoc @ pq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(216,axiom,
    ( out_ex985543062Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member1967978193chanID @ B @ ( out @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID,E: nat] :
              ( ( ( member1967978193chanID @ D @ ( out @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_out__exprChannelSingle__def) ).

thf(1036,plain,
    ( out_ex985543062Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member1967978193chanID @ B @ ( out @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID] :
              ( ( ( member1967978193chanID @ D @ ( out @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(153,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_sup__bot__left) ).

thf(809,plain,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(253,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
      = ( ( ine @ A @ ( secrecy_kE @ B ) )
        | ( member_Secrecy_KS @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_know_Osimps_I1_J) ).

thf(1168,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
      = ( ( ine @ A @ ( secrecy_kE @ B ) )
        | ( member_Secrecy_KS @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(273,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ? [C: set_Secrecy_KS] :
          ( ( B
            = ( insert_Secrecy_KS @ A @ C ) )
          & ~ ( member_Secrecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mk__disjoint__insert) ).

thf(1237,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ? [C: set_Secrecy_KS] :
          ( ( B
            = ( insert_Secrecy_KS @ A @ C ) )
          & ~ ( member_Secrecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(14,axiom,
    ! [A: secrecy_chanID,B: secrecy_chanID] :
      ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
        = ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_singleton__inject) ).

thf(333,plain,
    ! [A: secrecy_chanID,B: secrecy_chanID] :
      ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
        = ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(180,axiom,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kKS @ A )
        = ( secrecy_kKS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_KS_Oinject_I1_J) ).

thf(893,plain,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kKS @ A )
        = ( secrecy_kKS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(197,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ~ ( eoutM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correc990227761ionOut @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ F @ C )
                  & ( member1967978193chanID @ F @ B )
                  & ( member1967978193chanID @ F @ ( loc @ E ) ) )
             => ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_TBtheorem5b__notP1) ).

thf(962,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ~ ( eoutM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correc990227761ionOut @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ F @ C )
                  & ( member1967978193chanID @ F @ B )
                  & ( member1967978193chanID @ F @ ( loc @ E ) ) )
             => ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(144,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_sup__bot__right) ).

thf(777,plain,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(234,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_kE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_LocalSecretsComposition__ine2__k) ).

thf(1110,plain,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_kE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(250,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
                 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_LocalSecretsComposition__neg__s) ).

thf(1158,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
                 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(68,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( ~ ( member1967978193chanID @ A @ B )
       => ( member1967978193chanID @ A @ C ) )
     => ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_UnCI) ).

thf(511,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( ~ ( member1967978193chanID @ A @ B )
       => ( member1967978193chanID @ A @ C ) )
     => ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(118,axiom,
    ! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_singletonI) ).

thf(677,plain,
    ! [A: secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(289,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_correctCompositionKS__exprChannel__k__Pex) ).

thf(1305,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(226,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_correctCompositionKS__exprChannel__s__Pex) ).

thf(1078,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(31,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
      ( ( ~ ( member740727610specID @ A @ B )
       => ( A = C ) )
     => ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insertCI) ).

thf(385,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
      ( ( ~ ( member740727610specID @ A @ B )
       => ( A = C ) )
     => ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(129,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ( member1967978193chanID @ F @ B )
             => ( ( member1967978193chanID @ F @ ( ins @ E ) )
               => ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_TBlemma3b) ).

thf(715,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ( member1967978193chanID @ F @ B )
             => ( ( member1967978193chanID @ F @ ( ins @ E ) )
               => ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(282,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
      ( ( ? [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ A )
            & ( C @ D ) )
        | ? [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ B )
            & ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_bex__Un) ).

thf(1275,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
      ( ( ? [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ A )
            & ( C @ D ) )
        | ? [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ B )
            & ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(272,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ~ ! [C: set_Secrecy_KS] :
            ( ( B
              = ( insert_Secrecy_KS @ A @ C ) )
           => ( member_Secrecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Set_Oset__insert) ).

thf(1233,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ~ ! [C: set_Secrecy_KS] :
            ( ( B
              = ( insert_Secrecy_KS @ A @ C ) )
           => ( member_Secrecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(294,axiom,
    member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sg5) ).

thf(1327,plain,
    member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(269,axiom,
    ! [A: set_Secrecy_KS,B: secrecy_KS] :
      ( ( A = bot_bo1943466239ecy_KS )
     => ~ ( member_Secrecy_KS @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_equals0D) ).

thf(1222,plain,
    ! [A: set_Secrecy_KS,B: secrecy_KS] :
      ( ( A = bot_bo1943466239ecy_KS )
     => ~ ( member_Secrecy_KS @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(116,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member1967978193chanID @ D @ ( ins @ A ) )
         => ( ( member1967978193chanID @ D @ ( ins @ B ) )
            | ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_correctCompositionIn__prop1) ).

thf(670,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member1967978193chanID @ D @ ( ins @ A ) )
         => ( ( member1967978193chanID @ D @ ( ins @ B ) )
            | ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(230,axiom,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kKS @ A )
     != ( secrecy_sKS @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_KS_Odistinct_I1_J) ).

thf(1095,plain,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kKS @ A )
     != ( secrecy_sKS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(239,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
     => ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_not__know__s__not__eout) ).

thf(1127,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
     => ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(146,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ E @ B )
                  & ( member1967978193chanID @ E @ ( loc @ D ) ) )
             => ~ ( ine @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_TBtheorem4a__notP1) ).

thf(782,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ E @ B )
                  & ( member1967978193chanID @ E @ ( loc @ D ) ) )
             => ~ ( ine @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(219,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
     => ( ~ ( knowle945212990e_know @ C @ ( secrecy_sKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_know__composition__neg__ine__s) ).

thf(1046,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
     => ( ~ ( knowle945212990e_know @ C @ ( secrecy_sKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(4,axiom,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ C ) )
      = ( insert751661162chanID @ B @ ( insert751661162chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__commute) ).

thf(301,plain,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ C ) )
      = ( insert751661162chanID @ B @ ( insert751661162chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(279,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( ( insert_Secrecy_KS @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insert__absorb) ).

thf(1265,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( ( insert_Secrecy_KS @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(87,axiom,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
      ( ( ( sup_su1712599557specID @ A @ B )
        = bot_bo1785112429specID )
      = ( ( A = bot_bo1785112429specID )
        & ( B = bot_bo1785112429specID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_Un__empty) ).

thf(570,plain,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
      ( ( ( sup_su1712599557specID @ A @ B )
        = bot_bo1785112429specID )
      = ( ( A = bot_bo1785112429specID )
        & ( B = bot_bo1785112429specID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(130,axiom,
    ( is_sin1501507247specID
    = ( ^ [A: set_Secrecy_specID] :
        ? [B: secrecy_specID] :
          ( A
          = ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_is__singleton__def) ).

thf(719,plain,
    ( is_sin1501507247specID
    = ( ^ [A: set_Secrecy_specID] :
        ? [B: secrecy_specID] :
          ( A
          = ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(66,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID,D: set_Secrecy_specID] :
      ( ~ ( member740727610specID @ A @ B )
     => ( ~ ( member740727610specID @ C @ D )
       => ( ( ( insert1671894227specID @ A @ B )
            = ( insert1671894227specID @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Secrecy_specID] :
                  ( ( B
                    = ( insert1671894227specID @ C @ E ) )
                  & ~ ( member740727610specID @ C @ E )
                  & ( D
                    = ( insert1671894227specID @ A @ E ) )
                  & ~ ( member740727610specID @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_insert__eq__iff) ).

thf(504,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID,D: set_Secrecy_specID] :
      ( ~ ( member740727610specID @ A @ B )
     => ( ~ ( member740727610specID @ C @ D )
       => ( ( ( insert1671894227specID @ A @ B )
            = ( insert1671894227specID @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Secrecy_specID] :
                  ( ( B
                    = ( insert1671894227specID @ C @ E ) )
                  & ~ ( member740727610specID @ C @ E )
                  & ( D
                    = ( insert1671894227specID @ A @ E ) )
                  & ~ ( member740727610specID @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(93,axiom,
    ! [A: secrecy_Secrets] :
      ~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_empty__iff) ).

thf(587,plain,
    ! [A: secrecy_Secrets] :
      ~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(193,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_Un__empty__right) ).

thf(949,plain,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(78,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
      = ( ( member740727610specID @ A @ B )
        | ( member740727610specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_Un__iff) ).

thf(542,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
      = ( ( member740727610specID @ A @ B )
        | ( member740727610specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(52,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
      = ( ( A = B )
        | ( member740727610specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insert__iff) ).

thf(460,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
      = ( ( A = B )
        | ( member740727610specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(156,axiom,
    ! [A: secrecy_specID] :
      ( ( the_el827131246specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_the__elem__eq) ).

thf(817,plain,
    ! [A: secrecy_specID] :
      ( ( the_el827131246specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(110,axiom,
    ! [A: set_Secrecy_Secrets] :
      ( ( A != bot_bo1124690338ecrets )
     => ( ! [B: secrecy_Secrets,C: secrecy_Secrets] :
            ( ( member2138796287ecrets @ B @ A )
           => ( ( member2138796287ecrets @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1002224330ecrets @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_is__singletonI_H) ).

thf(638,plain,
    ! [A: set_Secrecy_Secrets] :
      ( ( A != bot_bo1124690338ecrets )
     => ( ! [B: secrecy_Secrets,C: secrecy_Secrets] :
            ( ( member2138796287ecrets @ B @ A )
           => ( ( member2138796287ecrets @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1002224330ecrets @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(247,axiom,
    ! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
     => ( ( A != B )
       => ( member_Secrecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_insertE) ).

thf(1147,plain,
    ! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
     => ( ( A != B )
       => ( member_Secrecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(275,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
     => ( ( eout @ B @ ( secrecy_sE @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
         => ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_eout__know__nonKS__s) ).

thf(1247,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member2138796287ecrets @ A @ ( specSecrets @ B ) )
     => ( ( eout @ B @ ( secrecy_sE @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_sKS @ A ) )
         => ( knowle945212990e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(199,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_sup__bot_Oright__neutral) ).

thf(969,plain,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(211,axiom,
    ( out_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member1967978193chanID @ D @ B )
             => ( ( member1967978193chanID @ D @ ( out @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member1967978193chanID @ D @ B )
                & ( member1967978193chanID @ D @ ( out @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_out__exprChannelSet__def) ).

thf(1013,plain,
    ( out_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member1967978193chanID @ D @ B )
             => ( ( member1967978193chanID @ D @ ( out @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member1967978193chanID @ D @ B )
                & ( member1967978193chanID @ D @ ( out @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(175,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_Un__empty__left) ).

thf(881,plain,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(12,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
      ( ( ~ ( member1967978193chanID @ A @ B )
       => ( A = C ) )
     => ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_insertCI) ).

thf(325,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
      ( ( ~ ( member1967978193chanID @ A @ B )
       => ( A = C ) )
     => ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(50,axiom,
    ! [A: set_Secrecy_Secrets] :
      ( ! [B: secrecy_Secrets] :
          ~ ( member2138796287ecrets @ B @ A )
     => ( A = bot_bo1124690338ecrets ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_equals0I) ).

thf(448,plain,
    ! [A: set_Secrecy_Secrets] :
      ( ! [B: secrecy_Secrets] :
          ~ ( member2138796287ecrets @ B @ A )
     => ( A = bot_bo1124690338ecrets ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(42,axiom,
    ! [A: secrecy_Secrets] :
      ~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_emptyE) ).

thf(421,plain,
    ! [A: secrecy_Secrets] :
      ~ ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(171,axiom,
    ( locStream
    = ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( loc @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_locStream__def) ).

thf(870,plain,
    ( locStream
    = ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( loc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(62,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_UnI2) ).

thf(492,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(11,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( insert751661162chanID @ A @ B )
     != bot_bo443197316chanID ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_insert__not__empty) ).

thf(321,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( insert751661162chanID @ A @ B )
     != bot_bo443197316chanID ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(106,axiom,
    ! [A: secrecy_specID,B: secrecy_specID] :
      ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
        = ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_singleton__inject) ).

thf(623,plain,
    ! [A: secrecy_specID,B: secrecy_specID] :
      ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
        = ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(111,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ( G
                = ( sup_su370684444chanID @ D @ F ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member1967978193chanID @ H @ D )
                   => ( member1967978193chanID @ H @ ( loc @ A ) ) )
               => ( ! [H: secrecy_chanID] :
                      ( ( member1967978193chanID @ H @ F )
                     => ( member1967978193chanID @ H @ ( loc @ A ) ) )
                 => ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_TBtheorem5b__notPQ) ).

thf(646,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ( G
                = ( sup_su370684444chanID @ D @ F ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member1967978193chanID @ H @ D )
                   => ( member1967978193chanID @ H @ ( loc @ A ) ) )
               => ( ! [H: secrecy_chanID] :
                      ( ( member1967978193chanID @ H @ F )
                     => ( member1967978193chanID @ H @ ( loc @ A ) ) )
                 => ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(159,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ( eout @ B @ ( secrecy_kE @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
         => ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_eout__know__nonKS__k) ).

thf(834,plain,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ( eout @ B @ ( secrecy_kE @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
         => ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(69,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_UnI1) ).

thf(514,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(20,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_insertI1) ).

thf(353,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(198,axiom,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
      = ( ( member2138796287ecrets @ A @ B )
        | ( member2138796287ecrets @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Un__iff) ).

thf(966,plain,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
      = ( ( member2138796287ecrets @ A @ B )
        | ( member2138796287ecrets @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(183,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_sup__bot_Oleft__neutral) ).

thf(905,plain,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(59,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B = bot_bo443197316chanID )
       => ~ ( ine @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_ine__empty__exprChannelSet) ).

thf(480,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B = bot_bo443197316chanID )
       => ~ ( ine @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(34,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
      ( ( ? [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ A )
            & ( C @ D ) )
        | ? [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ B )
            & ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_bex__Un) ).

thf(397,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
      ( ( ? [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ A )
            & ( C @ D ) )
        | ? [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ B )
            & ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(109,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member1967978193chanID @ E @ ( ins @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
           => ( ine @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_TBtheorem4a__P) ).

thf(634,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member1967978193chanID @ E @ ( ins @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
           => ( ine @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(174,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member1967978193chanID @ F @ ( out @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ D ) )
                & ( member1967978193chanID @ F @ B ) )
           => ( eoutM @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_TBtheore54b__P) ).

thf(877,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member1967978193chanID @ F @ ( out @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ D ) )
                & ( member1967978193chanID @ F @ B ) )
           => ( eoutM @ D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(195,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
      ( ( member1967978193chanID @ A @ B )
     => ( ( member1967978193chanID @ A @ ( ins @ C ) )
       => ( ( exprChannel @ A @ D )
         => ( ineM @ C @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_ineM__L1) ).

thf(956,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
      ( ( member1967978193chanID @ A @ B )
     => ( ( member1967978193chanID @ A @ ( ins @ C ) )
       => ( ( exprChannel @ A @ D )
         => ( ineM @ C @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(112,axiom,
    ( ine_ex1303305700Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member1967978193chanID @ B @ ( ins @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID,E: nat] :
              ( ( ( member1967978193chanID @ D @ ( ins @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_ine__exprChannelSingle__def) ).

thf(660,plain,
    ( ine_ex1303305700Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member1967978193chanID @ B @ ( ins @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID] :
              ( ( ( member1967978193chanID @ D @ ( ins @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(44,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_sup__bot__right) ).

thf(428,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(8,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
        = ( sup_su370684444chanID @ B @ C ) )
      = ( ( ( B = bot_bo443197316chanID )
          & ( C
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) )
        | ( ( B
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
          & ( C = bot_bo443197316chanID ) )
        | ( ( B
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
          & ( C
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_singleton__Un__iff) ).

thf(312,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( ( insert751661162chanID @ A @ bot_bo443197316chanID )
        = ( sup_su370684444chanID @ B @ C ) )
      = ( ( ( B = bot_bo443197316chanID )
          & ( C
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) )
        | ( ( B
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
          & ( C = bot_bo443197316chanID ) )
        | ( ( B
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) )
          & ( C
            = ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C )
      = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Un__insert__left) ).

thf(307,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ ( insert751661162chanID @ A @ B ) @ C )
      = ( insert751661162chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(51,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( A != bot_bo1785112429specID )
     => ( ! [B: secrecy_specID,C: secrecy_specID] :
            ( ( member740727610specID @ B @ A )
           => ( ( member740727610specID @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1501507247specID @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_is__singletonI_H) ).

thf(452,plain,
    ! [A: set_Secrecy_specID] :
      ( ( A != bot_bo1785112429specID )
     => ( ! [B: secrecy_specID,C: secrecy_specID] :
            ( ( member740727610specID @ B @ A )
           => ( ( member740727610specID @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1501507247specID @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(187,axiom,
    ( inStream
    = ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( ins @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_inStream__def) ).

thf(920,plain,
    ( inStream
    = ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( ins @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(29,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
     => ( out_ex985543062Single @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_out__exprChannelSet__Single) ).

thf(380,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
     => ( out_ex985543062Single @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(189,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ( loc @ D )
              = bot_bo443197316chanID )
           => ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_TBtheorem4a__empty) ).

thf(925,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ( loc @ D )
              = bot_bo443197316chanID )
           => ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(262,axiom,
    ! [A: secrecy_Secrets] :
      ( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
      = ( secrecy_sE @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_KS2Expression_Osimps_I2_J) ).

thf(1199,plain,
    ! [A: secrecy_Secrets] :
      ( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
      = ( secrecy_sE @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(141,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [H: secrecy_chanID] :
                  ( ( member1967978193chanID @ H @ D )
                 => ( member1967978193chanID @ H @ ( loc @ A ) ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member1967978193chanID @ H @ F )
                   => ( member1967978193chanID @ H @ ( loc @ A ) ) )
               => ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_TBtheorem4b__notPQ) ).

thf(761,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID,G: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [H: secrecy_chanID] :
                  ( ( member1967978193chanID @ H @ D )
                 => ( member1967978193chanID @ H @ ( loc @ A ) ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member1967978193chanID @ H @ F )
                   => ( member1967978193chanID @ H @ ( loc @ A ) ) )
               => ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(290,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( ( knowle945212990e_know @ B @ A )
            | ( knowle945212990e_know @ C @ A ) )
         => ( ( ( subcomponents @ D )
              = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_know__composition) ).

thf(1311,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( ( knowle945212990e_know @ B @ A )
            | ( knowle945212990e_know @ C @ A ) )
         => ( ( ( subcomponents @ D )
              = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(76,axiom,
    ! [A: set_Secrecy_chanID,B: secrecy_chanID] :
      ( ( A = bot_bo443197316chanID )
     => ~ ( member1967978193chanID @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_equals0D) ).

thf(534,plain,
    ! [A: set_Secrecy_chanID,B: secrecy_chanID] :
      ( ( A = bot_bo443197316chanID )
     => ~ ( member1967978193chanID @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(229,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_LocalSecretsComposition__neg1__k) ).

thf(1091,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(255,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ A @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ B @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( member_Secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_LocalSecretsComposition1) ).

thf(1174,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ A @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ B @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( member_Secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(97,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Un__empty__right) ).

thf(598,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(157,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eout @ C @ B )
            | ( eout @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_TBtheorem2a) ).

thf(820,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eout @ C @ B )
            | ( eout @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(84,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
      = ( sup_su370684444chanID @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_Un__left__absorb) ).

thf(561,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
      = ( sup_su370684444chanID @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(43,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member_Secrecy_Keys @ C @ ( specKeys @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member740727610specID @ D @ ( subcomponents @ A ) )
              & ( member_Secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_correctCompositionKS__subcomp1) ).

thf(424,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member_Secrecy_Keys @ C @ ( specKeys @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member740727610specID @ D @ ( subcomponents @ A ) )
              & ( member_Secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(148,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( ( sup_su1301156759ecy_KS @ A @ B )
        = bot_bo1943466239ecy_KS )
      = ( ( A = bot_bo1943466239ecy_KS )
        & ( B = bot_bo1943466239ecy_KS ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_sup__bot_Oeq__neutr__iff) ).

thf(788,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( ( sup_su1301156759ecy_KS @ A @ B )
        = bot_bo1943466239ecy_KS )
      = ( ( A = bot_bo1943466239ecy_KS )
        & ( B = bot_bo1943466239ecy_KS ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(155,axiom,
    ( is_emp1849217361specID
    = ( ^ [A: set_Secrecy_specID] : ( A = bot_bo1785112429specID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Set_Ois__empty__def) ).

thf(815,plain,
    ( is_emp1849217361specID
    = ( ^ [A: set_Secrecy_specID] : ( A = bot_bo1785112429specID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(133,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
     => ( ( eout @ A @ ( secrecy_kE @ B ) )
       => ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_eoutKnowCorrect__L1k) ).

thf(729,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
     => ( ( eout @ A @ ( secrecy_kE @ B ) )
       => ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(218,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_sE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_LocalSecretsComposition__ine2__s) ).

thf(1042,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_sE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(194,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eoutM @ D @ B @ C )
            | ( eoutM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_TBtheorem2b) ).

thf(952,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eoutM @ D @ B @ C )
            | ( eoutM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(169,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ine_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ F )
                 => ( member1967978193chanID @ G @ ( loc @ D ) ) )
             => ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_TBtheorem4b__notP2) ).

thf(862,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ine_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ F )
                 => ( member1967978193chanID @ G @ ( loc @ D ) ) )
             => ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(19,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ~ ( member1967978193chanID @ A @ B )
     => ( ~ ( member1967978193chanID @ A @ C )
       => ( ( ( insert751661162chanID @ A @ B )
            = ( insert751661162chanID @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_insert__ident) ).

thf(349,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ~ ( member1967978193chanID @ A @ B )
     => ( ~ ( member1967978193chanID @ A @ C )
       => ( ( ( insert751661162chanID @ A @ B )
            = ( insert751661162chanID @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(124,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( ineM @ A @ B @ C )
        | ( ineM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member1967978193chanID @ F @ ( ins @ A ) )
                  | ( member1967978193chanID @ F @ ( ins @ D ) ) )
                & ( member1967978193chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
           => ( ineM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_TBtheorem4b__PQ) ).

thf(693,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( ineM @ A @ B @ C )
        | ( ineM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member1967978193chanID @ F @ ( ins @ A ) )
                  | ( member1967978193chanID @ F @ ( ins @ D ) ) )
                & ( member1967978193chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
           => ( ineM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(108,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ F @ C )
                  & ( member1967978193chanID @ F @ B )
                  & ( member1967978193chanID @ F @ ( loc @ E ) ) )
             => ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_TBtheorem4b__notP1) ).

thf(630,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ F @ C )
                  & ( member1967978193chanID @ F @ B )
                  & ( member1967978193chanID @ F @ ( loc @ E ) ) )
             => ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(186,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ine @ C @ B )
            | ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_TBtheorem1a) ).

thf(916,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ine @ C @ B )
            | ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(60,axiom,
    ! [A: set_Secrecy_Secrets,B: secrecy_Secrets] :
      ( ( A = bot_bo1124690338ecrets )
     => ~ ( member2138796287ecrets @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_equals0D) ).

thf(484,plain,
    ! [A: set_Secrecy_Secrets,B: secrecy_Secrets] :
      ( ( A = bot_bo1124690338ecrets )
     => ~ ( member2138796287ecrets @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(23,axiom,
    ! [A: secrecy_chanID,B: secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_singleton__iff) ).

thf(361,plain,
    ! [A: secrecy_chanID,B: secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(256,axiom,
    ! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
      = ( ( A = B )
        | ( member_Secrecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insert__iff) ).

thf(1178,plain,
    ! [A: secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
      = ( ( A = B )
        | ( member_Secrecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(72,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B != bot_bo443197316chanID )
       => ( ine @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_ine__nonempty__exprChannelSet) ).

thf(522,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B != bot_bo443197316chanID )
       => ( ine @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(265,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_not__know__s__not__ine) ).

thf(1210,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(120,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
      ( ( ( sup_su1301156759ecy_KS @ A @ B )
        = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
      = ( ( ( A = bot_bo1943466239ecy_KS )
          & ( B
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) )
        | ( ( A
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
          & ( B = bot_bo1943466239ecy_KS ) )
        | ( ( A
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
          & ( B
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Un__singleton__iff) ).

thf(682,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
      ( ( ( sup_su1301156759ecy_KS @ A @ B )
        = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
      = ( ( ( A = bot_bo1943466239ecy_KS )
          & ( B
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) )
        | ( ( A
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
          & ( B = bot_bo1943466239ecy_KS ) )
        | ( ( A
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) )
          & ( B
            = ( insert_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(81,axiom,
    ! [A: set_Secrecy_specID,B: secrecy_specID] :
      ( ( A = bot_bo1785112429specID )
     => ~ ( member740727610specID @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_equals0D) ).

thf(551,plain,
    ! [A: set_Secrecy_specID,B: secrecy_specID] :
      ( ( A = bot_bo1785112429specID )
     => ~ ( member740727610specID @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(233,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle945212990e_know @ B @ A )
         => ( ( ( subcomponents @ D )
              = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_know__composition1) ).

thf(1106,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle945212990e_know @ B @ A )
         => ( ( ( subcomponents @ D )
              = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(286,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_insertI2) ).

thf(1296,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(114,axiom,
    ( is_sin1501507247specID
    = ( ^ [A: set_Secrecy_specID] :
          ( A
          = ( insert1671894227specID @ ( the_el827131246specID @ A ) @ bot_bo1785112429specID ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_is__singleton__the__elem) ).

thf(665,plain,
    ( is_sin1501507247specID
    = ( ^ [A: set_Secrecy_specID] :
          ( A
          = ( insert1671894227specID @ ( the_el827131246specID @ A ) @ bot_bo1785112429specID ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(278,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_correctCompositionKS__exprChannel__k__Qex) ).

thf(1259,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(103,axiom,
    ( sup_su370684444chanID
    = ( ^ [A: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( sup_su370684444chanID @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_Un__commute) ).

thf(615,plain,
    ( sup_su370684444chanID
    = ( ^ [A: set_Secrecy_chanID,B: set_Secrecy_chanID] : ( sup_su370684444chanID @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(295,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
                 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_LocalSecretsComposition__neg__k) ).

thf(1328,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
                 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(237,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_kE @ A ) )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_LocalSecretsComposition__neg__loc__k) ).

thf(1121,plain,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_kE @ A ) )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(270,axiom,
    ( notSpe1586871396tsExpr
    = ( ^ [A: secrecy_specID,B: list_S529945141ession] :
          ( ! [C: secrecy_Keys] :
              ( ( mem_Se1967555118ession @ ( secrecy_kE @ C ) @ B )
             => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
          & ! [C: secrecy_Secrets] :
              ( ( mem_Se1967555118ession @ ( secrecy_sE @ C ) @ B )
             => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_notSpecKeysSecretsExpr__def) ).

thf(1227,plain,
    ( notSpe1586871396tsExpr
    = ( ^ [A: secrecy_specID,B: list_S529945141ession] :
          ( ! [C: secrecy_Keys] :
              ( ( mem_Se1967555118ession @ ( secrecy_kE @ C ) @ B )
             => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
          & ! [C: secrecy_Secrets] :
              ( ( mem_Se1967555118ession @ ( secrecy_sE @ C ) @ B )
             => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(36,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( ( sup_su370684444chanID @ A @ B )
        = bot_bo443197316chanID )
      = ( ( A = bot_bo443197316chanID )
        & ( B = bot_bo443197316chanID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Un__empty) ).

thf(403,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( ( sup_su370684444chanID @ A @ B )
        = bot_bo443197316chanID )
      = ( ( A = bot_bo443197316chanID )
        & ( B = bot_bo443197316chanID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(209,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member2138796287ecrets @ C @ ( specSecrets @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member740727610specID @ D @ ( subcomponents @ A ) )
              & ( member2138796287ecrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_correctCompositionKS__subcomp2) ).

thf(1006,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member2138796287ecrets @ C @ ( specSecrets @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member740727610specID @ D @ ( subcomponents @ A ) )
              & ( member2138796287ecrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(244,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
     => ( ( eout @ A @ ( secrecy_sE @ B ) )
       => ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_eoutKnowCorrect__L1s) ).

thf(1138,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
     => ( ( eout @ A @ ( secrecy_sE @ B ) )
       => ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(95,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_ex985543062Single @ A @ B @ C )
     => ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_out__exprChannelSingle__Set) ).

thf(593,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_ex985543062Single @ A @ B @ C )
     => ( out_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(138,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( ( loc @ D )
              = bot_bo443197316chanID )
           => ( eout @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_TBtheorem5a__empty) ).

thf(742,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( ( loc @ D )
              = bot_bo443197316chanID )
           => ( eout @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(90,axiom,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
      ( ( ( sup_su1712599557specID @ A @ B )
        = bot_bo1785112429specID )
      = ( ( A = bot_bo1785112429specID )
        & ( B = bot_bo1785112429specID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_sup__bot_Oeq__neutr__iff) ).

thf(578,plain,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
      ( ( ( sup_su1712599557specID @ A @ B )
        = bot_bo1785112429specID )
      = ( ( A = bot_bo1785112429specID )
        & ( B = bot_bo1785112429specID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(173,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
      = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_Un__left__commute) ).

thf(874,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
      = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(246,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_correctCompositionKS__negQ) ).

thf(1143,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(56,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: set_Secrecy_chanID] :
      ( ( ineM @ A @ B @ C )
     => ( ineM @ A @ ( sup_su370684444chanID @ B @ D ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_ineM__Un1) ).

thf(471,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: set_Secrecy_chanID] :
      ( ( ineM @ A @ B @ C )
     => ( ineM @ A @ ( sup_su370684444chanID @ B @ D ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(176,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
     => ( ~ ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_know__composition__neg__ine__k) ).

thf(884,plain,
    ! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
     => ( ~ ( knowle945212990e_know @ C @ ( secrecy_kKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(16,axiom,
    ! [A: secrecy_chanID,B: secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_singletonD) ).

thf(339,plain,
    ! [A: secrecy_chanID,B: secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(225,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
      = ( ( eout @ A @ ( secrecy_sE @ B ) )
        = ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_eout__know__s) ).

thf(1075,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ B ) )
      = ( ( eout @ A @ ( secrecy_sE @ B ) )
        = ( ( member2138796287ecrets @ B @ ( specSecrets @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(61,axiom,
    ! [A: set_Secrecy_Secrets] :
      ( ( ! [B: secrecy_Secrets] :
            ~ ( member2138796287ecrets @ B @ A ) )
      = ( A = bot_bo1124690338ecrets ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_all__not__in__conv) ).

thf(489,plain,
    ! [A: set_Secrecy_Secrets] :
      ( ( ! [B: secrecy_Secrets] :
            ~ ( member2138796287ecrets @ B @ A ) )
      = ( A = bot_bo1124690338ecrets ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(94,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
      ( ( ! [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ A )
           => ( C @ D ) )
        & ! [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ B )
           => ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_ball__Un) ).

thf(590,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID > $o] :
      ( ( ! [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ ( sup_su370684444chanID @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ A )
           => ( C @ D ) )
        & ! [D: secrecy_chanID] :
            ( ( member1967978193chanID @ D @ B )
           => ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(119,axiom,
    ! [A: secrecy_specID] :
      ( ( correc965049635ionLoc @ A )
     => ( ( ( subcomponents @ A )
          = bot_bo1785112429specID )
       => ( ( loc @ A )
          = bot_bo443197316chanID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_subcomponents__loc) ).

thf(679,plain,
    ! [A: secrecy_specID] :
      ( ( correc965049635ionLoc @ A )
     => ( ( ( subcomponents @ A )
          = bot_bo1785112429specID )
       => ( ( loc @ A )
          = bot_bo443197316chanID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(249,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( ! [B: secrecy_KS] :
            ~ ( member_Secrecy_KS @ B @ A ) )
      = ( A = bot_bo1943466239ecy_KS ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_all__not__in__conv) ).

thf(1155,plain,
    ! [A: set_Secrecy_KS] :
      ( ( ! [B: secrecy_KS] :
            ~ ( member_Secrecy_KS @ B @ A ) )
      = ( A = bot_bo1943466239ecy_KS ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(126,axiom,
    ( sup_su1301156759ecy_KS
    = ( ^ [A: set_Secrecy_KS,B: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_Un__commute) ).

thf(706,plain,
    ( sup_su1301156759ecy_KS
    = ( ^ [A: set_Secrecy_KS,B: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(231,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle945212990e_know @ C @ A )
         => ( ( ( subcomponents @ D )
              = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_know__composition2) ).

thf(1099,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member_Secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle945212990e_know @ C @ A )
         => ( ( ( subcomponents @ D )
              = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle945212990e_know @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(241,axiom,
    ~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_a22) ).

thf(1131,plain,
    ~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(204,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ( ine_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member1967978193chanID @ F @ E )
                 => ( member1967978193chanID @ F @ ( loc @ C ) ) )
             => ~ ( ine @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_TBtheorem4a__notP2) ).

thf(984,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ( ine_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member1967978193chanID @ F @ E )
                 => ( member1967978193chanID @ F @ ( loc @ C ) ) )
             => ~ ( ine @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(131,axiom,
    ( eout
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member1967978193chanID @ C @ ( out @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_eout__def) ).

thf(721,plain,
    ( eout
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member1967978193chanID @ C @ ( out @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(26,axiom,
    ! [A: secrecy_chanID] :
      ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_empty__iff) ).

thf(371,plain,
    ! [A: secrecy_chanID] :
      ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(293,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_sE @ A ) )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_LocalSecretsComposition__neg__loc__s) ).

thf(1324,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_sE @ A ) )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member1967978193chanID @ C @ ( loc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(235,axiom,
    ! [A: secrecy_KS] :
      ~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_empty__iff) ).

thf(1114,plain,
    ! [A: secrecy_KS] :
      ~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(248,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
      ( ( ~ ( member_Secrecy_KS @ A @ B )
       => ( A = C ) )
     => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_insertCI) ).

thf(1150,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS] :
      ( ( ~ ( member_Secrecy_KS @ A @ B )
       => ( A = C ) )
     => ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(276,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( A != bot_bo1943466239ecy_KS )
     => ( ! [B: secrecy_KS,C: secrecy_KS] :
            ( ( member_Secrecy_KS @ B @ A )
           => ( ( member_Secrecy_KS @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1442426433ecy_KS @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_is__singletonI_H) ).

thf(1249,plain,
    ! [A: set_Secrecy_KS] :
      ( ( A != bot_bo1943466239ecy_KS )
     => ( ! [B: secrecy_KS,C: secrecy_KS] :
            ( ( member_Secrecy_KS @ B @ A )
           => ( ( member_Secrecy_KS @ C @ A )
             => ( B = C ) ) )
       => ( is_sin1442426433ecy_KS @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(221,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_correctCompositionKS__exprChannel__s__Qex) ).

thf(1060,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member1967978193chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(220,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ! [E: secrecy_Keys] :
              ( ( D
                = ( secrecy_kKS @ E ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
         => ( ! [E: secrecy_Secrets] :
                ( ( D
                  = ( secrecy_sKS @ E ) )
               => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                  & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
           => ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ B ) )
             => ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ C ) )
               => ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_LocalSecretsComposition__neg1) ).

thf(1050,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ! [E: secrecy_Keys] :
              ( ( D
                = ( secrecy_kKS @ E ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
         => ( ! [E: secrecy_Secrets] :
                ( ( D
                  = ( secrecy_sKS @ E ) )
               => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                  & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
           => ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ B ) )
             => ( ~ ( member_Secrecy_KS @ D @ ( localSecrets @ C ) )
               => ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(263,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_correctCompositionKS__exprChannel__k__Q) ).

thf(1202,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(274,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_correctCompositionKS__exprChannel__k__P) ).

thf(1241,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(67,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_sup__bot_Oright__neutral) ).

thf(508,plain,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(117,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( bot_bo1943466239ecy_KS
        = ( sup_su1301156759ecy_KS @ A @ B ) )
      = ( ( A = bot_bo1943466239ecy_KS )
        & ( B = bot_bo1943466239ecy_KS ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_sup__bot_Oneutr__eq__iff) ).

thf(674,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( bot_bo1943466239ecy_KS
        = ( sup_su1301156759ecy_KS @ A @ B ) )
      = ( ( A = bot_bo1943466239ecy_KS )
        & ( B = bot_bo1943466239ecy_KS ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(215,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ D )
                 => ( member1967978193chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member1967978193chanID @ G @ F )
                   => ( member1967978193chanID @ G @ ( loc @ A ) ) )
               => ~ ( ine @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_TBtheorem4a__notPQ) ).

thf(1026,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ D )
                 => ( member1967978193chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member1967978193chanID @ G @ F )
                   => ( member1967978193chanID @ G @ ( loc @ A ) ) )
               => ~ ( ine @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(83,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ~ ( ineM @ A @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_not__ine__ineM) ).

thf(558,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ~ ( ineM @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(224,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_sE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_LocalSecretsComposition__ine1__s) ).

thf(1071,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_sE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(113,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( ( sup_su1301156759ecy_KS @ A @ B )
        = bot_bo1943466239ecy_KS )
      = ( ( A = bot_bo1943466239ecy_KS )
        & ( B = bot_bo1943466239ecy_KS ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Un__empty) ).

thf(662,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( ( sup_su1301156759ecy_KS @ A @ B )
        = bot_bo1943466239ecy_KS )
      = ( ( A = bot_bo1943466239ecy_KS )
        & ( B = bot_bo1943466239ecy_KS ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(177,axiom,
    ( ineM
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member1967978193chanID @ D @ ( ins @ A ) )
          & ( member1967978193chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_ineM__def) ).

thf(888,plain,
    ( ineM
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member1967978193chanID @ D @ ( ins @ A ) )
          & ( member1967978193chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(232,axiom,
    ! [A: secrecy_KS,B: secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_singletonD) ).

thf(1103,plain,
    ! [A: secrecy_KS,B: secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(167,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ B ) @ C )
      = ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Un__insert__left) ).

thf(856,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ B ) @ C )
      = ( insert_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(288,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_kE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_LocalSecretsComposition__ine1__k) ).

thf(1301,plain,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_kE @ A ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(88,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_Un__absorb) ).

thf(573,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(135,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( is_sin1501507247specID @ A )
     => ~ ! [B: secrecy_specID] :
            ( A
           != ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_is__singletonE) ).

thf(733,plain,
    ! [A: set_Secrecy_specID] :
      ( ( is_sin1501507247specID @ A )
     => ~ ! [B: secrecy_specID] :
            ( A
           != ( insert1671894227specID @ B @ bot_bo1785112429specID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(98,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
     => ( ~ ( member1967978193chanID @ A @ B )
       => ( member1967978193chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_UnE) ).

thf(601,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
     => ( ~ ( member1967978193chanID @ A @ B )
       => ( member1967978193chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(283,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
           => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
             => ( ! [E: secrecy_Keys] :
                    ( ( D
                      = ( secrecy_kKS @ E ) )
                   => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                      & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
               => ( ! [E: secrecy_Secrets] :
                      ( ( D
                        = ( secrecy_sKS @ E ) )
                     => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                        & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
                 => ( ~ ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_LocalSecretsComposition__neg) ).

thf(1278,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
           => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
             => ( ! [E: secrecy_Keys] :
                    ( ( D
                      = ( secrecy_kKS @ E ) )
                   => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                      & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
               => ( ! [E: secrecy_Secrets] :
                      ( ( D
                        = ( secrecy_sKS @ E ) )
                     => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                        & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
                 => ( ~ ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member_Secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(3,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insertI2) ).

thf(298,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( member1967978193chanID @ A @ ( insert751661162chanID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(243,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
      = ( ( ine @ A @ ( secrecy_sE @ B ) )
        | ( member_Secrecy_KS @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_know_Osimps_I2_J) ).

thf(1135,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ B ) )
      = ( ( ine @ A @ ( secrecy_sE @ B ) )
        | ( member_Secrecy_KS @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(39,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_insertI1) ).

thf(412,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A @ ( insert1671894227specID @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(268,axiom,
    ! [A: secrecy_KS,B: secrecy_KS > $o] :
      ( ( member_Secrecy_KS @ A @ ( collect_Secrecy_KS @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mem__Collect__eq) ).

thf(1219,plain,
    ! [A: secrecy_KS,B: secrecy_KS > $o] :
      ( ( member_Secrecy_KS @ A @ ( collect_Secrecy_KS @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(158,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member1967978193chanID @ E @ ( ins @ A ) )
                  | ( member1967978193chanID @ E @ ( ins @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
           => ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_TBtheorem4a__PQ) ).

thf(824,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member1967978193chanID @ E @ ( ins @ A ) )
                  | ( member1967978193chanID @ E @ ( ins @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
           => ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(122,axiom,
    correctCompositionIn @ pq,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_cCompI) ).

thf(689,plain,
    correctCompositionIn @ pq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(1,conjecture,
    ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(296,plain,
    ~ ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(92,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( ! [B: secrecy_specID] :
            ~ ( member740727610specID @ B @ A ) )
      = ( A = bot_bo1785112429specID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_all__not__in__conv) ).

thf(584,plain,
    ! [A: set_Secrecy_specID] :
      ( ( ! [B: secrecy_specID] :
            ~ ( member740727610specID @ B @ A ) )
      = ( A = bot_bo1785112429specID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(201,axiom,
    ! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle945212990e_know @ A @ B )
     => ( ~ ( knowle945212990e_know @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correc965049635ionLoc @ D )
           => ( ( correctCompositionIn @ D )
             => ~ ( knowle945212990e_know @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_know__composition__neg1) ).

thf(975,plain,
    ! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle945212990e_know @ A @ B )
     => ( ~ ( knowle945212990e_know @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correc965049635ionLoc @ D )
           => ( ( correctCompositionIn @ D )
             => ~ ( knowle945212990e_know @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(162,axiom,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
     => ( ~ ( member2138796287ecrets @ A @ B )
       => ( member2138796287ecrets @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_UnE) ).

thf(843,plain,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) )
     => ( ~ ( member2138796287ecrets @ A @ B )
       => ( member2138796287ecrets @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(128,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( insert1671894227specID @ A @ B )
     != bot_bo1785112429specID ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_insert__not__empty) ).

thf(711,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( insert1671894227specID @ A @ B )
     != bot_bo1785112429specID ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(238,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( ~ ( member_Secrecy_KS @ A @ B )
       => ( member_Secrecy_KS @ A @ C ) )
     => ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_UnCI) ).

thf(1124,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( ~ ( member_Secrecy_KS @ A @ B )
       => ( member_Secrecy_KS @ A @ C ) )
     => ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(79,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( ? [B: secrecy_specID] : ( member740727610specID @ B @ A ) )
      = ( A != bot_bo1785112429specID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_ex__in__conv) ).

thf(545,plain,
    ! [A: set_Secrecy_specID] :
      ( ( ? [B: secrecy_specID] : ( member740727610specID @ B @ A ) )
      = ( A != bot_bo1785112429specID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(49,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_UnI2) ).

thf(445,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( member1967978193chanID @ A @ ( sup_su370684444chanID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(30,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C )
      = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_Un__assoc) ).

thf(382,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C )
      = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(281,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS,D: set_Secrecy_KS] :
      ( ~ ( member_Secrecy_KS @ A @ B )
     => ( ~ ( member_Secrecy_KS @ C @ D )
       => ( ( ( insert_Secrecy_KS @ A @ B )
            = ( insert_Secrecy_KS @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Secrecy_KS] :
                  ( ( B
                    = ( insert_Secrecy_KS @ C @ E ) )
                  & ~ ( member_Secrecy_KS @ C @ E )
                  & ( D
                    = ( insert_Secrecy_KS @ A @ E ) )
                  & ~ ( member_Secrecy_KS @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_insert__eq__iff) ).

thf(1271,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS,D: set_Secrecy_KS] :
      ( ~ ( member_Secrecy_KS @ A @ B )
     => ( ~ ( member_Secrecy_KS @ C @ D )
       => ( ( ( insert_Secrecy_KS @ A @ B )
            = ( insert_Secrecy_KS @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Secrecy_KS] :
                  ( ( B
                    = ( insert_Secrecy_KS @ C @ E ) )
                  & ~ ( member_Secrecy_KS @ C @ E )
                  & ( D
                    = ( insert_Secrecy_KS @ A @ E ) )
                  & ~ ( member_Secrecy_KS @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(64,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( ~ ( member740727610specID @ A @ B )
       => ( member740727610specID @ A @ C ) )
     => ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_UnCI) ).

thf(498,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( ~ ( member740727610specID @ A @ B )
       => ( member740727610specID @ A @ C ) )
     => ( member740727610specID @ A @ ( sup_su1712599557specID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(54,axiom,
    ! [A: secrecy_specID] :
      ~ ( member740727610specID @ A @ bot_bo1785112429specID ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_emptyE) ).

thf(466,plain,
    ! [A: secrecy_specID] :
      ~ ( member740727610specID @ A @ bot_bo1785112429specID ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(151,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
        = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_doubleton__eq__iff) ).

thf(804,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
        = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(202,axiom,
    ! [A: secrecy_specID,B: secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_singleton__iff) ).

thf(979,plain,
    ! [A: secrecy_specID,B: secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(260,axiom,
    ! [A: secrecy_KS] :
      ~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_emptyE) ).

thf(1194,plain,
    ! [A: secrecy_KS] :
      ~ ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(37,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_sup__bot__right) ).

thf(406,plain,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(236,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
            | ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_correctCompositionKS__PQ) ).

thf(1117,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ( ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
            | ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(86,axiom,
    ! [A: set_Secrecy_Secrets] :
      ( ( ? [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
      = ( A != bot_bo1124690338ecrets ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_ex__in__conv) ).

thf(567,plain,
    ! [A: set_Secrecy_Secrets] :
      ( ( ? [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
      = ( A != bot_bo1124690338ecrets ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(136,axiom,
    ! [A: secrecy_Secrets,B: secrecy_Secrets > $o] :
      ( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_mem__Collect__eq) ).

thf(737,plain,
    ! [A: secrecy_Secrets,B: secrecy_Secrets > $o] :
      ( ( member2138796287ecrets @ A @ ( collec836099393ecrets @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(46,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ! [B: secrecy_chanID] :
          ~ ( member1967978193chanID @ B @ A )
     => ( A = bot_bo443197316chanID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_equals0I) ).

thf(434,plain,
    ! [A: set_Secrecy_chanID] :
      ( ! [B: secrecy_chanID] :
          ~ ( member1967978193chanID @ B @ A )
     => ( A = bot_bo443197316chanID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(28,axiom,
    ! [A: secrecy_chanID] :
      ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_emptyE) ).

thf(377,plain,
    ! [A: secrecy_chanID] :
      ~ ( member1967978193chanID @ A @ bot_bo443197316chanID ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(205,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member1967978193chanID @ D @ ( ins @ B ) )
         => ( ( exprChannel @ D @ E )
           => ( ! [F: secrecy_chanID] :
                  ( ( member1967978193chanID @ F @ ( ins @ A ) )
                 => ~ ( exprChannel @ F @ E ) )
             => ( member1967978193chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_correctCompositionInLoc__exprChannel) ).

thf(990,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member1967978193chanID @ D @ ( ins @ B ) )
         => ( ( exprChannel @ D @ E )
           => ( ! [F: secrecy_chanID] :
                  ( ( member1967978193chanID @ F @ ( ins @ A ) )
                 => ~ ( exprChannel @ F @ E ) )
             => ( member1967978193chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(206,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
        = ( sup_su1712599557specID @ B @ C ) )
      = ( ( ( B = bot_bo1785112429specID )
          & ( C
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
        | ( ( B
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
          & ( C = bot_bo1785112429specID ) )
        | ( ( B
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
          & ( C
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_singleton__Un__iff) ).

thf(996,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( ( insert1671894227specID @ A @ bot_bo1785112429specID )
        = ( sup_su1712599557specID @ B @ C ) )
      = ( ( ( B = bot_bo1785112429specID )
          & ( C
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
        | ( ( B
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
          & ( C = bot_bo1785112429specID ) )
        | ( ( B
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) )
          & ( C
            = ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(178,axiom,
    ( bot_bo1909946299rets_o
    = ( ^ [A: secrecy_Secrets] : ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_bot__empty__eq) ).

thf(890,plain,
    ( bot_bo1909946299rets_o
    = ( ^ [A: secrecy_Secrets] : ( member2138796287ecrets @ A @ bot_bo1124690338ecrets ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(58,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
      = ( ( member1967978193chanID @ A @ B )
        | ( member1967978193chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Un__iff) ).

thf(477,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
      = ( ( member1967978193chanID @ A @ B )
        | ( member1967978193chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(140,axiom,
    ! [A: set_Secrecy_Secrets] :
      ( ( collec836099393ecrets
        @ ^ [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Collect__mem__eq) ).

thf(758,plain,
    ! [A: set_Secrecy_Secrets] :
      ( ( collec836099393ecrets
        @ ^ [B: secrecy_Secrets] : ( member2138796287ecrets @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(18,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID,D: set_Secrecy_chanID] :
      ( ~ ( member1967978193chanID @ A @ B )
     => ( ~ ( member1967978193chanID @ C @ D )
       => ( ( ( insert751661162chanID @ A @ B )
            = ( insert751661162chanID @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Secrecy_chanID] :
                  ( ( B
                    = ( insert751661162chanID @ C @ E ) )
                  & ~ ( member1967978193chanID @ C @ E )
                  & ( D
                    = ( insert751661162chanID @ A @ E ) )
                  & ~ ( member1967978193chanID @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_insert__eq__iff) ).

thf(345,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID,D: set_Secrecy_chanID] :
      ( ~ ( member1967978193chanID @ A @ B )
     => ( ~ ( member1967978193chanID @ C @ D )
       => ( ( ( insert751661162chanID @ A @ B )
            = ( insert751661162chanID @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set_Secrecy_chanID] :
                  ( ( B
                    = ( insert751661162chanID @ C @ E ) )
                  & ~ ( member1967978193chanID @ C @ E )
                  & ( D
                    = ( insert751661162chanID @ A @ E ) )
                  & ~ ( member1967978193chanID @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(101,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_Un__empty__left) ).

thf(609,plain,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(251,axiom,
    ! [A: secrecy_Secrets,B: secrecy_Secrets] :
      ( ( ( secrecy_sKS @ A )
        = ( secrecy_sKS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_KS_Oinject_I2_J) ).

thf(1162,plain,
    ! [A: secrecy_Secrets,B: secrecy_Secrets] :
      ( ( ( secrecy_sKS @ A )
        = ( secrecy_sKS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(107,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ~ ( member1967978193chanID @ D @ ( loc @ A ) )
         => ( ( member1967978193chanID @ D @ ( ins @ B ) )
           => ( member1967978193chanID @ D @ ( ins @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_correctCompositionIn__L1) ).

thf(626,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ~ ( member1967978193chanID @ D @ ( loc @ A ) )
         => ( ( member1967978193chanID @ D @ ( ins @ B ) )
           => ( member1967978193chanID @ D @ ( ins @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(13,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( insert751661162chanID @ A @ ( insert751661162chanID @ A @ B ) )
      = ( insert751661162chanID @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_insert__absorb2) ).

thf(330,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( insert751661162chanID @ A @ ( insert751661162chanID @ A @ B ) )
      = ( insert751661162chanID @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(164,axiom,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ B )
     => ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_UnI1) ).

thf(848,plain,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ B )
     => ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(71,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( eoutM @ A @ B @ C )
     => ( eout @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_eoutM__eout) ).

thf(520,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( eoutM @ A @ B @ C )
     => ( eout @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(196,axiom,
    ! [A: set_Secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
      = ( insert_Secrecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Un__insert__right) ).

thf(959,plain,
    ! [A: set_Secrecy_KS,B: secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ B @ C ) )
      = ( insert_Secrecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(145,axiom,
    ! [A: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_is__singletonI) ).

thf(780,plain,
    ! [A: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(212,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ineM @ D @ B @ C )
            | ( ineM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_TBtheorem1b) ).

thf(1015,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ineM @ D @ B @ C )
            | ( ineM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(33,axiom,
    ! [A: secrecy_specID] :
      ~ ( member740727610specID @ A @ bot_bo1785112429specID ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_empty__iff) ).

thf(394,plain,
    ! [A: secrecy_specID] :
      ~ ( member740727610specID @ A @ bot_bo1785112429specID ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(165,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member1967978193chanID @ E @ ( out @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
           => ( eout @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_TBtheorem45a__P) ).

thf(851,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member1967978193chanID @ E @ ( out @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ C ) ) )
           => ( eout @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(47,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ? [C: set_Secrecy_specID] :
          ( ( B
            = ( insert1671894227specID @ A @ C ) )
          & ~ ( member740727610specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mk__disjoint__insert) ).

thf(438,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ? [C: set_Secrecy_specID] :
          ( ( B
            = ( insert1671894227specID @ A @ C ) )
          & ~ ( member740727610specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(45,axiom,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
      ( ( bot_bo1785112429specID
        = ( sup_su1712599557specID @ A @ B ) )
      = ( ( A = bot_bo1785112429specID )
        & ( B = bot_bo1785112429specID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_sup__bot_Oneutr__eq__iff) ).

thf(431,plain,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
      ( ( bot_bo1785112429specID
        = ( sup_su1712599557specID @ A @ B ) )
      = ( ( A = bot_bo1785112429specID )
        & ( B = bot_bo1785112429specID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(188,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
      = ( ( eout @ A @ ( secrecy_kE @ B ) )
        = ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_eout__know__k) ).

thf(922,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ B ) )
      = ( ( eout @ A @ ( secrecy_kE @ B ) )
        = ( ( member_Secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(185,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ~ ( eout @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correc990227761ionOut @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ E @ B )
                  & ( member1967978193chanID @ E @ ( loc @ D ) ) )
             => ~ ( eout @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_TBtheorem5a__notP1) ).

thf(912,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ~ ( eout @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correc990227761ionOut @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ E @ B )
                  & ( member1967978193chanID @ E @ ( loc @ D ) ) )
             => ~ ( eout @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(121,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( member1967978193chanID @ D @ ( out @ A ) )
         => ( ( member1967978193chanID @ D @ ( out @ B ) )
            | ( member1967978193chanID @ D @ ( out @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_correctCompositionOut__prop1) ).

thf(685,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( member1967978193chanID @ D @ ( out @ A ) )
         => ( ( member1967978193chanID @ D @ ( out @ B ) )
            | ( member1967978193chanID @ D @ ( out @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(254,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_UnI1) ).

thf(1171,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(222,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( ord_le1802272080chanID @ ( out @ A ) @ ( ins @ B ) )
     => ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ C ) )
       => ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_adv__not__know2) ).

thf(1066,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( ord_le1802272080chanID @ ( out @ A ) @ ( ins @ B ) )
     => ( ~ ( knowle945212990e_know @ B @ ( secrecy_sKS @ C ) )
       => ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(170,axiom,
    ( insert_Secrecy_KS
    = ( ^ [A: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_insert__is__Un) ).

thf(868,plain,
    ( insert_Secrecy_KS
    = ( ^ [A: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(264,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
     => ( ~ ( member_Secrecy_KS @ A @ B )
       => ( member_Secrecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_UnE) ).

thf(1208,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
     => ( ~ ( member_Secrecy_KS @ A @ B )
       => ( member_Secrecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(75,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_sup__bot__left) ).

thf(531,plain,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(80,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ~ ( eoutM @ A @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_not__eout__eoutM) ).

thf(548,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set_Secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ~ ( eoutM @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(27,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C )
      = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_Un__insert__left) ).

thf(374,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ ( insert1671894227specID @ A @ B ) @ C )
      = ( insert1671894227specID @ A @ ( sup_su1712599557specID @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(154,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS )
        = ( sup_su1301156759ecy_KS @ B @ C ) )
      = ( ( ( B = bot_bo1943466239ecy_KS )
          & ( C
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) )
        | ( ( B
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
          & ( C = bot_bo1943466239ecy_KS ) )
        | ( ( B
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
          & ( C
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_singleton__Un__iff) ).

thf(812,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS )
        = ( sup_su1301156759ecy_KS @ B @ C ) )
      = ( ( ( B = bot_bo1943466239ecy_KS )
          & ( C
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) )
        | ( ( B
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
          & ( C = bot_bo1943466239ecy_KS ) )
        | ( ( B
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) )
          & ( C
            = ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(104,axiom,
    ! [A: set_Secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ B @ C ) )
      = ( insert1671894227specID @ B @ ( sup_su1712599557specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Un__insert__right) ).

thf(617,plain,
    ! [A: set_Secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ B @ C ) )
      = ( insert1671894227specID @ B @ ( sup_su1712599557specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(192,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( eoutM @ A @ B @ C )
        | ( eoutM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member1967978193chanID @ F @ ( out @ A ) )
                  | ( member1967978193chanID @ F @ ( out @ D ) ) )
                & ( member1967978193chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
           => ( eoutM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_TBtheorem5b__PQ) ).

thf(939,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( eoutM @ A @ B @ C )
        | ( eoutM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member1967978193chanID @ F @ ( out @ A ) )
                  | ( member1967978193chanID @ F @ ( out @ D ) ) )
                & ( member1967978193chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ E ) ) )
           => ( eoutM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(17,axiom,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
      = ( ( A = B )
        | ( member1967978193chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_insert__iff) ).

thf(342,plain,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
      = ( ( A = B )
        | ( member1967978193chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(21,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
      ( ( ( sup_su370684444chanID @ A @ B )
        = ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
      = ( ( ( A = bot_bo443197316chanID )
          & ( B
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) )
        | ( ( A
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
          & ( B = bot_bo443197316chanID ) )
        | ( ( A
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
          & ( B
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Un__singleton__iff) ).

thf(355,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: secrecy_chanID] :
      ( ( ( sup_su370684444chanID @ A @ B )
        = ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
      = ( ( ( A = bot_bo443197316chanID )
          & ( B
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) )
        | ( ( A
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
          & ( B = bot_bo443197316chanID ) )
        | ( ( A
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) )
          & ( B
            = ( insert751661162chanID @ C @ bot_bo443197316chanID ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(257,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
      ( ( ! [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ A )
           => ( C @ D ) )
        & ! [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ B )
           => ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_ball__Un) ).

thf(1181,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: secrecy_KS > $o] :
      ( ( ! [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ ( sup_su1301156759ecy_KS @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ A )
           => ( C @ D ) )
        & ! [D: secrecy_KS] :
            ( ( member_Secrecy_KS @ D @ B )
           => ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(160,axiom,
    ! [A: secrecy_Keys] :
      ( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
      = ( secrecy_kE @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_KS2Expression_Osimps_I1_J) ).

thf(836,plain,
    ! [A: secrecy_Keys] :
      ( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
      = ( secrecy_kE @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(73,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_sup__bot_Oleft__neutral) ).

thf(525,plain,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(208,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( insert1671894227specID @ A @ ( insert1671894227specID @ A @ B ) )
      = ( insert1671894227specID @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_insert__absorb2) ).

thf(1003,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( insert1671894227specID @ A @ ( insert1671894227specID @ A @ B ) )
      = ( insert1671894227specID @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(166,axiom,
    knowle945212990e_know @ pq @ m,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_knowPQ) ).

thf(855,plain,
    knowle945212990e_know @ pq @ m,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(123,axiom,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
      ( ( ( sup_su1712599557specID @ A @ B )
        = ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
      = ( ( ( A = bot_bo1785112429specID )
          & ( B
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
        | ( ( A
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
          & ( B = bot_bo1785112429specID ) )
        | ( ( A
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
          & ( B
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Un__singleton__iff) ).

thf(690,plain,
    ! [A: set_Secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
      ( ( ( sup_su1712599557specID @ A @ B )
        = ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
      = ( ( ( A = bot_bo1785112429specID )
          & ( B
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
        | ( ( A
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
          & ( B = bot_bo1785112429specID ) )
        | ( ( A
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) )
          & ( B
            = ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(172,axiom,
    ( eoutM
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member1967978193chanID @ D @ ( out @ A ) )
          & ( member1967978193chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_eoutM__def) ).

thf(872,plain,
    ( eoutM
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member1967978193chanID @ D @ ( out @ A ) )
          & ( member1967978193chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(40,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ~ ( member740727610specID @ A @ B )
     => ( ~ ( member740727610specID @ A @ C )
       => ( ( ( insert1671894227specID @ A @ B )
            = ( insert1671894227specID @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_insert__ident) ).

thf(414,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ~ ( member740727610specID @ A @ B )
     => ( ~ ( member740727610specID @ A @ C )
       => ( ( ( insert1671894227specID @ A @ B )
            = ( insert1671894227specID @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(38,axiom,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_Un__empty__right) ).

thf(409,plain,
    ! [A: set_Secrecy_specID] :
      ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(7,axiom,
    ( insert751661162chanID
    = ( ^ [A: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_insert__is__Un) ).

thf(310,plain,
    ( insert751661162chanID
    = ( ^ [A: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(149,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member1967978193chanID @ E @ ( out @ A ) )
                  | ( member1967978193chanID @ E @ ( out @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
           => ( eout @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_TBtheorem5a__PQ) ).

thf(791,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member1967978193chanID @ E @ ( out @ A ) )
                  | ( member1967978193chanID @ E @ ( out @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member1967978193chanID @ E @ ( loc @ D ) ) )
           => ( eout @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(259,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_correctCompositionKS__exprChannel__s__P) ).

thf(1188,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(217,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ~ ( member_Secrecy_KS @ A @ B )
     => ( ~ ( member_Secrecy_KS @ A @ C )
       => ( ( ( insert_Secrecy_KS @ A @ B )
            = ( insert_Secrecy_KS @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insert__ident) ).

thf(1038,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ~ ( member_Secrecy_KS @ A @ B )
     => ( ~ ( member_Secrecy_KS @ A @ C )
       => ( ( ( insert_Secrecy_KS @ A @ B )
            = ( insert_Secrecy_KS @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(53,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( ! [B: secrecy_chanID] :
            ~ ( member1967978193chanID @ B @ A ) )
      = ( A = bot_bo443197316chanID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_all__not__in__conv) ).

thf(463,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( ! [B: secrecy_chanID] :
            ~ ( member1967978193chanID @ B @ A ) )
      = ( A = bot_bo443197316chanID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(291,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( collect_Secrecy_KS
        @ ^ [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Collect__mem__eq) ).

thf(1317,plain,
    ! [A: set_Secrecy_KS] :
      ( ( collect_Secrecy_KS
        @ ^ [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(89,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_ex1303305700Single @ A @ B @ C )
     => ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_ine__exprChannelSingle__Set) ).

thf(576,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_ex1303305700Single @ A @ B @ C )
     => ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(15,axiom,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
      ( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
        = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_doubleton__eq__iff) ).

thf(336,plain,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
      ( ( ( insert751661162chanID @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) )
        = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(277,axiom,
    ~ ( knowle945212990e_know @ q @ m ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_not__knowQm) ).

thf(1257,plain,
    ~ ( knowle945212990e_know @ q @ m ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

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_14_Expression_Oinject_I2_J) ).

thf(703,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(214,axiom,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( ~ ( member2138796287ecrets @ A @ B )
       => ( member2138796287ecrets @ A @ C ) )
     => ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_UnCI) ).

thf(1023,plain,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( ~ ( member2138796287ecrets @ A @ B )
       => ( member2138796287ecrets @ A @ C ) )
     => ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(245,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( ? [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
      = ( A != bot_bo1943466239ecy_KS ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_ex__in__conv) ).

thf(1140,plain,
    ! [A: set_Secrecy_KS] :
      ( ( ? [B: secrecy_KS] : ( member_Secrecy_KS @ B @ A ) )
      = ( A != bot_bo1943466239ecy_KS ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(96,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_sup__bot__left) ).

thf(595,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(102,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insertI2) ).

thf(612,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( member740727610specID @ A @ ( insert1671894227specID @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(168,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
      = ( sup_su1301156759ecy_KS @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_Un__left__absorb) ).

thf(859,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
      = ( sup_su1301156759ecy_KS @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(163,axiom,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C )
      = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Un__assoc) ).

thf(845,plain,
    ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C )
      = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(227,axiom,
    ! [A: set_Secrecy_KS] :
      ( ! [B: secrecy_KS] :
          ~ ( member_Secrecy_KS @ B @ A )
     => ( A = bot_bo1943466239ecy_KS ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_equals0I) ).

thf(1084,plain,
    ! [A: set_Secrecy_KS] :
      ( ! [B: secrecy_KS] :
          ~ ( member_Secrecy_KS @ B @ A )
     => ( A = bot_bo1943466239ecy_KS ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(82,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
     => ( ~ ( member740727610specID @ A @ B )
       => ( member740727610specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_UnE) ).

thf(556,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( sup_su1712599557specID @ B @ C ) )
     => ( ~ ( member740727610specID @ A @ B )
       => ( member740727610specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(91,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
      = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_Un__left__commute) ).

thf(581,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C ) )
      = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(63,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( ( insert1671894227specID @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_insert__absorb) ).

thf(495,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ( ( insert1671894227specID @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(267,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
      = ( ( member_Secrecy_KS @ A @ B )
        | ( member_Secrecy_KS @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Un__iff) ).

thf(1216,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C ) )
      = ( ( member_Secrecy_KS @ A @ B )
        | ( member_Secrecy_KS @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(210,axiom,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Un__absorb) ).

thf(1010,plain,
    ! [A: set_Secrecy_KS] :
      ( ( sup_su1301156759ecy_KS @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(25,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( ( insert751661162chanID @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insert__absorb) ).

thf(368,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( ( insert751661162chanID @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(142,axiom,
    ! [A: secrecy_chanID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_sE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_sE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_sE @ B ) )
         => ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
            & ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_LocalSecretsComposition__exprChannel__s) ).

thf(771,plain,
    ! [A: secrecy_chanID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_sE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_sE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_sE @ B ) )
         => ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
            & ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(190,axiom,
    ! [A: secrecy_chanID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_kE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_kE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_kE @ B ) )
         => ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
            & ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_LocalSecretsComposition__exprChannel__k) ).

thf(931,plain,
    ! [A: secrecy_chanID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_kE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_kE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_kE @ B ) )
         => ( ~ ( member1967978193chanID @ A @ ( ins @ C ) )
            & ~ ( member1967978193chanID @ A @ ( ins @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(77,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_Un__empty__left) ).

thf(539,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(70,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_UnI1) ).

thf(517,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ( member1967978193chanID @ A @ ( sup_su370684444chanID @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(10,axiom,
    ! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_singletonI) ).

thf(319,plain,
    ! [A: secrecy_chanID] : ( member1967978193chanID @ A @ ( insert751661162chanID @ A @ bot_bo443197316chanID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(5,axiom,
    ! [A: set_Secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ B @ C ) )
      = ( insert751661162chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Un__insert__right) ).

thf(304,plain,
    ! [A: set_Secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ B @ C ) )
      = ( insert751661162chanID @ B @ ( sup_su370684444chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(32,axiom,
    ! [A: set_Secrecy_specID] :
      ( ! [B: secrecy_specID] :
          ~ ( member740727610specID @ B @ A )
     => ( A = bot_bo1785112429specID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_equals0I) ).

thf(390,plain,
    ! [A: set_Secrecy_specID] :
      ( ! [B: secrecy_specID] :
          ~ ( member740727610specID @ B @ A )
     => ( A = bot_bo1785112429specID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(181,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( exprChannel @ C @ B )
       => ~ ( member1967978193chanID @ C @ ( ins @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_ine__ins__neg1) ).

thf(896,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( exprChannel @ C @ B )
       => ~ ( member1967978193chanID @ C @ ( ins @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(139,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ D )
                 => ( member1967978193chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member1967978193chanID @ G @ F )
                   => ( member1967978193chanID @ G @ ( loc @ A ) ) )
               => ~ ( eout @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_TBtheorem5a__notPQ) ).

thf(748,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set_Secrecy_chanID,E: secrecy_Expression,F: set_Secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ D )
                 => ( member1967978193chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member1967978193chanID @ G @ F )
                   => ( member1967978193chanID @ G @ ( loc @ A ) ) )
               => ~ ( eout @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(134,axiom,
    ( ine
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member1967978193chanID @ C @ ( ins @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ine__def) ).

thf(731,plain,
    ( ine
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member1967978193chanID @ C @ ( ins @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(41,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member_Secrecy_Keys @ C @ ( specKeys @ B ) )
         => ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_correctCompositionKS__subcomp3) ).

thf(418,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member_Secrecy_Keys @ C @ ( specKeys @ B ) )
         => ( member_Secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(147,axiom,
    ( insert1671894227specID
    = ( ^ [A: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_insert__is__Un) ).

thf(786,plain,
    ( insert1671894227specID
    = ( ^ [A: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(266,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_correctCompositionKS__negP) ).

thf(1212,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(182,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ( out_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member1967978193chanID @ F @ E )
                 => ( member1967978193chanID @ F @ ( loc @ C ) ) )
             => ~ ( eout @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_TBtheorem5a__notP2) ).

thf(899,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set_Secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert1671894227specID @ D @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ( out_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member1967978193chanID @ F @ E )
                 => ( member1967978193chanID @ F @ ( loc @ C ) ) )
             => ~ ( eout @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(115,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member2138796287ecrets @ C @ ( specSecrets @ B ) )
         => ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_correctCompositionKS__subcomp4) ).

thf(667,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member740727610specID @ B @ ( subcomponents @ A ) )
       => ( ( member2138796287ecrets @ C @ ( specSecrets @ B ) )
         => ( member2138796287ecrets @ C @ ( specSecrets @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(285,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_insertI1) ).

thf(1294,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(242,axiom,
    ! [A: secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_singletonI) ).

thf(1133,plain,
    ! [A: secrecy_KS] : ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(9,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ? [C: set_Secrecy_chanID] :
          ( ( B
            = ( insert751661162chanID @ A @ C ) )
          & ~ ( member1967978193chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mk__disjoint__insert) ).

thf(315,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ? [C: set_Secrecy_chanID] :
          ( ( B
            = ( insert751661162chanID @ A @ C ) )
          & ~ ( member1967978193chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(271,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_LocalSecretsComposition__neg1__s) ).

thf(1229,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
           => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(99,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ~ ! [C: set_Secrecy_specID] :
            ( ( B
              = ( insert1671894227specID @ A @ C ) )
           => ( member740727610specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Set_Oset__insert) ).

thf(603,plain,
    ! [A: secrecy_specID,B: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ B )
     => ~ ! [C: set_Secrecy_specID] :
            ( ( B
              = ( insert1671894227specID @ A @ C ) )
           => ( member740727610specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(207,axiom,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kE @ A )
     != ( secrecy_sE @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Expression_Odistinct_I1_J) ).

thf(999,plain,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kE @ A )
     != ( secrecy_sE @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(105,axiom,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kE @ A )
        = ( secrecy_kE @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Expression_Oinject_I1_J) ).

thf(620,plain,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kE @ A )
        = ( secrecy_kE @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(85,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( ? [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
      = ( A != bot_bo443197316chanID ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_ex__in__conv) ).

thf(564,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( ? [B: secrecy_chanID] : ( member1967978193chanID @ B @ A ) )
      = ( A != bot_bo443197316chanID ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(150,axiom,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ B )
     => ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_UnI2) ).

thf(801,plain,
    ! [A: secrecy_Secrets,B: set_Secrecy_Secrets,C: set_Secrecy_Secrets] :
      ( ( member2138796287ecrets @ A @ B )
     => ( member2138796287ecrets @ A @ ( sup_su1029080330ecrets @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(57,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( ( sup_su370684444chanID @ A @ B )
        = bot_bo443197316chanID )
      = ( ( A = bot_bo443197316chanID )
        & ( B = bot_bo443197316chanID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_sup__bot_Oeq__neutr__iff) ).

thf(474,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( ( sup_su370684444chanID @ A @ B )
        = bot_bo443197316chanID )
      = ( ( A = bot_bo443197316chanID )
        & ( B = bot_bo443197316chanID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(252,axiom,
    ! [A: secrecy_KS > $o,B: secrecy_KS] :
      ( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
     => ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_KS_Oinduct) ).

thf(1165,plain,
    ! [A: secrecy_KS > $o,B: secrecy_KS] :
      ( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
     => ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(22,axiom,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
     => ( ( A != B )
       => ( member1967978193chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_insertE) ).

thf(358,plain,
    ! [A: secrecy_chanID,B: secrecy_chanID,C: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ ( insert751661162chanID @ B @ C ) )
     => ( ( A != B )
       => ( member1967978193chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(152,axiom,
    ( outStream
    = ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( out @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_outStream__def) ).

thf(807,plain,
    ( outStream
    = ( ^ [A: secrecy_specID] : ( (=) @ set_Secrecy_chanID @ ( out @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(284,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_correctCompositionKS__exprChannel__s__Q) ).

thf(1288,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member1967978193chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member1967978193chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(35,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_sup__bot_Oright__neutral) ).

thf(400,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(261,axiom,
    ( bot_bot_Secrecy_KS_o
    = ( ^ [A: secrecy_KS] : ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_bot__empty__eq) ).

thf(1197,plain,
    ( bot_bot_Secrecy_KS_o
    = ( ^ [A: secrecy_KS] : ( member_Secrecy_KS @ A @ bot_bo1943466239ecy_KS ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(161,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ E )
           => ~ ( ineM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_TBtheorem3b) ).

thf(839,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ E )
           => ~ ( ineM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(137,axiom,
    ( ine_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member1967978193chanID @ D @ B )
             => ( ( member1967978193chanID @ D @ ( ins @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member1967978193chanID @ D @ B )
                & ( member1967978193chanID @ D @ ( ins @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_ine__exprChannelSet__def) ).

thf(740,plain,
    ( ine_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member1967978193chanID @ D @ B )
             => ( ( member1967978193chanID @ D @ ( ins @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member1967978193chanID @ D @ B )
                & ( member1967978193chanID @ D @ ( ins @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(240,axiom,
    ( m
    = ( secrecy_sKS @ secret ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_a2) ).

thf(1129,plain,
    ( m
    = ( secrecy_sKS @ secret ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(280,axiom,
    ! [A: secrecy_KS,B: secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_singleton__iff) ).

thf(1268,plain,
    ! [A: secrecy_KS,B: secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ ( insert_Secrecy_KS @ B @ bot_bo1943466239ecy_KS ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(213,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_TBtheorem3a) ).

thf(1019,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert1671894227specID @ A @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(74,axiom,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( bot_bo443197316chanID
        = ( sup_su370684444chanID @ A @ B ) )
      = ( ( A = bot_bo443197316chanID )
        & ( B = bot_bo443197316chanID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_sup__bot_Oneutr__eq__iff) ).

thf(528,plain,
    ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( bot_bo443197316chanID
        = ( sup_su370684444chanID @ A @ B ) )
      = ( ( A = bot_bo443197316chanID )
        & ( B = bot_bo443197316chanID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(184,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member1967978193chanID @ D @ ( ins @ A ) )
         => ( ( member1967978193chanID @ D @ ( ins @ B ) )
            | ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_correctCompositionIn__L2) ).

thf(908,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member1967978193chanID @ D @ ( ins @ A ) )
         => ( ( member1967978193chanID @ D @ ( ins @ B ) )
            | ( member1967978193chanID @ D @ ( ins @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(132,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
      ( ~ ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( out_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ F )
                 => ( member1967978193chanID @ G @ ( loc @ D ) ) )
             => ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_TBtheorem5b__notP2) ).

thf(723,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set_Secrecy_chanID] :
      ( ~ ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ E @ ( insert1671894227specID @ A @ bot_bo1785112429specID ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( out_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member1967978193chanID @ G @ F )
                 => ( member1967978193chanID @ G @ ( loc @ D ) ) )
             => ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(203,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_not__know__k__not__ine) ).

thf(982,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(287,axiom,
    ~ ( ine @ q @ ( secrecy_sE @ secret ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_sg6a) ).

thf(1299,plain,
    ~ ( ine @ q @ ( secrecy_sE @ secret ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(48,axiom,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_sup__bot_Oleft__neutral) ).

thf(442,plain,
    ! [A: set_Secrecy_chanID] :
      ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(65,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
     => ( ( A != B )
       => ( member740727610specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_insertE) ).

thf(501,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ C ) )
     => ( ( A != B )
       => ( member740727610specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(100,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
     => ( ine_ex1303305700Single @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ine__exprChannelSet__Single) ).

thf(607,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ ( insert751661162chanID @ B @ bot_bo443197316chanID ) @ C )
     => ( ine_ex1303305700Single @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(292,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
         => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
           => ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_correctCompositionKS__neg1) ).

thf(1320,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert1671894227specID @ B @ ( insert1671894227specID @ C @ bot_bo1785112429specID ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ B ) )
         => ( ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ C ) )
           => ~ ( member_Secrecy_KS @ D @ ( specKeysSecrets @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(55,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( ineM @ A @ B @ C )
     => ( ine @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_ineM__ine) ).

thf(469,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression] :
      ( ( ineM @ A @ B @ C )
     => ( ine @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(191,axiom,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member1967978193chanID @ F @ ( ins @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ D ) )
                & ( member1967978193chanID @ F @ B ) )
           => ( ineM @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_TBtheorem4b__P) ).

thf(935,plain,
    ! [A: secrecy_specID,B: set_Secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert1671894227specID @ A @ ( insert1671894227specID @ E @ bot_bo1785112429specID ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member1967978193chanID @ F @ ( ins @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member1967978193chanID @ F @ ( loc @ D ) )
                & ( member1967978193chanID @ F @ B ) )
           => ( ineM @ D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(258,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_18_KS_Oexhaust) ).

thf(1184,plain,
    ! [A: secrecy_KS] :
      ( ! [B: secrecy_Keys] :
          ( A
         != ( secrecy_kKS @ B ) )
     => ~ ! [B: secrecy_Secrets] :
            ( A
           != ( secrecy_sKS @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(143,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ~ ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_not__know__k__not__eout) ).

thf(775,plain,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member_Secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ~ ( knowle945212990e_know @ B @ ( secrecy_kKS @ A ) )
       => ( ( knowle233900195orrect @ B @ ( secrecy_kKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(228,axiom,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_UnI2) ).

thf(1088,plain,
    ! [A: secrecy_KS,B: set_Secrecy_KS,C: set_Secrecy_KS] :
      ( ( member_Secrecy_KS @ A @ B )
     => ( member_Secrecy_KS @ A @ ( sup_su1301156759ecy_KS @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(223,axiom,
    ( ( subcomponents @ pq )
    = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_subPQ) ).

thf(1069,plain,
    ( ( subcomponents @ pq )
    = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(24,axiom,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ~ ! [C: set_Secrecy_chanID] :
            ( ( B
              = ( insert751661162chanID @ A @ C ) )
           => ( member1967978193chanID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_Set_Oset__insert) ).

thf(364,plain,
    ! [A: secrecy_chanID,B: set_Secrecy_chanID] :
      ( ( member1967978193chanID @ A @ B )
     => ~ ! [C: set_Secrecy_chanID] :
            ( ( B
              = ( insert751661162chanID @ A @ C ) )
           => ( member1967978193chanID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(127,axiom,
    ! [A: secrecy_specID,B: secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_singletonD) ).

thf(708,plain,
    ! [A: secrecy_specID,B: secrecy_specID] :
      ( ( member740727610specID @ A @ ( insert1671894227specID @ B @ bot_bo1785112429specID ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(200,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ C ) )
      = ( insert1671894227specID @ B @ ( insert1671894227specID @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_insert__commute) ).

thf(972,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: set_Secrecy_specID] :
      ( ( insert1671894227specID @ A @ ( insert1671894227specID @ B @ C ) )
      = ( insert1671894227specID @ B @ ( insert1671894227specID @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(1334,plain,
    $false,
    inference(e,[status(thm)],[892,1036,809,1168,1237,333,893,962,777,1110,1158,511,677,1305,1078,385,715,1275,1233,1327,1222,670,1095,1127,782,1046,301,1265,570,719,504,587,949,542,460,817,638,1147,1247,969,1013,881,325,448,421,870,492,321,623,646,834,514,353,966,905,480,397,634,877,956,660,428,312,307,452,920,380,925,1199,761,1311,534,1091,1174,598,820,561,424,788,815,729,1042,952,862,349,693,630,916,484,361,1178,522,1210,682,551,1106,1296,665,1259,615,1328,1121,1227,403,1006,1138,593,742,578,874,1143,471,884,339,1075,489,590,679,1155,706,1099,1131,984,721,371,1324,1114,1150,1249,1060,1050,1202,1241,508,674,1026,558,1071,662,888,1103,856,1301,573,733,601,1278,298,1135,412,1219,824,689,296,584,975,843,711,1124,545,445,382,1271,498,466,804,979,1194,406,1117,567,737,434,377,990,996,890,477,758,345,609,1162,626,330,848,520,959,780,1015,394,851,438,431,922,912,685,1171,1066,868,1208,531,548,374,812,617,939,342,355,1181,836,525,1003,855,690,872,414,409,310,791,1188,1038,463,1317,576,336,1257,703,1023,1140,595,612,859,845,1084,556,581,495,1216,1010,368,771,931,539,517,319,304,390,896,748,731,418,786,1212,899,667,1294,1133,315,1229,603,999,620,564,801,474,1165,358,807,1288,400,1197,839,740,1129,1268,1019,528,908,723,982,1299,442,501,607,1320,469,935,1184,775,1088,1069,364,708,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : ITP091^1 : TPTP v8.2.0. Released v7.5.0.
% 0.05/0.14  % Command  : run_Leo-III %s %d
% 0.12/0.34  % Computer : n002.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat May 18 16:22:54 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.96/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.15/1.35  % [INFO] 	 Parsing done (372ms). 
% 2.29/1.36  % [INFO] 	 Running in sequential loop mode. 
% 3.22/1.73  % [INFO] 	 eprover registered as external prover. 
% 3.22/1.74  % [INFO] 	 cvc4 registered as external prover. 
% 3.36/1.74  % [INFO] 	 Scanning for conjecture ... 
% 3.60/1.89  % [INFO] 	 Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ... 
% 4.39/2.07  % [INFO] 	 Axiom selection finished. Selected 293 axioms (removed 62 axioms). 
% 5.30/2.38  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 5.30/2.41  % [INFO] 	 Type checking passed. 
% 5.30/2.42  % [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 ... 
% 23.20/6.92  % External prover 'e' found a proof!
% 23.20/6.92  % [INFO] 	 Killing All external provers ... 
% 23.20/6.93  % Time passed: 6430ms (effective reasoning time: 5556ms)
% 23.20/6.93  % 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)>
% 23.38/6.93  % Axioms used in derivation (293): fact_6_cCompLoc, fact_60_ex__in__conv, fact_164_is__singletonI_H, fact_139_singletonD, fact_189_TBtheorem4b__PQ, fact_56_ex__in__conv, fact_153_KS2Expression_Osimps_I2_J, fact_342_eout__know__nonKS__s, fact_37_insert__iff, fact_155_KS2Expression_Osimps_I1_J, fact_50_all__not__in__conv, fact_278_Un__absorb, fact_134_singleton__iff, fact_20_LocalSecretsComposition__ine2__s, fact_211_bot__empty__eq, fact_177_correctCompositionIn__L2, fact_217_LocalSecretsComposition__neg__loc__k, fact_55_empty__iff, fact_161_is__singletonI_H, fact_11_KS_Odistinct_I1_J, fact_284_Un__left__commute, fact_328_out__exprChannelSingle__Set, fact_213_bot__empty__eq, fact_102_Collect__mem__eq, fact_323_correctCompositionKS__subcomp4, fact_256_UnE, fact_53_empty__iff, fact_227_know__composition1, fact_184_subcomponents__loc, fact_208_inStream__def, fact_133_doubleton__eq__iff, fact_312_sup__bot__left, fact_131_insert__not__empty, fact_344_TBtheore54b__P, fact_138_singleton__iff, fact_289_Un__empty__right, fact_291_singleton__Un__iff, fact_115_insertI2, fact_78_mk__disjoint__insert, fact_15_know__composition__neg1, fact_228_know__composition2, fact_124_insertE, fact_90_insert__absorb, fact_246_Un__iff, fact_41_insert__absorb2, fact_82_insert__commute, fact_128_singleton__inject, fact_114_insertI2, fact_236_notSpecKeysSecretsExpr__def, fact_252_Un__insert__right, fact_226_know__composition, fact_104_insert__ident, fact_301_sup__bot_Oright__neutral, fact_75_emptyE, fact_159_is__singleton__the__elem, fact_218_correctCompositionKS__exprChannel__s__Qex, fact_181_ineM__ine, fact_10_cCompI, fact_110_Set_Oset__insert, fact_68_equals0D, fact_337_TBtheorem5b__notP1, fact_295_Un__singleton__iff, fact_302_sup__bot_Oright__neutral, fact_97_mem__Collect__eq, fact_183_correctCompositionIn__L1, fact_28_singletonI, fact_77_mk__disjoint__insert, fact_261_UnI1, fact_187_TBtheorem4a__notPQ, fact_237_UnCI, fact_254_Un__insert__left, fact_255_Un__insert__left, fact_311_sup__bot_Oeq__neutr__iff, fact_85_insert__eq__iff, fact_334_eoutM__eout, fact_109_Set_Oset__insert, fact_27_singletonI, fact_285_Un__empty__left, fact_309_sup__bot_Oeq__neutr__iff, fact_234_LocalSecretsComposition__neg__s, fact_352_TBtheorem5a__PQ, fact_81_insert__commute, fact_271_bex__Un, fact_259_UnE, fact_306_sup__bot_Oleft__neutral, fact_333_not__eout__eoutM, fact_247_Un__empty, fact_204_TBtheorem4a__P, fact_327_TBtheorem5a__notP2, fact_232_correctCompositionKS__exprChannel__k__Qex, fact_145_the__elem__eq, fact_22_TBtheorem1a, fact_63_equals0I, fact_21_LocalSecretsComposition__neg1__s, fact_322_TBtheorem2a, fact_172_TBtheorem4a__empty, fact_29_LocalSecretsComposition1, fact_201_ine__exprChannelSet__Single, fact_195_ine__exprChannelSingle__def, fact_171_know_Osimps_I1_J, fact_290_Un__empty__right, fact_303_sup__bot_Oneutr__eq__iff, fact_349_out__exprChannelSet__def, fact_230_correctCompositionKS__exprChannel__k__Q, fact_282_Un__left__absorb, fact_149_LocalSecretsComposition__ine1__k, fact_286_Un__empty__left, fact_130_insert__not__empty, fact_307_sup__bot_Oleft__neutral, fact_272_bex__Un, fact_203_TBlemma3b, fact_292_singleton__Un__iff, fact_9_subPQ, fact_46_all__not__in__conv, fact_288_Un__empty__right, fact_324_correctCompositionKS__subcomp3, fact_5_sg6a, fact_71_emptyE, fact_175_Set_Ois__empty__def, fact_263_UnI1, fact_294_Un__singleton__iff, fact_281_Un__left__absorb, fact_353_outStream__def, fact_0_not__knowQm, fact_248_Un__empty, fact_266_UnI2, fact_65_equals0I, fact_88_insert__absorb, fact_147_LocalSecretsComposition__neg1__k, fact_220_correctCompositionKS__exprChannel__s__Q, fact_83_insert__eq__iff, fact_154_Expression_Oinject_I1_J, fact_151_is__singletonI, fact_320_correctCompositionKS__subcomp1, fact_249_Un__empty, fact_240_UnCI, fact_340_not__know__k__not__eout, fact_16_know__composition__neg__ine__s, fact_346_TBtheorem45a__P, fact_345_TBtheorem5b__PQ, fact_341_eout__know__k, fact_18_KS_Oexhaust, fact_185_TBtheorem4b__notPQ, fact_321_correctCompositionKS__subcomp2, fact_258_UnE, fact_113_insertI2, fact_163_is__singletonI_H, fact_305_sup__bot_Oneutr__eq__iff, fact_225_correctCompositionKS__negQ, fact_279_Un__commute, fact_297_insert__is__Un, fact_313_sup__bot__left, fact_158_Expression_Odistinct_I1_J, fact_148_LocalSecretsComposition__ine2__k, fact_17_not__know__s__not__ine, fact_269_UnI2, fact_54_empty__iff, fact_251_Un__insert__right, fact_329_out__exprChannelSet__Single, fact_12_KS_Oinduct, fact_129_singleton__inject, fact_196_LocalSecretsComposition__exprChannel__s, fact_30_insertCI, fact_3_sg5, fact_194_ineM__L1, fact_150_know__composition__neg__ine__k, fact_4_KS_Oinject_I2_J, fact_273_ball__Un, fact_182_TBtheorem4b__notP1, fact_216_LocalSecretsComposition__neg__loc__s, fact_188_TBtheorem4a__notP2, fact_338_eout__know__nonKS__k, fact_318_ineM__Un1, fact_40_insert__absorb2, fact_192_ine__ins__neg1, fact_73_emptyE, fact_275_Un__assoc, fact_61_equals0I, fact_222_correctCompositionKS__PQ, fact_66_equals0D, fact_197_LocalSecretsComposition__exprChannel__k, fact_296_Un__singleton__iff, fact_186_TBtheorem4b__notP2, fact_268_UnI2, fact_169_is__singleton__def, fact_314_sup__bot__left, fact_19_LocalSecretsComposition__ine1__s, fact_270_UnI2, fact_76_mk__disjoint__insert, fact_105_insert__ident, fact_119_insertI1, fact_23_TBtheorem3a, fact_143_singletonD, fact_336_TBtheorem5b__notP2, fact_308_sup__bot_Oleft__neutral, fact_64_equals0I, fact_98_Collect__mem__eq, fact_310_sup__bot_Oeq__neutr__iff, fact_304_sup__bot_Oneutr__eq__iff, fact_118_insertI1, fact_180_not__ine__ineM, fact_193_ineM__def, fact_315_sup__bot__right, fact_174_TBtheorem3b, fact_207_locStream__def, fact_347_eout__def, fact_103_insert__ident, fact_276_Un__assoc, fact_317_sup__bot__right, fact_59_ex__in__conv, fact_31_insertCI, fact_231_correctCompositionKS__exprChannel__k__Pex, fact_351_correctCompositionOut__prop1, fact_123_insertE, fact_58_ex__in__conv, fact_260_UnE, fact_191_ine__def, fact_206_TBtheorem4b__P, fact_93_mem__Collect__eq, fact_283_Un__left__commute, fact_319_TBtheorem5a__empty, fact_48_all__not__in__conv, fact_69_equals0D, fact_205_TBtheorem4a__PQ, fact_178_correctCompositionIn__prop1, fact_36_insert__iff, fact_235_LocalSecretsComposition__neg__k, fact_179_TBtheorem4a__notP1, fact_241_UnCI, fact_300_sup__bot_Oright__neutral, fact_144_LocalSecretsComposition__neg1, fact_2_knowPQ, fact_199_ine__empty__exprChannelSet, fact_316_sup__bot__right, fact_51_empty__iff, fact_280_Un__commute, fact_70_equals0D, fact_339_eoutKnowCorrect__L1k, fact_108_Set_Oset__insert, fact_239_UnCI, fact_250_Un__insert__right, fact_223_correctCompositionKS__neg1, fact_244_Un__iff, fact_325_TBtheorem5a__notP1, fact_221_correctCompositionKS__exprChannel__s__P, fact_331_eout__know__s, fact_132_doubleton__eq__iff, fact_49_all__not__in__conv, fact_299_insert__is__Un, fact_335_TBtheorem2b, fact_354_adv__not__know2, fact_190_ine__exprChannelSet__def, fact_265_UnI1, fact_35_insert__iff, fact_229_correctCompositionKS__exprChannel__k__P, fact_287_Un__empty__left, fact_125_insertE, fact_1_a2, fact_277_Un__absorb, fact_14_Expression_Oinject_I2_J, fact_348_eoutM__def, fact_13_KS_Oinject_I1_J, fact_166_not__know__k__not__ine, fact_293_singleton__Un__iff, fact_242_Un__iff, fact_32_insertCI, fact_350_out__exprChannelSingle__def, fact_7_a22, fact_264_UnI1, fact_142_singletonD, fact_200_ine__exprChannelSingle__Set, fact_332_not__know__s__not__eout, fact_8_know_Osimps_I2_J, fact_173_TBtheorem1b, fact_89_insert__absorb, fact_343_eoutKnowCorrect__L1s, fact_120_insertI1, fact_219_correctCompositionKS__exprChannel__s__Pex, fact_202_correctCompositionInLoc__exprChannel, fact_198_ine__nonempty__exprChannelSet, fact_74_emptyE, fact_137_singleton__iff, fact_24_singletonI, fact_298_insert__is__Un, fact_274_ball__Un, fact_326_TBtheorem5a__notPQ, fact_330_TBtheorem5b__notPQ, fact_253_Un__insert__left, fact_224_correctCompositionKS__negP, fact_233_LocalSecretsComposition__neg, fact_167_is__singletonE, fact_245_Un__iff, fact_84_insert__eq__iff
% 23.38/6.93  % No. of inferences in proof: 590
% 23.38/6.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6430 ms resp. 5556 ms w/o parsing
% 24.62/7.21  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.62/7.22  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------