TSTP Solution File: SWV796-1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV796-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : Fri May 19 12:18:35 EDT 2023

% Result   : Unsatisfiable 28.84s 6.24s
% Output   : Refutation 29.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  684
% Syntax   : Number of formulae    : 1292 ( 535 unt;  77 typ;   0 def)
%            Number of atoms       : 2317 ( 700 equ;   0 cnn)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives : 19140 (1116   ~;1102   |;   0   &;16922   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  102 ( 102   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   79 (  77 usr;  25 con; 0-4 aty)
%            Number of variables   : 3670 (   0   ^;3670   !;   0   ?;3670   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
    hBOOL: $i > $o ).

thf(c_in_type,type,
    c_in: $i > $i > $i > $i ).

thf(c_Message_Omsg_OCrypt_type,type,
    c_Message_Omsg_OCrypt: $i > $i > $i ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(c_Public_OshrK_type,type,
    c_Public_OshrK: $i ).

thf(v_A_type,type,
    v_A: $i ).

thf(c_Message_Omsg_OMPair_type,type,
    c_Message_Omsg_OMPair: $i > $i > $i ).

thf(c_Message_Omsg_ONonce_type,type,
    c_Message_Omsg_ONonce: $i > $i ).

thf(v_NA_type,type,
    v_NA: $i ).

thf(c_Message_Omsg_OAgent_type,type,
    c_Message_Omsg_OAgent: $i > $i ).

thf(v_B_type,type,
    v_B: $i ).

thf(c_Message_Omsg_OKey_type,type,
    c_Message_Omsg_OKey: $i ).

thf(v_K_type,type,
    v_K: $i ).

thf(v_X_type,type,
    v_X: $i ).

thf(c_Message_Oparts_type,type,
    c_Message_Oparts: $i > $i ).

thf(c_Event_Oknows_type,type,
    c_Event_Oknows: $i > $i > $i ).

thf(c_Message_Oagent_OSpy_type,type,
    c_Message_Oagent_OSpy: $i ).

thf(v_evs_type,type,
    v_evs: $i ).

thf(tc_Message_Omsg_type,type,
    tc_Message_Omsg: $i ).

thf(c_Message_Oanalz_type,type,
    c_Message_Oanalz: $i > $i ).

thf(c_Event_Obad_type,type,
    c_Event_Obad: $i ).

thf(tc_Message_Oagent_type,type,
    tc_Message_Oagent: $i ).

thf(c_NS__Shared__Mirabelle_Ons__shared_type,type,
    c_NS__Shared__Mirabelle_Ons__shared: $i ).

thf(tc_List_Olist_type,type,
    tc_List_Olist: $i > $i ).

thf(tc_Event_Oevent_type,type,
    tc_Event_Oevent: $i ).

thf(v_NB_type,type,
    v_NB: $i ).

thf(c_Event_Oevent_OSays_type,type,
    c_Event_Oevent_OSays: $i > $i > $i > $i ).

thf(c_List_Oset_type,type,
    c_List_Oset: $i > $i > $i ).

thf(class_Lattices_Oupper__semilattice_type,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
    c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).

thf(tc_bool_type,type,
    tc_bool: $i ).

thf(class_Lattices_Obounded__lattice_type,type,
    class_Lattices_Obounded__lattice: $i > $o ).

thf(tc_fun_type,type,
    tc_fun: $i > $i > $i ).

thf(tc_nat_type,type,
    tc_nat: $i ).

thf(c_Set_Oinsert_type,type,
    c_Set_Oinsert: $i > $i > $i > $i ).

thf(c_Orderings_Obot__class_Obot_type,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

thf(c_Orderings_Otop__class_Otop_type,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

thf(class_Lattices_Olattice_type,type,
    class_Lattices_Olattice: $i > $o ).

thf(c_List_Oappend_type,type,
    c_List_Oappend: $i > $i > $i > $i ).

thf(c_List_Olist_ONil_type,type,
    c_List_Olist_ONil: $i > $i ).

thf(c_List_Olist_OCons_type,type,
    c_List_Olist_OCons: $i > $i > $i > $i ).

thf(c_lessequals_type,type,
    c_lessequals: $i > $i > $i > $o ).

thf(c_Set_Oimage_type,type,
    c_Set_Oimage: $i > $i > $i > $i > $i ).

thf(class_Orderings_Obot_type,type,
    class_Orderings_Obot: $i > $o ).

thf(c_Event_Oevent_OGets_type,type,
    c_Event_Oevent_OGets: $i > $i > $i ).

thf(c_Event_Oevent_ONotes_type,type,
    c_Event_Oevent_ONotes: $i > $i > $i ).

thf(class_Orderings_Otop_type,type,
    class_Orderings_Otop: $i > $o ).

thf(class_HOL_Oord_type,type,
    class_HOL_Oord: $i > $o ).

thf(c_Message_Osynth_type,type,
    c_Message_Osynth: $i > $i ).

thf(c_Message_Omsg_OHash_type,type,
    c_Message_Omsg_OHash: $i > $i ).

thf(c_Message_OHPair_type,type,
    c_Message_OHPair: $i > $i > $i ).

thf(c_Public_Okeymode_OEncryption_type,type,
    c_Public_Okeymode_OEncryption: $i ).

thf(c_Public_Okeymode_OSignature_type,type,
    c_Public_Okeymode_OSignature: $i ).

thf(class_Orderings_Olinorder_type,type,
    class_Orderings_Olinorder: $i > $o ).

thf(c_Message_OinvKey_type,type,
    c_Message_OinvKey: $i ).

thf(c_Public_OpublicKey_type,type,
    c_Public_OpublicKey: $i > $i ).

thf(c_Event_OinitState_type,type,
    c_Event_OinitState: $i > $i ).

thf(c_Message_Oagent_OServer_type,type,
    c_Message_Oagent_OServer: $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(v_x_type,type,
    v_x: $i ).

thf(c_Message_OkeysFor_type,type,
    c_Message_OkeysFor: $i > $i ).

thf(c_Event_Oused_type,type,
    c_Event_Oused: $i > $i ).

thf(c_Message_Oanalzp_type,type,
    c_Message_Oanalzp: $i > $i > $o ).

thf(c_NS__Shared__Mirabelle_OIssues_type,type,
    c_NS__Shared__Mirabelle_OIssues: $i > $i > $i > $i > $o ).

thf(c_Message_OsymKeys_type,type,
    c_Message_OsymKeys: $i ).

thf(c_NS__Shared__Mirabelle_Ons__sharedp_type,type,
    c_NS__Shared__Mirabelle_Ons__sharedp: $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1_type,type,
    v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1: $i > $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XIssues__def__1_type,type,
    v_sko__NS__Shared__Mirabelle__XIssues__def__1: $i > $i > $i > $i > $i ).

thf(c_Public_Osko__Public__XNonce__supply1__1__1_type,type,
    c_Public_Osko__Public__XNonce__supply1__1__1: $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1_type,type,
    v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1: $i > $i > $i > $i ).

thf(c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1_type,type,
    c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1: $i > $i > $i > $i ).

thf(c_Message_Osko__Message__Xanalz__insert__eq__I__1__1_type,type,
    c_Message_Osko__Message__Xanalz__insert__eq__I__1__1: $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1_type,type,
    v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1: $i > $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__1_type,type,
    v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__1: $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__2_type,type,
    v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__2: $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1_type,type,
    v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1: $i > $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1_type,type,
    v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1: $i > $i > $i > $i > $i ).

thf(477,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insertI_0) ).

thf(1665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).

thf(1036,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(629,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__synthD_0) ).

thf(1469,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(340,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS4_0) ).

thf(1369,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(426,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).

thf(1559,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(504,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__neq__HPair_0) ).

thf(1729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__idem_0) ).

thf(1237,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_0) ).

thf(1083,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(941,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Message_OinvKey @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey_0) ).

thf(1549,plain,
    ! [A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Message_OinvKey @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( B = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).

thf(1110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( B = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I36_J_0) ).

thf(1686,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(645,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(123,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(892,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(440,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OInj_0) ).

thf(1586,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(809,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(575,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS4_0) ).

thf(1879,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1337,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(248,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_OOops_0) ).

thf(1168,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(557,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(1840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(28,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(666,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(546,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).

thf(1818,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(564,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Public_OshrK @ A )
     != ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).

thf(1855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Public_OshrK @ A )
     != ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(514,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).

thf(1750,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(596,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).

thf(1924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).

thf(1290,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Hash_0) ).

thf(1068,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1618,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(431,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS2_0) ).

thf(1569,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ( ( hAPP @ c_Message_OinvKey @ A )
        = A )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__K_0) ).

thf(1544,plain,
    ! [A: $i] :
      ( ( ( hAPP @ c_Message_OinvKey @ A )
        = A )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).

thf(1305,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(369,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).

thf(1437,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ A @ B @ C @ D ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Issues__def_0) ).

thf(1443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ A @ B @ C @ D ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(541,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__partsD_0) ).

thf(1808,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_0) ).

thf(1205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(236,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).

thf(1142,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_3) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(4,negated_conjecture,
    ~ ( hBOOL @ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(614,plain,
    ~ ( hBOOL @ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(489,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I31_J_0) ).

thf(1692,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1173,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).

thf(1486,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(1671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(570,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).

thf(1867,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1233,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__notin__image__Key_0) ).

thf(1327,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(698,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(594,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__parts_0) ).

thf(1919,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(520,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing_0) ).

thf(1761,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).

thf(1063,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(670,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(495,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_1) ).

thf(1705,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OMPair @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).

thf(1196,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OMPair @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(512,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).

thf(1746,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(555,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS3_0) ).

thf(1835,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS1_0) ).

thf(1441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(841,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(973,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(601,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Agent_0) ).

thf(1935,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).

thf(1386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__trans_0) ).

thf(1529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(539,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).

thf(1803,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil @ A )
     != ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ B @ A @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(213,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).

thf(1095,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert2_0) ).

thf(1243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(229,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(1127,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).

thf(1650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(467,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_List_Oset @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_0) ).

thf(1645,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_List_Oset @ B @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(595,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( hAPP @ c_Message_Omsg_OKey @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).

thf(1921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( hAPP @ c_Message_Omsg_OKey @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(587,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I8_J_0) ).

thf(1904,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(406,axiom,
    ~ ( hBOOL @ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).

thf(1518,plain,
    ~ ( hBOOL @ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__into__used_0) ).

thf(1265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(494,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__1 @ C @ E ) @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__2 @ C @ E ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_B__trusts__NS5_0) ).

thf(1703,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__1 @ C @ E ) @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__2 @ C @ E ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).

thf(1254,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(459,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).

thf(1628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(50,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(724,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(534,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( c_Message_Oanalzp @ A @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) )
      | ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OCrypt @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_ODecrypt_0) ).

thf(1792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( c_Message_Oanalzp @ A @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) )
      | ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OCrypt @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Public_OshrK @ A ) )
      = ( hAPP @ c_Public_OshrK @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).

thf(1871,plain,
    ! [A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ c_Public_OshrK @ A ) )
      = ( hAPP @ c_Public_OshrK @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(323,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(1330,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(258,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1191,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(136,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(917,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(751,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(435,axiom,
    hBOOL @ ( c_in @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONil_0) ).

thf(1577,plain,
    hBOOL @ ( c_in @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(377,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OEncryption ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OSignature ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Oinduct_0) ).

thf(1455,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OEncryption ) )
      | ~ ( hBOOL @ ( hAPP @ A @ c_Public_Okeymode_OSignature ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__neq__HPair_0) ).

thf(1462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__notin__image__publicKey_0) ).

thf(1132,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(581,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analzD_0) ).

thf(1892,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(238,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Nonce_0) ).

thf(1147,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(284,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 @ A @ C @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ E @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OAgent @ E ) ) ) ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_secrecy__lemma_0) ).

thf(1247,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 @ A @ C @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ E @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OAgent @ E ) ) ) ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1479,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1013,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(509,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(1741,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(430,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).

thf(1568,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I37_J_0) ).

thf(1815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ B ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__freshK_2) ).

thf(1362,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ B ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ B @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing__imp__Un_0) ).

thf(1100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__pubK_0) ).

thf(1087,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(404,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ J ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ A ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_3) ).

thf(1514,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ J ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ A ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(317,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ ( c_Message_Omsg_OCrypt @ E @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ H @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).

thf(1319,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ ( c_Message_Omsg_OCrypt @ E @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ H @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(870,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
      = ( c_Event_OinitState @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).

thf(1890,plain,
    ! [A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
      = ( c_Event_OinitState @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(66,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(756,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(499,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
     != ( hAPP @ c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).

thf(1714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
     != ( hAPP @ c_Public_OshrK @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_1) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(590,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).

thf(1911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(565,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).

thf(1858,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(551,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).

thf(1828,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(345,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
      | ( A = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).

thf(1383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
      | ( A = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(483,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oinsert @ A @ B @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Key__image_0) ).

thf(1677,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oinsert @ A @ B @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__neq__HPair_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(438,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1581,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(605,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).

thf(1946,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OHash_0) ).

thf(1465,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OHash @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I47_J_0) ).

thf(1040,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OHash @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(461,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OAgent @ A )
       != ( c_Message_Omsg_OAgent @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I1_J_0) ).

thf(1632,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OAgent @ A )
       != ( c_Message_Omsg_OAgent @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(485,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1682,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( C
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_0) ).

thf(1136,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( C
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(99,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__Un_0) ).

thf(834,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(240,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) ) @ c_Message_OsymKeys @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKey__neq__priEK_0) ).

thf(1151,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) ) @ c_Message_OsymKeys @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq_0) ).

thf(937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(254,axiom,
    hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).

thf(1183,plain,
    hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).

thf(1283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__notin__image__privateKey_0) ).

thf(1051,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(821,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(598,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cert__A__form_0) ).

thf(1928,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Key_0) ).

thf(1215,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(583,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Notes_0) ).

thf(1896,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(578,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(201,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).

thf(1072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(170,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(998,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
     != ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).

thf(1345,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
     != ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(368,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONonce @ A )
       != ( c_Message_Omsg_ONonce @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I3_J_0) ).

thf(1433,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONonce @ A )
       != ( c_Message_Omsg_ONonce @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).

thf(1521,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OFst_0) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(774,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(604,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).

thf(1943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(262,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth_0) ).

thf(1201,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_0) ).

thf(1104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(491,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).

thf(1697,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(568,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__trans_0) ).

thf(1863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( C
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(925,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(261,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1199,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Gets_0) ).

thf(1153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(530,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Message_OinvKey @ A )
       != ( hAPP @ c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__eq_0) ).

thf(1783,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Message_OinvKey @ A )
       != ( hAPP @ c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).

thf(1311,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(507,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I18_J_0) ).

thf(1736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(462,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).

thf(1636,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
       != ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).

thf(1074,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
       != ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(448,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( hAPP @ c_Message_Omsg_OKey @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I39_J_0) ).

thf(1604,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( hAPP @ c_Message_Omsg_OKey @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(592,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).

thf(1915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(496,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_1) ).

thf(1708,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(523,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS5_0) ).

thf(1768,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(798,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__knows__A_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ C )
       != ( c_Message_Oanalz @ D ) )
      | ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
        = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cong_0) ).

thf(1274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ C )
       != ( c_Message_Oanalz @ D ) )
      | ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
        = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(585,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).

thf(1900,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(957,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(746,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(329,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).

thf(1343,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1255,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(227,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).

thf(1123,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(251,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ c_Public_OshrK @ B ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ A @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_2) ).

thf(1174,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ c_Public_OshrK @ B ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ A @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).

thf(1217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__mono_0) ).

thf(729,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(334,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( hAPP @ c_Message_Omsg_OKey @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).

thf(1355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( hAPP @ c_Message_Omsg_OKey @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(437,axiom,
    ! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__shrK_0) ).

thf(1580,plain,
    ! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(399,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_1) ).

thf(1502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(515,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).

thf(1751,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(549,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__increasing_0) ).

thf(1824,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(80,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(788,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(455,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1619,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
      = ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(577,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I11_J_0) ).

thf(1883,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(427,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).

thf(1560,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(10,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(625,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(424,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ C @ tc_Message_Omsg ) ) ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).

thf(1555,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ C @ tc_Message_Omsg ) ) ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(579,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).

thf(1888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I35_J_0) ).

thf(1457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(457,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Hash_0) ).

thf(1624,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(889,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(532,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Notes__rev_1) ).

thf(1787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OSnd_0) ).

thf(1079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(67,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(757,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(230,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_0) ).

thf(1128,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(304,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
      = ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__image__Key_0) ).

thf(1291,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
      = ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(267,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).

thf(1210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(473,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Message_Omsg_OKey @ A )
       != ( hAPP @ c_Message_Omsg_OKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).

thf(1656,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Message_Omsg_OKey @ A )
       != ( hAPP @ c_Message_Omsg_OKey @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(34,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(682,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(355,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__shrK_0) ).

thf(1407,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(433,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OInj_0) ).

thf(1573,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(974,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(353,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ D @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Says__rev_0) ).

thf(1402,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ D @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(58,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(226,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ E )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__authenticates__and__keydist__to__B_0) ).

thf(1121,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ E )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq_1) ).

thf(980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__freshK_1) ).

thf(1096,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(1006,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( A = C )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__freshK_0) ).

thf(1719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( A = C )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(336,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I9_J_0) ).

thf(1360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_1) ).

thf(1350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(562,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_0) ).

thf(1851,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_1) ).

thf(1772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OHash @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I32_J_0) ).

thf(1534,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OHash @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(535,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq__I_1) ).

thf(1794,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(6,negated_conjecture,
    hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(610,plain,
    hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(517,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono_0) ).

thf(1755,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(857,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(351,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).

thf(1397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(322,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).

thf(1329,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OCrypt @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).

thf(1160,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OCrypt @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).

thf(1028,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(474,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ E )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_B__Issues__A_0) ).

thf(1659,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ E )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(64,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(753,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(508,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cut_0) ).

thf(1739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(364,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).

thf(1424,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

thf(642,plain,
    ! [A: $i] :
      ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(439,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).

thf(1584,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(602,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) )
     != ( hAPP @ c_Public_OshrK @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priEK__noteq__shrK_0) ).

thf(1937,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ A ) )
     != ( hAPP @ c_Public_OshrK @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(542,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__notin__image__shrK_0) ).

thf(1810,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__spies_0) ).

thf(1207,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1644,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(43,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(706,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(362,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__not__used_0) ).

thf(1419,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I1_J_0) ).

thf(1414,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(558,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I11_J_0) ).

thf(1842,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1612,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_1) ).

thf(1155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(511,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_2) ).

thf(1744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(622,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(441,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1588,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Gets__rev_0) ).

thf(1249,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma2_0) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(417,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_0) ).

thf(1539,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ E ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(654,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I34_J_0) ).

thf(1932,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(984,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_Set_Oimage @ B @ C @ D @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(537,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__append_0) ).

thf(1799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(366,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth_0) ).

thf(1429,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).

thf(1599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(779,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(410,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1525,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
      | ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
      | ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(550,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I33_J_0) ).

thf(1825,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Decrypt_H_0) ).

thf(1324,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OHash @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I45_J_0) ).

thf(1114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OHash @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(647,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(527,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Agent__neq__HPair_0) ).

thf(1776,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__image__eq_1) ).

thf(1263,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(519,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).

thf(1759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).

thf(1393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(544,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).

thf(1814,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).

thf(1241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(528,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth__eq_1) ).

thf(1779,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_1) ).

thf(1695,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(498,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(249,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( A
        = ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ E ) ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__S__message__form_1) ).

thf(1170,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( A
        = ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ E ) ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__trans_0) ).

thf(1187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(476,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ B @ C @ A @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ B @ C @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Issues__def_1) ).

thf(1663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ B @ C @ A @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ B @ C @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(247,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).

thf(1167,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(453,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).

thf(1616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(505,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__synth_0) ).

thf(1732,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(588,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OHash @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I14_J_0) ).

thf(1906,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OHash @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(468,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).

thf(1648,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
     != ( hAPP @ c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).

thf(1251,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
     != ( hAPP @ c_Public_OshrK @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(342,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth__eq_0) ).

thf(1374,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
      = ( c_List_Olist_OCons @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I2_J_0) ).

thf(1219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(95,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(824,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_0) ).

thf(1301,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(444,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Nonce_0) ).

thf(1595,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(129,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(904,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(553,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).

thf(1833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

thf(694,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__notin__image__privateKey_0) ).

thf(1125,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).

thf(1652,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(347,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).

thf(1388,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).

thf(1701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).

thf(1520,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(45,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(711,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OFst_0) ).

thf(1226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalzp @ A @ B )
      | ~ ( c_Message_Oanalzp @ A @ ( c_Message_Omsg_OMPair @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).

thf(1488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I10_J_0) ).

thf(1139,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(611,plain,
    ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(569,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__publicKey_0) ).

thf(1865,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ C ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__parts__subset__parts_0) ).

thf(1239,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_0) ).

thf(1332,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__HPair_0) ).

thf(1092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1090,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(704,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(148,axiom,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Osimps_I1_J_0) ).

thf(947,plain,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(482,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert_0) ).

thf(1675,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(531,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1786,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(479,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_0) ).

thf(1669,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Set_Oimage @ c_Public_OshrK @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(295,axiom,
    hBOOL @ ( c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).

thf(1271,plain,
    hBOOL @ ( c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1371,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I46_J_0) ).

thf(1058,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(219,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).

thf(1107,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(266,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).

thf(1209,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

thf(900,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(582,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__HPair_0) ).

thf(1894,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__shrK_0) ).

thf(1011,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Public_OshrK @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(418,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS2_0) ).

thf(1542,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Event_Oused @ E ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(502,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1722,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(312,axiom,
    ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ v_x )
    = ( c_in @ v_x @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp__ns__shared__eq_0) ).

thf(1307,plain,
    ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ v_x )
    = ( c_in @ v_x @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(863,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
      = ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_2) ).

thf(1853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__HPair_0) ).

thf(1408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(78,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(784,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__cut_0) ).

thf(1117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Public_OshrK @ A )
     != ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).

thf(1048,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Public_OshrK @ A )
     != ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ A @ D @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(166,axiom,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__idem_0) ).

thf(990,plain,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(996,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I19_J_0) ).

thf(1492,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(447,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).

thf(1603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(880,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__notin__initState_0) ).

thf(1043,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Says_0) ).

thf(1801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(432,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).

thf(1571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).

thf(1376,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OBody_0) ).

thf(1439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).

thf(1667,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(384,axiom,
    ( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__empty_0) ).

thf(1471,plain,
    ( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(13,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(631,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1339,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insertI_0) ).

thf(1557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(816,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1,negated_conjecture,
    hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NA ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ v_X ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(609,plain,
    hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NA ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ v_K ) @ v_X ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_OFake_0) ).

thf(1630,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(589,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__emptyE_0) ).

thf(1909,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1838,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(895,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).

thf(1177,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) )
      | ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(547,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).

thf(1820,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).

thf(700,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Crypt_0) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != ( c_List_Olist_ONil @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(626,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(915,plain,
    ! [A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(71,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(769,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).

thf(1460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__keysFor_0) ).

thf(1293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(142,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(932,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).

thf(1061,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(607,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1952,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(133,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(597,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1926,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).

thf(1474,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(492,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__image__eq_0) ).

thf(1699,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Set_Oimage @ c_Message_OinvKey @ B @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(373,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_0) ).

thf(1445,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_1) ).

thf(1015,plain,
    ! [A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(5,negated_conjecture,
    hBOOL @ ( c_in @ v_evs @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(608,plain,
    hBOOL @ ( c_in @ v_evs @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).

thf(1113,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(171,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(1000,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
       != ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(338,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Key_0) ).

thf(1364,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(428,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_1) ).

thf(1562,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(636,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(283,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Agent_0) ).

thf(1245,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(851,plain,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__image__Key_0) ).

thf(1102,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ C @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(358,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Agent__synth_0) ).

thf(1413,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(458,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 @ A @ E @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__not__see__encrypted__key_0) ).

thf(1626,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 @ A @ E @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ A ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ F @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ G ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).

thf(722,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(573,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).

thf(1873,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(263,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
      = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__def_0) ).

thf(1203,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
      = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).

thf(1467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
      = ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(486,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_1) ).

thf(1684,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(298,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).

thf(1277,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_0) ).

thf(1134,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(237,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_1) ).

thf(1145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ C ) @ A ) @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ D ) @ B @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(65,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(754,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(422,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__synth__analz_1) ).

thf(1551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).

thf(1081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(560,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oset @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_0) ).

thf(1845,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oset @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(855,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I44_J_0) ).

thf(1025,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1400,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).

thf(887,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(954,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(413,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).

thf(1531,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(215,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Hash_0) ).

thf(1098,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(420,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
      = ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__Key_0) ).

thf(1547,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) )
      = ( c_Set_Oimage @ c_Message_Omsg_OKey @ A @ tc_nat @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(513,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS5_0) ).

thf(1748,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ E @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ G ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ H ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ I @ A @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(524,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OFst_0) ).

thf(1770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(200,axiom,
    ( ( c_Event_OinitState @ c_Message_Oagent_OServer )
    = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__Server_0) ).

thf(1070,plain,
    ( ( c_Event_OinitState @ c_Message_Oagent_OServer )
    = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Message_Oagent_OServer ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(114,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

thf(872,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(516,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I4_J_0) ).

thf(1753,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OHash @ B ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(293,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OOops_0) ).

thf(1267,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(276,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1230,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
        = ( c_Set_Oimage @ A @ C @ D @ E ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(390,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ ( c_Public_Osko__Public__XNonce__supply1__1__1 @ A ) ) @ ( c_Event_Oused @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__supply1_0) ).

thf(1484,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ ( c_Public_Osko__Public__XNonce__supply1__1__1 @ A ) ) @ ( c_Event_Oused @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(533,axiom,
    ! [A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_1) ).

thf(1790,plain,
    ! [A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(463,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__mono_0) ).

thf(1637,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(82,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(791,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(1038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != B )
      | ( A
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(278,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__notin__used__empty_0) ).

thf(1235,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(207,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut_0) ).

thf(1085,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(484,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(1679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) )
      | ( A = D )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_0) ).

thf(1130,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(301,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_2) ).

thf(1285,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(130,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(907,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

thf(1053,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Otop @ A )
      | ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).

thf(1499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(316,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1317,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(552,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I13_J_0) ).

thf(1830,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(521,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
     != ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).

thf(1763,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) )
     != ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(59,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).

thf(744,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(522,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).

thf(1766,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(3,negated_conjecture,
    ~ ( hBOOL @ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(613,plain,
    ~ ( hBOOL @ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
       != ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).

thf(1221,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Public_OpublicKey @ A ) @ B )
       != ( hAPP @ ( c_Public_OpublicKey @ C ) @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_0) ).

thf(1353,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).

thf(1427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(536,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).

thf(1797,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(174,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(1008,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(500,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).

thf(1717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(876,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I17_J_0) ).

thf(1404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ c_Message_OsymKeys @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__pubK_0) ).

thf(1358,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) @ c_Message_OsymKeys @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(584,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).

thf(1898,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(289,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).

thf(1257,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(656,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oimage @ A @ B @ C @ D )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(181,axiom,
    ( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__empty_0) ).

thf(1023,plain,
    ( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(400,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS4__lemma_0) ).

thf(1504,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(727,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(212,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(978,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ A )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(576,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).

thf(1881,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_4) ).

thf(1272,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(7,negated_conjecture,
    ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(612,plain,
    ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(603,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_5) ).

thf(1940,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( hAPP @ c_Message_Omsg_OKey @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I30_J_0) ).

thf(1421,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( hAPP @ c_Message_Omsg_OKey @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(469,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Un_0) ).

thf(1649,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(141,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(931,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(423,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_1) ).

thf(1553,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(606,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Public_OshrK @ A )
       != ( hAPP @ c_Public_OshrK @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__injective_0) ).

thf(1949,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Public_OshrK @ A )
       != ( hAPP @ c_Public_OshrK @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(472,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).

thf(1654,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).

thf(1517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ C @ D ) @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(529,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1 @ A @ B @ C ) @ A @ B ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_ONonce @ E ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ F @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ F ) @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NS4__implies__NS3_0) ).

thf(1781,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1 @ A @ B @ C ) @ A @ B ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ D @ ( c_Message_Omsg_ONonce @ E ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ F @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ F ) @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ B ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).

thf(1108,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).

thf(1157,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(318,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OHash @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I38_J_0) ).

thf(1321,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OHash @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(554,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OAgent_0) ).

thf(1834,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(591,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 @ A @ B @ C @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_B__trusts__NS3_0) ).

thf(1913,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 @ A @ B @ C @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(559,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1844,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(36,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_ONil @ A )
       != ( c_List_Oappend @ B @ C @ A ) )
      | ( B
        = ( c_List_Olist_ONil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).

thf(1448,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
      = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_2) ).

thf(1189,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
      = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).

thf(1010,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(348,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).

thf(1390,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(434,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Agent_0) ).

thf(1575,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).

thf(844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(376,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1453,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).

thf(1734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(540,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert_0) ).

thf(1807,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(771,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq__I_0) ).

thf(1590,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 @ B @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(320,axiom,
    ! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).

thf(1326,plain,
    ! [A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(154,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(963,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(464,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).

thf(1639,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(389,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( hAPP @ c_Message_Omsg_OKey @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I12_J_0) ).

thf(1481,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( hAPP @ c_Message_Omsg_OKey @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(409,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ A @ F ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Oops__parts__spies_0) ).

thf(1523,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ D @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ A @ F ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(168,axiom,
    class_HOL_Oord @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(995,plain,
    class_HOL_Oord @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(328,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).

thf(1341,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(61,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(748,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(53,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(731,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(79,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(786,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(567,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
      = ( c_Message_OHPair @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__eq__HPair_2) ).

thf(1861,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
      = ( c_Message_OHPair @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(488,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( D = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_HPair__eq__MPair_1) ).

thf(1689,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( D = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(134,axiom,
    class_Lattices_Olattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(914,plain,
    class_Lattices_Olattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I16_J_0) ).

thf(1193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).

thf(1077,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).

thf(1212,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_1) ).

thf(1661,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_1) ).

thf(1309,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(190,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS3_0) ).

thf(1045,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( hBOOL @ ( c_in @ D @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).

thf(1614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Notes__rev_0) ).

thf(1607,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).

thf(763,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).

thf(684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma1_0) ).

thf(1348,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(465,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Nonce_0) ).

thf(1642,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nonce__Key__image__eq_0) ).

thf(1578,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ B @ tc_nat @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(967,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_List_Oappend @ A @ B @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS1_0) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(93,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(574,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I15_J_0) ).

thf(1876,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(310,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).

thf(1303,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(81,axiom,
    class_Orderings_Obot @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(790,plain,
    class_Orderings_Obot @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(111,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(865,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
      = ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(55,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(735,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(403,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).

thf(1512,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(526,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).

thf(1774,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(503,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).

thf(1725,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).

thf(1280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OHash @ A )
       != ( c_Message_Omsg_OHash @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I5_J_0) ).

thf(950,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OHash @ A )
       != ( c_Message_Omsg_OHash @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(100,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(835,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(443,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_0) ).

thf(1380,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ C ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ B ) @ D @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).

thf(1527,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).

thf(1673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(112,axiom,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Osimps_I2_J_0) ).

thf(867,plain,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(518,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth_0) ).

thf(1757,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(566,axiom,
    ( ( c_Event_OinitState @ c_Message_Oagent_OSpy )
    = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__Spy_0) ).

thf(1859,plain,
    ( ( c_Event_OinitState @ c_Message_Oagent_OSpy )
    = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ c_Public_OshrK @ c_Event_Obad @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Set_Oimage @ c_Message_Omsg_OKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ c_Public_Okeymode_OSignature ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).

thf(801,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(315,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_2) ).

thf(1314,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( c_in @ C @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ D @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ G ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ I @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ F ) @ J ) ) ) ) ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un_0) ).

thf(1495,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth_0) ).

thf(1335,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__MPair_0) ).

thf(1056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(955,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(450,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      = ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I56_J_0) ).

thf(1610,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
      = ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(84,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Otop @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(796,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Otop @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(126,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

thf(897,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(357,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cert__A__form_1) ).

thf(1410,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ D ) ) ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ D @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(767,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_OHPair @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__neq__HPair_0) ).

thf(1033,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_OHPair @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(302,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1288,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(497,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_new__keys__not__used_0) ).

thf(1710,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(153,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(960,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(15,axiom,
    class_Lattices_Oupper__semilattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(635,plain,
    class_Lattices_Oupper__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(385,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).

thf(1473,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ ( hAPP @ c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(720,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OInj_0) ).

thf(1165,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(120,axiom,
    class_Orderings_Otop @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(886,plain,
    class_Orderings_Otop @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_2) ).

thf(1742,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ ( c_Set_Oimage @ c_Message_OinvKey @ ( c_Set_Oimage @ ( c_Public_OpublicKey @ A ) @ C @ tc_Message_Oagent @ tc_nat ) @ tc_nat @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ C @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(928,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(165,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).

thf(987,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ c_Message_OsymKeys @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__priK_0) ).

thf(1261,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( c_in @ ( hAPP @ c_Message_OinvKey @ ( hAPP @ ( c_Public_OpublicKey @ A ) @ B ) ) @ c_Message_OsymKeys @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1537,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).

thf(1019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) ) @ ( c_List_Oset @ F @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ F @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ F ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS2_0) ).

thf(1500,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) ) @ ( c_List_Oset @ F @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ F @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ D ) @ E ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ F ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OInj_0) ).

thf(1299,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ A @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1621,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(599,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_B__trusts__NS5__lemma_0) ).

thf(1930,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ D ) @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ A @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Omsg_OAgent @ A ) ) ) ) ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(414,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 @ C @ F @ E ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS4_0) ).

thf(1532,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ E @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ( hBOOL @ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 @ C @ F @ E ) @ ( hAPP @ c_Message_Omsg_OKey @ C ) ) ) ) @ ( c_List_Oset @ E @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ G ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ D ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ E ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(860,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Olist_ONil @ C ) )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(131,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__insert_0) ).

thf(908,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(992,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != A )
      | ( B
        = ( c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(445,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Notes_0) ).

thf(1431,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(586,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_0) ).

thf(1902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

thf(691,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
        = ( c_Orderings_Otop__class_Otop @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).

thf(1367,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(138,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I57_J_0) ).

thf(923,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).

thf(1184,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(561,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(393,axiom,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(1490,plain,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).

thf(1416,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).

thf(1088,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1812,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ B @ C ) )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).

thf(708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(659,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( B = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).

thf(1565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
      | ( B = c_Message_Oagent_OSpy )
      | ~ ( hBOOL @ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(593,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).

thf(1917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ ( hAPP @ c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      | ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(676,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oappend @ A @ B @ C )
       != ( c_List_Oappend @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(361,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ D @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ F ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__S__message__form_0) ).

thf(1417,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) )
      | ~ ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ c_Public_OshrK @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Message_Oagent @ tc_bool ) ) @ tc_Message_Oagent @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( c_in @ B @ c_NS__Shared__Mirabelle_Ons__shared @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
      | ~ ( hBOOL @ ( c_in @ ( c_Event_Oevent_OSays @ D @ E @ ( c_Message_Omsg_OCrypt @ ( hAPP @ c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ F ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ G ) @ ( c_Message_Omsg_OMPair @ ( hAPP @ c_Message_Omsg_OKey @ C ) @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(571,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).

thf(1870,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(158,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__increasing_0) ).

thf(972,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(4908,plain,
    $false,
    inference(e,[status(thm)],[1665,1036,629,1469,1369,1559,1729,1237,909,1083,941,1179,1549,1110,1686,645,892,1586,809,1879,1337,1168,760,893,1840,666,1818,1295,1855,1750,1924,1290,1068,1618,1569,1544,878,1305,1437,1443,1808,873,1205,1142,1269,614,1692,1173,1486,1671,1867,1233,1327,698,1919,1761,945,1063,670,1497,1705,1196,1746,1835,1441,841,973,1935,1386,1529,1803,651,829,1095,1243,1127,1650,1645,1921,1904,1518,1265,1703,1228,1254,1628,724,1792,1871,1330,619,1191,917,751,1577,1455,1462,1132,902,853,1892,1147,1247,1479,1013,1741,1568,1815,1362,1100,1087,1514,1319,870,1890,756,1714,1450,1911,1858,1828,1383,1677,806,1581,1946,1465,1040,1632,1682,1136,834,1151,937,1183,1283,1051,821,1928,1215,1896,1886,1072,998,1345,1433,1521,1119,774,1943,1201,1104,1697,1863,661,793,925,1199,1153,1783,1311,1736,1636,1074,1604,1915,1708,1768,714,798,1163,1274,1900,957,746,1343,1255,1123,1174,1217,729,1355,1580,1502,1751,1824,788,1619,1883,1560,625,1555,1888,1457,1624,889,1787,1079,757,1128,1291,1210,1656,682,1407,1573,974,1402,742,1121,980,1096,1006,1719,1360,1350,1851,1772,1534,1794,1017,610,1755,857,1397,1329,1160,1028,1659,753,1739,1424,642,1584,1937,1810,1207,1644,706,1419,1414,1842,1612,970,1155,1744,622,1588,1249,1297,1539,654,1932,984,1799,1429,1599,779,1525,1825,1324,1114,647,1776,1263,1759,1393,1814,1241,1779,1695,921,1712,1170,1187,1663,1167,1616,1732,1906,1648,1251,1374,733,1219,824,1301,1595,904,1833,694,1125,772,1652,1388,1701,1520,826,711,1226,1488,1139,611,1865,1239,1332,1092,1090,704,947,1224,1675,1786,1669,1271,1371,1058,1107,1209,900,1894,1011,1542,1722,1307,863,1853,1408,784,1117,1048,736,990,996,1492,1603,880,649,1043,1801,1571,1376,1439,1667,811,1471,631,1339,1557,816,609,1630,1909,1838,895,943,1177,1820,848,700,1149,964,626,915,769,1460,1293,668,932,1061,1952,912,1926,1474,1699,1445,883,1015,608,1113,1000,1477,1364,1562,636,1245,851,1102,1413,1626,722,1873,1203,1467,680,663,1684,1277,1134,1509,1145,754,1551,1081,749,1845,855,1025,1400,887,954,1531,1098,1547,776,1748,1003,1770,1070,872,1753,1267,1230,1484,673,1790,1637,791,1038,717,1235,1085,1679,1130,1285,907,1053,1499,1317,1830,1763,744,1766,613,1221,1353,1506,1427,1797,1008,1717,876,1404,1358,1898,1257,656,1023,1504,727,1094,978,1881,1272,612,1940,1421,1649,931,1553,1949,1654,1517,1781,1108,1157,1321,1834,1913,976,1844,688,1448,1189,1010,1390,1575,844,1453,1734,1807,771,1590,1326,813,963,1639,1481,632,1822,1523,781,995,1341,748,731,786,1861,1030,1689,914,1193,1077,1212,1661,1309,1045,1614,1607,763,832,684,1348,1642,1578,967,1395,818,1876,1303,790,865,735,1512,1774,1725,1280,950,835,1593,1380,1527,1673,867,1757,1859,801,1314,1495,1335,1056,1065,696,955,1610,796,897,1410,767,1033,1288,1710,960,635,1473,720,1165,886,1742,928,740,987,1261,1537,1019,1500,1299,1621,1930,839,1532,860,908,992,1597,1431,1902,691,803,1367,935,923,1184,1848,1490,1416,639,1088,1812,708,659,1565,1917,676,1417,1870,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV796-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri May 19 02:38:21 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.85/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.50/1.07  % [INFO] 	 Parsing done (228ms). 
% 1.83/1.08  % [INFO] 	 Running in sequential loop mode. 
% 2.21/1.27  % [INFO] 	 eprover registered as external prover. 
% 2.21/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 2.21/1.28  % [INFO] 	 Scanning for conjecture ... 
% 2.73/1.41  % [INFO] 	 Found a conjecture and 615 axioms. Running axiom selection ... 
% 3.44/1.56  % [INFO] 	 Axiom selection finished. Selected 600 axioms (removed 15 axioms). 
% 4.03/1.71  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.03/1.73  % [INFO] 	 Type checking passed. 
% 4.03/1.73  % [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 ... 
% 28.84/6.24  % External prover 'e' found a proof!
% 28.84/6.24  % [INFO] 	 Killing All external provers ... 
% 28.84/6.24  % Time passed: 5716ms (effective reasoning time: 5159ms)
% 28.84/6.24  % 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)>
% 28.84/6.24  % Axioms used in derivation (600): clsarity_nat__HOL_Oord, cls_Key__image__eq_0, cls_Crypt__notin__initState_0, cls_NS4__implies__NS3_0, cls_synth_OHash_0, cls_shrK__in__initState_0, cls_subset__insert_1, cls_bot__fun__eq_0, cls_analz__image__freshK__lemma_5, cls_not__parts__not__analz_0, cls_top__fun__eq_0, cls_set__subset__Cons_0, cls_parts_OBody_0, cls_msg_Osimps_I47_J_0, cls_MPair__synth__analz_0, cls_symKeys__invKey__iff_0, cls_sup__ge1_0, cls_privateKey__image__eq_1, cls_Un__subset__iff_0, cls_parts__partsD_0, cls_equalityI_0, cls_sup__top__left_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_parts_OInj_0, cls_parts_OFst_0, cls_Says__S__message__form_0, cls_B__trusts__NS5_0, cls_A__trusts__NS2_0, cls_B__trusts__NS5__lemma_0, cls_MPair__used_0, cls_Cons__eq__append__conv_5, cls_knows__Notes_0, cls_subset__image__iff_2, cls_set__ConsD_0, cls_set__empty2_1, cls_initState__subset__knows_0, cls_HPair__eq_0, cls_empty__is__image_1, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_subset__empty_1, cls_pushes_I9_J_0, cls_synth__analz__mono_0, cls_append__self__conv_0, cls_secrecy__lemma_0, cls_used__Says_0, cls_sup__bot__right_0, cls_insert__code_1, cls_Issues__def_0, cls_list_Oinject_0, cls_analz__subset__iff_1, cls_Says__imp__used_0, cls_knows__Says_0, cls_analz__image__freshK__simps_I56_J_0, cls_Agent__synth_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_in__set__conv__decomp_1, cls_Un__commute_0, cls_ns__sharedp_ONS3_0, cls_analz__cong_0, cls_UnCI_1, cls_set__empty_1, cls_parts__image__Key_0, cls_insert__absorb_0, cls_used__Notes_0, cls_cert__A__form_0, cls_ns__sharedp_ONS4_0, cls_unique__session__keys_0, cls_msg_Osimps_I34_J_0, cls_mem__def_1, cls_msg_Osimps_I49_J_0, clsarity_nat__Orderings_Olinorder, cls_analz__insert__freshK_0, cls_msg_Osimps_I6_J_1, cls_Says__imp__parts__knows__Spy_0, cls_analz__subset__parts_0, cls_HPair__def_0, cls_empty__iff_0, cls_not__Cons__self2_0, cls_Fake__parts__insert_0, cls_ns__shared_OOops_0, cls_MPair__eq__HPair_1, cls_msg_Osimps_I45_J_0, cls_msg_Osimps_I12_J_0, cls_insert__iff_1, cls_eq__Nil__appendI_0, cls_knows__subset__knows__Says_0, cls_Nonce__supply1_0, cls_Gets__imp__knows__agents_0, cls_le__sup__iff_0, cls_knows__subset__knows__Cons_0, cls_append__eq__Cons__conv_4, cls_Crypt__synth__eq_1, cls_analz__idem_0, cls_insert__subset_0, cls_self__append__conv_0, cls_Crypt__synth__analz_0, cls_same__append__eq_0, clsarity_fun__Lattices_Oupper__semilattice, cls_HPair__eq__MPair_0, cls_set__rev__mp_0, cls_msg_Osimps_I3_J_0, cls_append__Cons_0, cls_ns__sharedp_ONS2_0, cls_analz__image__freshK__lemma_4, cls_ns__sharedp_OOops_0, cls_subset__insert__iff_2, cls_publicKey__into__used_0, cls_Key__synth__eq_1, cls_parts__empty_0, cls_NS3__msg__in__parts__spies_0, cls_shrK__in__knows_0, cls_shrK__image__eq_1, cls_agent_Osimps_I5_J_0, cls_analz__image__freshK__lemma_2, cls_analz__image__freshK__simps_I61_J_0, clsarity_fun__Orderings_Otop, cls_ns__sharedp_OFake_0, cls_initState__Spy_0, cls_synth__insert_0, cls_Un__left__commute_0, cls_Key__image__eq_1, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_privateKey__image__eq_2, cls_keysFor__insert__Hash_0, cls_synth_OCrypt_0, cls_knows__Nil_0, cls_analz__insert__Hash_0, cls_Says__imp__spies_0, cls_in__set__conv__decomp__first_2, cls_Server__not__bad_0, cls_analz__image__freshK__simps_I65_J_0, cls_parts__insert__HPair_0, cls_analz__Crypt__if_1, cls_pushes_I11_J_0, cls_le__supI_0, cls_Un__subset__iff_1, cls_append1__eq__conv_1, cls_parts__increasing_0, cls_append__eq__append__conv2_4, cls_Un__empty_2, cls_le__iff__sup_1, cls_knows__Spy__Notes_1, cls_Hash__notin__image__Key_0, cls_invKey__image__eq_1, cls_HPair__eq__MPair_2, cls_msg_Osimps_I7_J_0, cls_rangeI_0, cls_parts__subset__iff_1, cls_initState__Server_0, cls_rev__image__eqI_0, cls_privateKey__notin__image__publicKey_0, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_ns__shared_ONS4_0, cls_empty__is__image_0, cls_synth__synthD_0, cls_shrK__notin__image__publicKey_0, cls_analz__cut_0, cls_in__parts__UnE_0, cls_keymode_Oinduct_0, cls_le__iff__sup_0, cls_publicKey__inject_0, cls_HPair__eq_1, cls_Fake__parts__sing__imp__Un_0, cls_spies__Gets__rev_0, cls_in__set__conv__decomp__last_2, cls_synth_OMPair_0, cls_Un__UNIV__right_0, cls_Un__absorb2_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_lemma1_0, cls_Key__not__used_0, cls_parts__mono_0, cls_parts__emptyE_0, cls_used__nil__subset_0, cls_parts__insert__MPair_0, cls_symKeys__invKey__iff_1, cls_Nil__is__append__conv_0, cls_pushes_I4_J_0, cls_sup__eq__bot__eq2_0, cls_append__Nil2_0, cls_Un__upper2_0, cls_analz__empty_0, cls_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_Issues__def_1, cls_msg_Osimps_I44_J_0, cls_analz__subset__iff_0, cls_append__self__conv2_0, cls_self__append__conv2_0, cls_msg_Osimps_I40_J_0, cls_subset__iff_0, cls_insert__code_2, cls_msg_Osimps_I38_J_0, cls_parts__Un_0, cls_parts_OSnd_0, clsarity_fun__HOL_Oord, cls_pushes_I5_J_0, cls_self__append__conv2_1, cls_analz__mono__contra_I3_J_0, cls_event_Osimps_I9_J_0, cls_Spy__spies__bad__privateKey_0, cls_ns__shared_ONil_0, cls_privateKey__notin__image__shrK_0, cls_singleton__iff_1, cls_Spy__spies__bad__shrK_0, cls_symKey__neq__priEK_0, cls_event_Osimps_I6_J_0, cls_subset__empty_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_A__trusts__NS4_0, cls_pushes_I8_J_0, cls_spies__Notes__rev_1, cls_parts__insert_0, cls_msg_Osimps_I14_J_0, cls_analz__conj__parts_0, cls_append__Nil_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_ns__shared_ONS1_0, cls_append__eq__append__conv2_5, cls_append__eq__Cons__conv_5, cls_doubleton__eq__iff_2, cls_set__empty2_0, cls_Spy__analz__shrK_1, cls_image__insert_0, cls_shrK__in__used_0, cls_append__is__Nil__conv_2, cls_synth__analz__insert__eq_0, cls_event_Osimps_I3_J_0, cls_UNIV__not__empty_0, cls_keysFor__insert__MPair_0, cls_Nonce__notin__used__empty_0, cls_parts__insert__Agent_0, cls_synth__trans_0, cls_Un__insert__left_0, cls_Says__imp__analz__Spy_0, cls_cert__A__form_1, clsarity_nat__Orderings_Obot, cls_Fake__analz__insert_0, cls_A__authenticates__and__keydist__to__B_0, cls_sym__shrK_0, cls_msg_Osimps_I7_J_1, cls_Says__Server__message__form_2, cls_knows__Gets_0, cls_agent_Osimps_I4_J_0, cls_insert__subset_1, cls_Spy__see__shrK_0, cls_new__keys__not__used_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_analz_OFst_0, cls_set__eq__subset_2, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_analz_OInj_0, cls_Nonce__synth__eq_1, cls_parts__insertI_0, cls_Key__neq__HPair_0, cls_msg_Osimps_I46_J_0, cls_shrK__neq__priK_0, cls_synth__increasing_0, cls_ns__sharedp_ONil_0, cls_Un__subset__iff_2, cls_msg_Osimps_I19_J_0, cls_analzp_OFst_0, cls_msg_Osimps_I1_J_0, cls_Nonce__neq__HPair_0, cls_publicKey__notin__image__privateKey_0, cls_privateKey__neq__publicKey_0, cls_linorder__linear_0, cls_Un__empty_0, clsarity_fun__Lattices_Olattice, cls_HPair__synth__analz_0, cls_analz__parts_0, cls_ns__sharedp__ns__shared__eq_0, cls_pushes_I12_J_0, cls_image__empty_0, cls_subset__trans_0, cls_analz__image__freshK__lemma_3, cls_insert__is__Un_0, cls_msg_Osimps_I4_J_0, cls_self__append__conv_1, cls_keysFor__insert__HPair_0, cls_MPair__eq__HPair_0, cls_pushes_I2_J_0, cls_not__Cons__self_0, cls_insertI1_0, cls_msg_Osimps_I36_J_0, cls_append__same__eq_0, cls_analz__insert__Crypt__subset_0, cls_analzp_ODecrypt_0, cls_MPair__synth_1, cls_empty__not__insert_0, cls_sup__assoc_0, cls_analz__Crypt__if_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_le__supE_0, cls_analz__insert__cong_0, cls_msg_Osimps_I48_J_0, cls_msg_Osimps_I39_J_0, cls_parts__cut__eq_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_msg_Osimps_I16_J_0, cls_msg_Osimps_I35_J_0, cls_event_Osimps_I2_J_1, cls_append__assoc_0, cls_ns__shared_OFake_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup1E_0, cls_synth__Un_0, cls_Un__UNIV__left_0, cls_parts__cut_0, cls_analz__image__freshK__simps_I57_J_0, cls_sup__least_0, cls_subset__refl_0, cls_analz__shrK__Decrypt_0, cls_analz__insert__Agent_0, cls_parts__subset__iff_0, cls_synth__subset__iff_1, cls_analz__Un_0, cls_analz_ODecrypt_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_sup__top__right_0, cls_shrK__notin__image__privateKey_0, cls_not__symKeys__priK_0, cls_image__Un_0, cls_publicKey__notin__image__shrK_0, cls_sup1CI_1, cls_insertCI_0, cls_Notes__imp__knows__Spy_0, cls_msg_Osimps_I42_J_0, cls_Spy__not__see__encrypted__key_0, cls_Crypt__synth__eq_0, cls_invKey__K_0, cls_Spy__in__bad_0, cls_singletonE_0, cls_insert__Key__image_0, cls_parts__insert__knows__A_0, cls_Crypt__synth__analz_1, clsarity_nat__Lattices_Olattice, cls_UNIV__I_0, cls_HPair__synth__analz_1, cls_msg_Osimps_I13_J_0, cls_image__iff_2, cls_spies__pubK_0, cls_analzp_OSnd_0, cls_analz__spies__pubK_0, cls_bot1E_0, cls_Fake__analz__eq_0, cls_parts__insert__Hash_0, cls_event_Osimps_I1_J_1, cls_Notes__imp__used_0, cls_analz__mono__contra_I2_J_0, cls_analz__insert__HPair_0, cls_priK__in__initState_0, cls_parts__insert2_0, cls_bex__empty_0, cls_unique__session__keys_3, cls_top1I_0, cls_event_Osimps_I7_J_0, cls_insert__mono_0, cls_analzp_OInj_0, cls_le__supI2_0, cls_synth__analz__insert__eq_1, cls_analz__image__freshK__lemma_0, cls_Un__assoc_0, cls_A__trusts__NS4__lemma_0, cls_publicKey__neq__privateKey_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_shrK__injective_0, cls_synth_OInj_0, cls_synth__idem_0, cls_msg_Osimps_I15_J_0, cls_publicKey__image__eq_2, cls_msg_Osimps_I18_J_0, cls_UnE_0, cls_subset__insertI2_0, cls_Un__absorb_0, cls_MPair__used_1, cls_parts__trans_0, cls_parts__analz_0, cls_event_Osimps_I2_J_0, cls_Crypt__notin__used__empty_0, cls_neq__shrK_0, cls_usedI_0, cls_parts__insert__Key_0, cls_analz__analzD_0, cls_invKey__eq_0, clsarity_bool__Lattices_Olattice, cls_keysFor__insert__Agent_0, cls_event_Osimps_I4_J_0, cls_Spy__see__shrK_1, cls_publicKey__image__eq_0, cls_pubK__neq__shrK_0, cls_MPair__synth__analz_2, cls_bot__empty__eq_0, cls_analz__insert__MPair_0, cls_msg_Osimps_I30_J_0, cls_list_Osimps_I3_J_0, clsarity_bool__Lattices_Obounded__lattice, cls_Says__Server__message__form_1, cls_invKey__shrK_0, cls_Crypt__Spy__analz__bad_0, cls_parts__Un__subset2_0, cls_insert__subset_2, cls_le__supI1_0, cls_sup__left__idem_0, cls_insert__not__empty_0, cls_keymode_Osimps_I2_J_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_Spy__analz__shrK_0, cls_subsetD_0, cls_Key__synth_0, cls_Hash__synth__analz_0, cls_keysFor__insert__Nonce_0, cls_analz__synth__Un_0, cls_sup__fun__eq_0, cls_pushes_I1_J_0, cls_Crypt__synth_0, cls_set__append_0, cls_subset__singletonD_0, cls_event_Osimps_I8_J_0, cls_priEK__noteq__shrK_0, cls_insert__absorb2_0, cls_analz__mono_0, cls_analz_OSnd_0, cls_Crypt__imp__keysFor_0, cls_append__is__Nil__conv_1, cls_Nonce__synth__eq_0, cls_doubleton__eq__iff_1, cls_analz__mono__contra_I1_J_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_Nonce__synth_0, cls_analz__insert__eq_0, cls_parts__insert__Nonce_0, cls_analz__analz__Un_0, cls_synth__subset__iff_0, cls_Un__left__absorb_0, cls_msg_Osimps_I5_J_0, cls_event_Osimps_I1_J_0, cls_Crypt__notin__image__Key_0, cls_keymode_Osimps_I1_J_0, cls_Cons__eq__appendI_0, cls_Crypt__synth_1, cls_ns__shared_ONS3_0, cls_Hash__synth_0, cls_MPair__synth_0, cls_append__is__Nil__conv_0, cls_msg_Osimps_I17_J_0, cls_inf__sup__aci_I5_J_0, cls_append__eq__appendI_0, cls_singleton__inject_0, cls_initState__into__used_0, cls_subset__insert_0, cls_sup__idem_0, cls_msg_Osimps_I41_J_0, cls_Cons__eq__append__conv_4, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_msg_Osimps_I32_J_0, cls_knows__subset__knows__Notes_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_keysFor__parts__insert_0, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_HPair__synth__analz_2, cls_privateKey__image__eq_0, cls_msg_Osimps_I31_J_0, cls_analz__increasing_0, cls_Un__empty_1, cls_parts__Un__subset1_0, cls_unique__session__keys_1, cls_Fake__parts__sing_0, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_analz__image__Key_0, cls_analz__insert__eq__I_1, cls_B__trusts__NS3_0, cls_Un__least_0, cls_set__empty_0, cls_ns__shared_ONS2_0, cls_sup1CI_0, cls_shrK__neq__pubK_0, cls_not__symKeys__pubK_0, cls_sup__ge2_0, cls_Says__S__message__form_1, cls_Oops__parts__spies_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_Nil__is__append__conv_2, cls_ns__shared_ONS5_0, cls_lemma2_0, cls_ns__sharedp_ONS5_0, cls_image__eqI_0, cls_subset__UNIV_0, cls_analz__insert__freshK_1, cls_unique__session__keys_2, cls_analz__insertI_0, cls_image__subset__iff_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_knows__Spy__subset__knows__Spy__Says_0, cls_spies__Notes__rev_0, cls_parts__idem_0, cls_invKey_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_analz__insert__eq__I_0, cls_insert__code_0, cls_subset__insertI_0, cls_analz__trans_0, cls_used__Gets_0, cls_msg_Osimps_I6_J_0, cls_Nonce__notin__initState_0, cls_Says__imp__knows_0, cls_analz__subset__cong_0, cls_analz__insert__freshK_2, cls_sup__bot__left_0, cls_insert__image_0, cls_shrK__image__eq_0, cls_msg_Osimps_I10_J_0, cls_analz__Decrypt_H_0, cls_used__parts__subset__parts_0, cls_insert__commute_0, cls_insert__iff_2, cls_B__Issues__A_0, cls_keysFor__insert__Key_0, cls_Crypt__neq__HPair_0, cls_gen__analz__insert__eq_0, cls_HPair__eq__MPair_1, cls_Hash__synth__analz_1, cls_MPair__synth__analz_1, cls_knows__imp__Says__Gets__Notes__initState_0, cls_Fake__parts__insert__in__Un_0, cls_append1__eq__conv_0, cls_analz__insert__Key_0, cls_Un__insert__right_0, cls_publicKey__inject_1, cls_Says__Server__message__form_0, cls_Agent__neq__HPair_0, cls_list_Osimps_I2_J_0, cls_event_Osimps_I5_J_0, cls_sup__absorb1_0, cls_privateKey__into__used_0, cls_Nonce__Key__image__eq_0, cls_knows__Spy__Notes_0, cls_priK__neq__shrK_0, cls_parts__synth_0, cls_invKey__image__eq_0, cls_image__is__empty_0, cls_analz__image__freshK__lemma_1, cls_equalityE_0, cls_msg_Osimps_I37_J_0, cls_keysFor__insert__Crypt_0, cls_MPair__eq__HPair_2, cls_imageI_0, cls_parts__insert__Crypt_0, cls_Hash__neq__HPair_0, cls_ns__sharedp_ONS1_0, cls_msg_Osimps_I33_J_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_ball__empty_0, cls_synth__mono_0, cls_analz__insert__Nonce_0, cls_synth_OAgent_0, cls_Notes__imp__knows_0, cls_msg_Osimps_I11_J_0, cls_subset__insert__iff_1, cls_Crypt__imp__invKey__keysFor_0, cls_pushes_I6_J_0, clsarity_bool__Orderings_Otop, cls_publicKey__in__initState_0, cls_publicKey__image__eq_1, cls_analz__into__parts_0, cls_predicate1D_0, cls_spies__Says__rev_0, cls_synth__cut_0, cls_analz__insert_0, cls_parts__insert__spies_0
% 28.84/6.24  % No. of inferences in proof: 1215
% 28.84/6.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5716 ms resp. 5159 ms w/o parsing
% 29.19/6.43  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.19/6.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------