Leo-III---1.8.0.UNS-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV768-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:00:30 AM UTC 2026

% Result   : Unsatisfiable 15.68s 7.34s
% Output   : Refutation 17.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  571
% Syntax   : Number of formulae    : 1143 ( 445 unt;   0 typ;   0 def)
%            Number of atoms       : 2293 ( 578 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 17816 (1140   ~;1150   |;   0   &;15526   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   87 (  85 usr;  27 con; 0-4 aty)
%            Number of variables   : 3480 (   0   ^;3480   !;   0   ?;3480   :)

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

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

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

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

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

thf(v_evs2_decl,type,
    v_evs2: $i ).

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

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

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

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

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

thf(v_KAB_decl,type,
    v_KAB: $i ).

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

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

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

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

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

thf(v_A_H_decl,type,
    v_A_H: $i ).

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

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

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

thf(v_Aa_decl,type,
    v_Aa: $i ).

thf(v_Ba_decl,type,
    v_Ba: $i ).

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

thf(v_NAa_decl,type,
    v_NAa: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Lattices_Oboolean__algebra_decl,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

thf(c_HOL_Ouminus__class_Ouminus_decl,type,
    c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).

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

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

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

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

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

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

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

thf(c_Fun_Oinj__on_decl,type,
    c_Fun_Oinj__on: $i > $i > $i > $i > $o ).

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

thf(class_Orderings_Opreorder_decl,type,
    class_Orderings_Opreorder: $i > $o ).

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

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

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

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

thf(c_Message_OinvKey_decl,type,
    c_Message_OinvKey: $i > $i ).

thf(c_List_Oremdups_decl,type,
    c_List_Oremdups: $i > $i > $i ).

thf(c_List_Odistinct_decl,type,
    c_List_Odistinct: $i > $i > $o ).

thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

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

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

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

thf(class_HOL_Ouminus_decl,type,
    class_HOL_Ouminus: $i > $o ).

thf(class_Orderings_Oorder_decl,type,
    class_Orderings_Oorder: $i > $o ).

thf(c_List_Olist__inter_decl,type,
    c_List_Olist__inter: $i > $i > $i > $i ).

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

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

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

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

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

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

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

thf(c_List_Olists_decl,type,
    c_List_Olists: $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1_decl,type,
    v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1: $i > $i > $i > $i ).

thf(t_b_decl,type,
    t_b: $i ).

thf(c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1_decl,type,
    c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1: $i > $i > $i ).

thf(c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2_decl,type,
    c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Set__XrangeE__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__XrangeE__1__1: $i > $i > $i > $i > $i ).

thf(c_List_Olength__unique_decl,type,
    c_List_Olength__unique: $i > $i > $i ).

thf(c_Public_Osko__Public__XNonce__supply1__1__1_decl,type,
    c_Public_Osko__Public__XNonce__supply1__1__1: $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1_decl,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_decl,type,
    c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1: $i > $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1_decl,type,
    v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1: $i > $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1_decl,type,
    v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1: $i > $i > $i > $i ).

thf(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1_decl,type,
    v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1: $i > $i > $i > $i > $i ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).

thf(1322,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(205,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).

thf(1036,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS1_0) ).

thf(1337,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(403,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( J @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unique__session__keys_0) ).

thf(1469,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( J @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( H @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(277,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__used_0) ).

thf(1190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(480,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).

thf(1633,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(526,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
      = ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(1729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
      = ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(117,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

thf(846,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(145,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__insert_0) ).

thf(909,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(893,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( D @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( D @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).

thf(1686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__Key_0) ).

thf(1501,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(809,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(446,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__mono_0) ).

thf(1559,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__freshK_1) ).

thf(1083,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(171,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(962,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(666,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(325,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).

thf(1295,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(3,negated_conjecture,
    ~ ( tc_Message_Omsg @ ( v_evs2 @ c_Event_Oused @ ( v_KAB @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(582,plain,
    ~ ( tc_Message_Omsg @ ( v_evs2 @ c_Event_Oused @ ( v_KAB @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( B @ c_List_Oremdups ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_0) ).

thf(1596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( B @ c_List_Oremdups ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(49,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(683,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(730,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(450,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1569,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(440,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).

thf(1544,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).

thf(873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
      = ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(434,axiom,
    tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Fun_Oinj__on ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__shrK_0) ).

thf(1533,plain,
    tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Fun_Oinj__on ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

thf(614,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth_1) ).

thf(1437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).

thf(861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(269,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__lists__conv_1) ).

thf(1173,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(257,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( A
        = ( E @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__S__message__form_1) ).

thf(1142,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( A
        = ( E @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(313,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(416,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS2_0) ).

thf(1497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).

thf(1078,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).

thf(1671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OInj_0) ).

thf(1137,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(797,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ouminus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ouminus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(309,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).

thf(1260,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK_1) ).

thf(1063,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(350,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Agent__synth_0) ).

thf(1354,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(397,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( F @ ( A @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Oops__parts__spies_0) ).

thf(1458,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( F @ ( A @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(541,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS4_0) ).

thf(1761,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__lists__conv_2) ).

thf(1342,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(913,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(421,axiom,
    tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONil_0) ).

thf(1507,plain,
    tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 ) @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( c_Message_Oagent_OSpy @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__imp__Says__Notes__initState_0) ).

thf(1222,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 ) @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( B @ ( A @ c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 ) @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( c_Message_Oagent_OSpy @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(111,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).

thf(829,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(1001,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( C @ c_Event_Oused ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_used__Gets_0) ).

thf(1127,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( C @ c_Event_Oused ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(885,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS1_0) ).

thf(1386,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(432,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I56_J_0) ).

thf(1529,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(561,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__lists__conv__set_0) ).

thf(1803,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

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

thf(1265,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(535,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( C @ c_lessequals ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__trans_0) ).

thf(1746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( C @ c_lessequals ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(898,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(366,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__lists__conv_0) ).

thf(1391,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Oappend ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1441,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(488,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( A = C )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__freshK_0) ).

thf(1650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( A = C )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(486,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__image__eq_2) ).

thf(1645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(524,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS3_0) ).

thf(1724,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).

thf(1475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

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

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__image__eq_1) ).

thf(1254,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(321,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1287,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(491,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS5_0) ).

thf(1660,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(340,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_usedI_0) ).

thf(1330,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(15,negated_conjecture,
    ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_KAB @ c_Message_Omsg_OCrypt ) @ ( v_Ba @ ( v_Aa @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_14) ).

thf(587,plain,
    ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_KAB @ c_Message_Omsg_OCrypt ) @ ( v_Ba @ ( v_Aa @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_OInj_0) ).

thf(1511,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(802,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(156,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

thf(934,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(399,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).

thf(1462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(374,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(1409,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).

thf(724,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(556,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).

thf(1792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__Un_0) ).

thf(1430,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(332,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Key_0) ).

thf(1313,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Decrypt_H_0) ).

thf(1279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(817,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).

thf(853,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__image__Key_0) ).

thf(1247,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_nat @ ( A @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(513,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_OinvKey )
      = ( A @ ( c_Public_OshrK @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).

thf(1704,plain,
    ! [A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_OinvKey )
      = ( A @ ( c_Public_OshrK @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth_0) ).

thf(1115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insertI_0) ).

thf(1479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__remdups_0) ).

thf(1609,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).

thf(969,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != ( B @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I17_J_0) ).

thf(1347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_1) ).

thf(1572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).

thf(1013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).

thf(770,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(532,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1741,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(518,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).

thf(646,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(503,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( B @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( F @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( B @ ( A @ ( C @ ( B @ ( A @ v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1 ) ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NS4__implies__NS3_0) ).

thf(1682,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( B @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( F @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( B @ ( A @ ( C @ ( B @ ( A @ v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__1 ) ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(571,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(14,negated_conjecture,
    tc_Message_Omsg @ ( v_evs2 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_KAB @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_13) ).

thf(574,plain,
    tc_Message_Omsg @ ( v_evs2 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_KAB @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).

thf(1677,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(173,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(328,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_Message_Omsg @ ( C @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).

thf(1664,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_Message_Omsg @ ( C @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).

thf(1040,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(242,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( G @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__Server__message__form_0) ).

thf(1109,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( G @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(378,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I12_J_0) ).

thf(1418,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(28,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

thf(623,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).

thf(1183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(319,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

thf(1283,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(361,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I3_J_0) ).

thf(1377,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).

thf(1215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(129,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

thf(877,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(956,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(475,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__image__eq_1) ).

thf(1622,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(349,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cert__A__form_1) ).

thf(1351,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

thf(660,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

thf(998,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(988,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).

thf(1405,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1521,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(509,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__partsD_0) ).

thf(1696,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(448,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( C @ ( D @ ( B @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_0) ).

thf(1564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( C @ ( D @ ( B @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(18,axiom,
    tc_bool @ class_Lattices_Obounded__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(602,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(981,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey_0) ).

thf(766,plain,
    ! [A: $i] :
      ( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(558,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).

thf(1796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(221,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(1072,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__Agent_0) ).

thf(1206,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(153,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(925,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(551,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I8_J_0) ).

thf(1783,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__freshK_2) ).

thf(1311,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(544,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1768,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
       != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).

thf(1067,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
       != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(529,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).

thf(1736,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

thf(1047,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_lessequals ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__trans_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_lessequals ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(315,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( J @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unique__session__keys_2) ).

thf(1274,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( J @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(231,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).

thf(1091,plain,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(825,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(428,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Nonce_0) ).

thf(1519,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(451,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__image__eq_0) ).

thf(1570,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(290,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).

thf(1217,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(537,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( B @ c_Message_Oanalz ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).

thf(1751,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( B @ c_Message_Oanalz ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(494,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).

thf(1666,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(630,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(523,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OAgent_0) ).

thf(1723,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

thf(910,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(208,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS3_0) ).

thf(1042,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( E @ c_Message_Omsg_ONonce @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(166,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).

thf(952,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(351,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I1_J_0) ).

thf(1355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(456,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).

thf(1580,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(94,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(788,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(474,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( J @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unique__session__keys_1) ).

thf(1619,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( J @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(916,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(356,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I30_J_0) ).

thf(1365,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(16,negated_conjecture,
    ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( v_A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
    | ~ ( tc_Message_Omsg @ ( v_evs2 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
    | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OCrypt ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_15) ).

thf(583,plain,
    ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_A @ c_Message_Omsg_OAgent @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_OMPair ) @ ( v_A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( v_A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
    | ~ ( tc_Message_Omsg @ ( v_evs2 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
    | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_NB @ c_Message_Omsg_ONonce @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_K @ c_Message_Omsg_OCrypt ) @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(263,axiom,
    tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).

thf(1159,plain,
    tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(553,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( A @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ ( C @ ( B @ ( A @ v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 ) ) ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_B__trusts__NS3_0) ).

thf(1787,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( A @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ ( C @ ( B @ ( A @ v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 ) ) ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(287,axiom,
    ( ( ( v_x @ ( t_b @ ( t_a @ tc_fun ) @ ( v_A @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
      = ( t_b @ ( v_x @ ( v_A @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
    | ~ ( t_b @ class_HOL_Ouminus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def__raw_0) ).

thf(1210,plain,
    ( ( ( v_x @ ( t_b @ ( t_a @ tc_fun ) @ ( v_A @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
      = ( t_b @ ( v_x @ ( v_A @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
    | ~ ( t_b @ class_HOL_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).

thf(757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(318,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(1281,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(176,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__increasing_0) ).

thf(974,plain,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(194,axiom,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).

thf(1012,plain,
    ! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
        = ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).

thf(1032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
        = ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(466,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(1602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(568,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).

thf(1819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(476,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(1624,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(373,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__synthD_0) ).

thf(1407,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(546,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__analzD_0) ).

thf(1772,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(948,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth__eq_0) ).

thf(1328,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).

thf(1375,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__image__eq_0) ).

thf(1111,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).

thf(1587,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).

thf(1425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(521,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I13_J_0) ).

thf(1719,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).

thf(1360,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(348,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__shrK_0) ).

thf(1350,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(462,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

thf(1592,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(13,negated_conjecture,
    v_A = v_Aa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_12) ).

thf(578,plain,
    v_A = v_Aa,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(697,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_4) ).

thf(1234,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(435,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).

thf(1534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(557,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__parts_0) ).

thf(1794,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(1017,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(449,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__Nonce_0) ).

thf(1567,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
      | ( B = c_Message_Oagent_OSpy )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( A @ ( B @ c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 ) ) @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).

thf(1493,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL )
      | ( B = c_Message_Oagent_OSpy )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( A @ ( B @ c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 ) ) @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( B @ c_Message_Oanalz ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).

thf(1160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( B @ c_Message_Oanalz ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(354,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( D @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__S__message__form_0) ).

thf(1361,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( D @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(323,axiom,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).

thf(1292,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(531,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_nat @ tc_fun ) @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__mono_0) ).

thf(1739,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_nat @ tc_fun ) @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__cut_0) ).

thf(1075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( D @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).

thf(637,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(511,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1700,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(391,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( J @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( B @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unique__session__keys_3) ).

thf(1446,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( J @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( I @ c_Message_Omsg_OMPair ) @ ( H @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( H @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( B @ ( G @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(485,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(1644,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I31_J_0) ).

thf(1612,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(534,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).

thf(1744,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ c_List_Odistinct ) )
      | ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_0) ).

thf(1028,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(226,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).

thf(1082,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(564,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).

thf(1810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(555,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(1791,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(310,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).

thf(1263,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(236,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__notin__image__publicKey_0) ).

thf(1099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).

thf(701,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__imp__keysFor_0) ).

thf(1249,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
     != ( C @ ( c_Public_OshrK @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).

thf(1231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
     != ( C @ ( c_Public_OshrK @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).

thf(1192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(559,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).

thf(1799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).

thf(1393,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(477,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_new__keys__not__used_0) ).

thf(1627,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(570,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Public_OshrK @ hAPP ) )
       != ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__injective_0) ).

thf(1825,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Public_OshrK @ hAPP ) )
       != ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(337,axiom,
    ! [B: $i,A: $i] : ( A @ tc_List_Olist @ ( A @ ( B @ c_List_Olists ) @ ( A @ c_List_Olist_ONil @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lists_ONil_0) ).

thf(1324,plain,
    ! [B: $i,A: $i] : ( A @ tc_List_Olist @ ( A @ ( B @ c_List_Olists ) @ ( A @ c_List_Olist_ONil @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(396,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).

thf(1456,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(362,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).

thf(1382,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
        = ( B @ c_Message_Oparts ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).

thf(1131,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
        = ( B @ c_Message_Oparts ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).

thf(654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(211,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__symKeys__priK_0) ).

thf(1050,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(465,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I36_J_0) ).

thf(1599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).

thf(1246,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).

thf(1434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(334,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

thf(1318,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_2) ).

thf(1241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(549,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).

thf(1779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).

thf(805,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(508,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert_0) ).

thf(1695,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).

thf(921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

thf(657,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).

thf(1170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(401,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).

thf(1466,plain,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
       != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).

thf(1187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
       != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__notin__image__shrK_0) ).

thf(1515,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I16_J_0) ).

thf(1167,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I2_J_0) ).

thf(1185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(283,axiom,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__notin__used__empty_0) ).

thf(1202,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

thf(792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(566,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK_2) ).

thf(1814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( C @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__image__Key_0) ).

thf(1086,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( C @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(517,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).

thf(1712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).

thf(1054,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(773,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(4,negated_conjecture,
    tc_nat @ ( c_Message_OsymKeys @ ( v_KAB @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(586,plain,
    tc_nat @ ( c_Message_OsymKeys @ ( v_KAB @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1727,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(502,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth__eq_1) ).

thf(1680,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I1_J_0) ).

thf(1548,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).

thf(745,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(463,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1595,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(10,negated_conjecture,
    v_K = v_KAB,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).

thf(573,plain,
    v_K = v_KAB,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(479,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__synth_0) ).

thf(1631,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XrangeE__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeE_0) ).

thf(1251,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XrangeE__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(618,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
        = ( A @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_HOL_Ouminus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).

thf(1146,plain,
    ! [B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
        = ( A @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_HOL_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( D @ ( B @ c_List_Olist__inter ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_1) ).

thf(1754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( D @ ( B @ c_List_Olist__inter ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__notin__image__shrK_0) ).

thf(1698,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_OFst_0) ).

thf(1103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(975,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).

thf(732,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(472,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).

thf(1615,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(87,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(772,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__image__eq_0) ).

thf(1388,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(74,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).

thf(743,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(2,negated_conjecture,
    tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_evs2 @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(579,plain,
    tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_evs2 @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).

thf(1403,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I10_J_0) ).

thf(1124,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(11,negated_conjecture,
    v_B = v_Ba,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).

thf(584,plain,
    v_B = v_Ba,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).

thf(1154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).

thf(1007,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(53,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).

thf(694,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).

thf(875,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(9,negated_conjecture,
    v_B = v_Ba,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).

thf(577,plain,
    v_B = v_Ba,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OInj_0) ).

thf(1256,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(293,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OOops_0) ).

thf(1226,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(412,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).

thf(1488,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(641,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(496,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__mono_0) ).

thf(1669,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(157,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(936,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(5,negated_conjecture,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_NAa @ c_Message_Omsg_ONonce @ ( v_Ba @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_A_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(572,plain,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs2 @ c_List_Oset ) @ ( v_NAa @ c_Message_Omsg_ONonce @ ( v_Ba @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( v_Aa @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( v_A_H @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(515,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I37_J_0) ).

thf(1707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(22,axiom,
    tc_bool @ class_Lattices_Oboolean__algebra,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

thf(611,plain,
    tc_bool @ class_Lattices_Oboolean__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__mono_0) ).

thf(713,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).

thf(1239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(341,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).

thf(1332,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).

thf(1092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(543,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I11_J_0) ).

thf(1765,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__see__shrK_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(400,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( C @ c_lessequals ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__trans_0) ).

thf(1464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( C @ c_lessequals ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

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

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(499,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS5_0) ).

thf(1675,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ ( I @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( H @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( D @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(255,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).

thf(1139,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(419,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__analz__shrK_1) ).

thf(1503,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

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

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
        = ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(358,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1371,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).

thf(1635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(528,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) )
     != ( C @ ( B @ c_Public_OpublicKey @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).

thf(1733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) )
     != ( C @ ( B @ c_Public_OpublicKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).

thf(1058,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(240,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(1107,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).

thf(1194,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

thf(900,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(439,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( G @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ ( E @ ( A @ v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 ) ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__not__see__encrypted__key_0) ).

thf(1542,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( G @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ ( E @ ( A @ v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 ) ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(522,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(507,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).

thf(1690,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(388,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A__trusts__NS4__lemma_0) ).

thf(1439,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma1_0) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(92,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).

thf(784,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(246,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).

thf(1117,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).

thf(1589,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).

thf(990,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(880,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).

thf(649,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(560,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Nonce_0) ).

thf(1122,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(123,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

thf(863,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(270,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1175,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(811,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1080,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(344,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).

thf(1339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(858,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

thf(609,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(527,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__analz__shrK_0) ).

thf(1731,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).

thf(726,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(621,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).

thf(848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(138,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(895,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(260,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A
        = ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__Server__message__form_2) ).

thf(1149,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( G @ ( F @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OCrypt ) @ ( B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ( A
        = ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(148,axiom,
    tc_bool @ class_HOL_Ouminus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).

thf(915,plain,
    tc_bool @ class_HOL_Ouminus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_Message_Oagent_OSpy )
      | ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
        = ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Gets_0) ).

thf(1344,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_Message_Oagent_OSpy )
      | ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
        = ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth_0) ).

thf(1177,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(155,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I57_J_0) ).

thf(932,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oset ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__append_0) ).

thf(1688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oset ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(135,axiom,
    tc_bool @ class_Orderings_Otop,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(890,plain,
    tc_bool @ class_Orderings_Otop,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(495,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).

thf(1667,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma2_0) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1460,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).

thf(1293,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).

thf(668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).

thf(685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(181,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(405,axiom,
    tc_nat @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(1474,plain,
    tc_nat @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(959,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(1015,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).

thf(986,plain,
    ! [A: $i] :
      ( ( A @ c_List_Olist_ONil )
      = ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__notin__image__publicKey_0) ).

thf(1113,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(407,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__Key__image__eq_0) ).

thf(1477,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(415,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__increasing_0) ).

thf(1496,plain,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(562,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cert__A__form_0) ).

thf(1805,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( F @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

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

thf(1213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(768,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(827,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(431,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

thf(1528,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).

thf(868,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ c_List_Olist_ONil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(188,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(1000,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(386,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( F @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( F @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( F @ c_List_Oset ) @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A__trusts__NS2_0) ).

thf(1435,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( F @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( F @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( F @ c_List_Oset ) @ ( E @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
        = ( B @ c_Message_Oanalz @ c_Message_Osynth ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).

thf(1413,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
        = ( B @ c_Message_Oanalz @ c_Message_Osynth ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(64,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(47,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_OinvKey )
       != ( B @ c_Message_OinvKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__eq_0) ).

thf(675,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_OinvKey )
       != ( B @ c_Message_OinvKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(492,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__synth_0) ).

thf(1662,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(540,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).

thf(1758,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(286,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( E @ c_Message_Omsg_OAgent @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ ( C @ ( A @ v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 ) ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_secrecy__lemma_0) ).

thf(1208,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( E @ c_Message_Omsg_OAgent @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( D @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ ( C @ ( A @ v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 ) ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).

thf(944,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(402,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( E @ ( F @ ( C @ v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 ) ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A__trusts__NS4_0) ).

thf(1467,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( E @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( E @ ( F @ ( C @ v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 ) ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
      = ( A @ c_Message_Oanalz ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__idem_0) ).

thf(1684,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
      = ( A @ c_Message_Oanalz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(316,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( H @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OCrypt ) @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).

thf(1277,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( H @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OCrypt ) @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).

thf(1134,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(423,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).

thf(1509,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(159,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).

thf(939,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(404,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_ONS2_0) ).

thf(1472,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OServer @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( E @ ( A @ c_Message_Omsg_OAgent @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1145,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(273,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__Key_0) ).

thf(1181,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

thf(836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( A
       != ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(97,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(795,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).

thf(680,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(12,negated_conjecture,
    v_K = v_KAB,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_11) ).

thf(580,plain,
    v_K = v_KAB,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).

thf(1070,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(887,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(467,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey )
     != ( C @ ( c_Public_OshrK @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).

thf(1647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey )
     != ( C @ ( c_Public_OshrK @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(167,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(954,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(739,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) )
     != ( C @ ( B @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) )
     != ( C @ ( B @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

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

thf(1267,plain,
    ( ( v_x @ c_NS__Shared__Mirabelle_Ons__sharedp )
    = ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_x @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

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

thf(1230,plain,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(235,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).

thf(1098,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(185,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Osynth )
      = ( A @ c_Message_Osynth ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__idem_0) ).

thf(993,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Osynth )
      = ( A @ c_Message_Osynth ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(776,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(536,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).

thf(1748,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).

thf(1003,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(545,axiom,
    ! [A: $i] :
      ( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
      = ( A @ c_Event_OinitState ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Nil_0) ).

thf(1770,plain,
    ! [A: $i] :
      ( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
      = ( A @ c_Event_OinitState ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).

thf(705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(470,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(1611,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I35_J_0) ).

thf(1400,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(417,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).

thf(1499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(519,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__increasing_0) ).

thf(1716,plain,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

thf(717,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(552,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).

thf(1785,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(542,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).

thf(1763,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oanalz )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__synth_0) ).

thf(1285,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oanalz )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(36,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).

thf(643,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(907,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__symKeys__pubK_0) ).

thf(1300,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).

thf(1452,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(482,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).

thf(1637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(1038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(8,negated_conjecture,
    ( v_NA
    = ( v_NAa @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).

thf(585,plain,
    ( v_NA
    = ( v_NAa @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).

thf(1085,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(6,negated_conjecture,
    ~ ( tc_Message_Omsg @ ( v_evs2 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(576,plain,
    ~ ( tc_Message_Omsg @ ( v_evs2 @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( v_K @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(490,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).

thf(1658,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

thf(703,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(436,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1536,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).

thf(1023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_1) ).

thf(1702,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(600,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(382,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I19_J_0) ).

thf(1427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(520,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).

thf(1717,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(359,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).

thf(1372,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(612,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( D @ ( A @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Says_0) ).

thf(1617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( D @ ( A @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(411,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(1485,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(212,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( C @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keysFor__insert__MPair_0) ).

thf(1052,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( C @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insertI_0) ).

thf(1585,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_Message_Oagent_OSpy )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_Message_Oagent_OSpy )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(256,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_OOops_0) ).

thf(1140,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( B @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( E @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( G @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( E @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( E @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( D @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ ( B @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(379,axiom,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( A @ c_Event_Oused @ ( A @ c_Public_Osko__Public__XNonce__supply1__1__1 @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__supply1_0) ).

thf(1421,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( A @ c_Event_Oused @ ( A @ c_Public_Osko__Public__XNonce__supply1__1__1 @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

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

thf(627,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).

thf(1316,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(443,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).

thf(1553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(7,negated_conjecture,
    v_A = v_Aa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(581,plain,
    v_A = v_Aa,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(375,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).

thf(1412,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(453,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Un_0) ).

thf(1575,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I34_J_0) ).

thf(1807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(241,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(1108,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) )
       != ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) )
       != ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(51,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

thf(688,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(142,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

thf(903,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(550,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).

thf(1781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).

thf(891,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).

thf(1289,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).

thf(844,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(394,axiom,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).

thf(1453,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(461,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).

thf(1590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(699,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(483,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I18_J_0) ).

thf(1639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(422,axiom,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__shrK_0) ).

thf(1508,plain,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(409,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Event_OinitState @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).

thf(1481,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Event_OinitState @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(478,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

thf(632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).

thf(1523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(93,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(786,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(139,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

thf(896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(76,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(748,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).

thf(946,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__cut_0) ).

thf(1101,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1244,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(569,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz ) )
      | ( ( A @ c_Message_Oanalz )
       != ( B @ c_Message_Oanalz ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).

thf(1822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz ) )
      | ( ( A @ c_Message_Oanalz )
       != ( B @ c_Message_Oanalz ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(186,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

thf(995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_List_Olist_ONil ) )
      | ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(445,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).

thf(1558,plain,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Notes_0) ).

thf(1777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(514,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).

thf(1706,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_spies__pubK_0) ).

thf(1077,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(425,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1513,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(112,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__Un_0) ).

thf(832,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I9_J_0) ).

thf(1309,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( C @ c_Message_Omsg_ONonce @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(390,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).

thf(1444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__notin__initState_0) ).

thf(1045,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).

thf(800,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(468,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__see__shrK_1) ).

thf(1607,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(82,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(763,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(547,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).

thf(1774,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(455,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__analz_0) ).

thf(1578,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OFst_0) ).

thf(1678,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(833,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(441,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__shared_OFake_0) ).

thf(1546,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_1) ).

thf(1395,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).

thf(1673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(95,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).

thf(790,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(539,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).

thf(1757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(603,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__cut_0) ).

thf(1642,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).

thf(752,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).

thf(950,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( B @ ( A @ c_List_Oset ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).

thf(1097,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( B @ ( A @ c_List_Oset ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(150,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Oremdups ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).

thf(918,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( A @ c_List_Olist_ONil )
       != ( A @ ( B @ c_List_Oremdups ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(355,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Key__not__used_0) ).

thf(1363,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(567,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_5) ).

thf(1816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).

thf(1335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(447,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).

thf(1561,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(218,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ c_Message_Oanalz @ ( B @ c_Message_Oanalz @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).

thf(1065,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ c_Message_Oanalz @ ( B @ c_Message_Oanalz @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(266,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1165,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(955,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(533,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).

thf(1742,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).

thf(1056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(554,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).

thf(1789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(43,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).

thf(664,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(516,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).

thf(1710,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Message_Osynth @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(281,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1197,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(115,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(839,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(67,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
        = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) )
      | ( ( C @ c_Message_Oanalz )
       != ( D @ c_Message_Oanalz ) )
      | ( ( A @ c_Message_Oanalz )
       != ( B @ c_Message_Oanalz ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__cong_0) ).

thf(1236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz )
        = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz ) )
      | ( ( C @ c_Message_Oanalz )
       != ( D @ c_Message_Oanalz ) )
      | ( ( A @ c_Message_Oanalz )
       != ( B @ c_Message_Oanalz ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(251,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MPair__used_1) ).

thf(1129,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(1,negated_conjecture,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(575,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_B @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).

thf(1152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olength__unique ) )
        = ( C @ ( B @ c_List_Olength__unique ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).

thf(1357,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olength__unique ) )
        = ( C @ ( B @ c_List_Olength__unique ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(850,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

thf(871,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
      = ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Agent_0) ).

thf(1505,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__image__eq_1) ).

thf(1120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts_OBody_0) ).

thf(1384,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(437,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1537,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(457,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
       != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).

thf(1582,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
       != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(335,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS4_0) ).

thf(1320,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL )
      | ( tc_Message_Omsg @ ( E @ c_Event_Oused @ ( D @ c_Message_Omsg_ONonce @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( B @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) @ ( A @ ( F @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Event_Oevent @ ( E @ ( D @ c_Message_Omsg_ONonce @ ( C @ c_Message_Omsg_OCrypt ) @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(193,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

thf(1009,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
       != ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(413,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__Server__message__form_1) ).

thf(1490,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( E @ c_List_Oset ) @ ( A @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OCrypt ) @ ( D @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( E @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ c_Message_Omsg_OAgent @ ( C @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Message_Omsg_OMPair ) @ ( B @ ( c_Public_OshrK @ hAPP ) @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).

thf(1416,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

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

thf(639,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_0) ).

thf(1088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( tc_Message_Omsg @ ( tc_nat @ ( B @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(972,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(489,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).

thf(1653,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(940,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).

thf(923,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
      = ( A @ c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(530,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( tc_Message_Omsg @ ( tc_nat @ ( C @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK_0) ).

thf(1737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_bool @ ( tc_nat @ tc_fun ) @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( tc_Message_Omsg @ ( tc_nat @ ( C @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__idem_0) ).

thf(1204,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(392,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( ( A @ c_Message_OinvKey )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__K_0) ).

thf(1449,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( ( A @ c_Message_OinvKey )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(565,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Agent_0) ).

thf(1812,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(1878,plain,
    $false,
    inference(e,[status(thm)],[1322,1036,1337,1469,1190,1633,1729,846,909,893,1179,1686,1501,809,1559,1105,1083,962,666,1295,1200,582,1005,1596,683,730,1569,741,1544,873,878,1533,614,1437,861,1173,1142,1269,1497,1078,1671,1137,797,715,814,1260,1063,1354,1458,1761,1342,913,1507,1222,930,829,1001,1127,885,1386,1529,1803,1265,1746,898,1391,1576,782,1441,1650,1645,1724,1475,1228,1482,1254,1287,1660,1330,587,1511,802,1455,934,1462,1409,724,1792,1430,1313,1279,817,853,1247,1704,1115,1479,1609,969,606,1347,1572,1013,770,1741,1398,1714,646,1682,1828,937,574,1677,966,905,1302,1664,1040,1109,1418,623,1183,1283,1377,1215,877,734,956,866,1622,1351,660,998,988,1405,1521,1696,1564,602,981,766,1796,1072,1206,942,925,761,1783,1311,1768,1067,1736,1047,1163,1274,1091,825,1021,1519,1570,1217,1751,1666,630,1723,910,1042,952,1355,1580,788,1619,1423,916,1365,625,583,1159,1787,1210,757,1281,710,974,1012,1032,1602,1819,1624,1195,1407,1772,948,1328,1375,1111,1587,1425,1719,1360,1350,1592,578,697,1234,1534,1794,1017,1567,1493,1160,1361,1292,1739,1075,637,1700,1446,1644,1612,1744,1028,1082,1810,1791,1263,1099,701,1249,1297,1231,1192,1799,779,1393,1627,1825,1324,1539,1456,1382,1131,654,1060,1050,1599,1246,1434,1318,1241,1779,805,1695,921,657,1170,1035,1466,1187,1515,1167,1185,662,1202,792,1814,1086,765,1712,1054,773,586,1727,1680,1548,745,1595,573,1631,1251,618,1146,1754,1698,1103,819,975,732,1615,772,1388,743,579,1403,1124,584,1154,1007,694,875,577,1256,1226,1488,641,1669,936,572,1707,611,713,1239,1332,1092,1765,1258,1464,1224,1675,1139,1503,1271,1371,1635,1733,1058,1107,979,1194,900,1542,1722,737,1690,1439,1307,784,1117,1589,990,880,649,1801,616,1122,863,1175,811,1080,1339,858,609,1731,726,621,848,1325,895,1149,915,1344,1177,932,1688,890,1667,1556,1460,1293,668,685,983,1474,959,883,1015,986,1113,1477,1496,1805,1213,768,827,1528,868,1000,1435,1413,722,675,1662,1758,1208,944,1467,1684,1277,1134,1509,749,939,1472,1145,1181,836,795,680,580,1070,887,1605,1647,954,739,1368,1267,1531,1230,1098,993,776,1748,1003,1770,705,1611,1400,707,1499,673,1716,1432,717,1785,1763,1285,643,907,1300,1452,1637,1038,585,1085,576,1658,703,1536,1023,1702,600,1427,1717,1372,612,1617,1485,1052,1585,1094,1140,1421,627,1316,1553,581,1412,1517,759,1575,1807,1108,976,688,903,1781,891,1289,844,1453,1590,699,963,1639,1508,1481,1629,632,1523,786,896,748,946,1101,1244,1822,995,1558,1030,1777,1706,1077,1513,832,1309,1444,1045,800,1607,763,1774,1578,1678,833,1546,1395,1673,790,1757,603,1642,752,950,1097,918,1363,1816,807,1335,1561,1065,1165,955,1742,1056,1789,664,1710,1197,839,728,1236,1129,575,1152,1357,822,850,691,871,1505,1120,1384,1537,1582,1019,1320,1009,1490,1416,639,1088,972,1653,940,923,1737,1204,1449,1812]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV768-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.10  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.44  % Computer : n011.cluster.edu
% 0.13/0.44  % Model    : x86_64 x86_64
% 0.13/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44  % Memory   : 8046.5625MB
% 0.13/0.44  % OS       : Linux 6.8.0-71-generic
% 0.13/0.44  % CPULimit : 300
% 0.13/0.44  % WCLimit  : 300
% 0.13/0.44  % DateTime : Sat Sep 26 14:55:44 UTC 2026
% 0.13/0.44  % CPUTime  : 
% 0.13/0.44  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.79/1.10  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.91/1.67  % [INFO] 	 Parsing done (556ms). 
% 1.91/1.69  % [INFO] 	 Running in sequential loop mode. 
% 2.82/2.25  % [INFO] 	 eprover registered as external prover. 
% 2.82/2.26  % [INFO] 	 Scanning for conjecture ... 
% 3.66/2.63  % [INFO] 	 Found a conjecture (or negated_conjecture) and 562 axioms. Running axiom selection ... 
% 4.49/3.06  % [INFO] 	 Axiom selection finished. Selected 555 axioms (removed 7 axioms). 
% 5.69/3.46  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.95/3.51  % [INFO] 	 Type checking passed. 
% 5.95/3.52  % [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 ... 
% 15.68/7.34  % External prover 'e' found a proof!
% 15.68/7.34  % [INFO] 	 Killing All external provers ... 
% 15.68/7.34  % Time passed: 6724ms (effective reasoning time: 5638ms)
% 15.68/7.34  % Axioms used in derivation (555): clsarity_nat__HOL_Oord, cls_Key__image__eq_0, cls_Crypt__notin__initState_0, cls_NS4__implies__NS3_0, cls_shrK__in__initState_0, cls_parts_OBody_0, cls_minus__le__iff_0, cls_subset__insert_1, cls_Compl__subset__Compl__iff_1, cls_append__in__lists__conv_2, cls_analz__image__freshK__lemma_5, cls_not__parts__not__analz_0, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_set__subset__Cons_0, cls_MPair__synth__analz_0, cls_symKeys__invKey__iff_0, cls_sup__ge1_0, cls_Says__S__message__form_0, cls_Un__subset__iff_0, cls_order__eq__iff_0, cls_A__trusts__NS2_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_MPair__used_0, cls_Cons__eq__append__conv_5, cls_knows__Notes_0, cls_pushes_I9_J_0, cls_subset__image__iff_2, cls_set__ConsD_0, cls_initState__subset__knows_0, cls_secrecy__lemma_0, cls_inj__image__eq__iff_0, cls_image__mono_0, cls_insert__code_1, cls_le__funD_0, cls_synth__analz__mono_0, cls_append__self__conv_0, cls_list_Oinject_0, cls_parts__image__Key_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_fun__Compl__def_0, clsarity_fun__Orderings_Oorder, cls_analz__cong_0, cls_UnCI_1, cls_insert__absorb_0, cls_analz__subset__parts_0, cls_not__Cons__self2_0, cls_cert__A__form_0, cls_ns__sharedp_ONS4_0, cls_unique__session__keys_0, cls_msg_Osimps_I34_J_0, cls_compl__eq__compl__iff_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_Fake__parts__insert_0, cls_ns__shared_OOops_0, cls_msg_Osimps_I12_J_0, cls_insert__iff_1, cls_eq__Nil__appendI_0, cls_knows__subset__knows__Says_0, cls_Gets__imp__knows__agents_0, cls_set__rev__mp_0, cls_inj__on__Un__image__eq__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_inj__image__subset__iff_0, cls_Nonce__supply1_0, cls_le__sup__iff_0, cls_ComplD_0, cls_msg_Osimps_I3_J_0, cls_append__Cons_0, cls_ns__sharedp_ONS2_0, cls_analz__image__freshK__lemma_4, cls_inj__image__mem__iff_0, cls_subset__insert__iff_2, cls_synth__insert_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_synth_OCrypt_0, cls_knows__Nil_0, cls_Compl__partition_0, cls_distinct_Osimps_I2_J_0, cls_lists_ONil_0, cls_ns__sharedp_OOops_0, cls_publicKey__into__used_0, cls_inj__image__Compl__subset_0, cls_sup__compl__top_0, cls_Key__synth__eq_1, cls_analz__image__freshK__simps_I61_J_0, clsarity_fun__Orderings_Otop, cls_ns__sharedp_OFake_0, cls_Un__left__commute_0, cls_Key__image__eq_1, clsarity_bool__HOL_Oord, cls_set__mp_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_le__iff__sup_1, cls_analz__Crypt__if_1, cls_knows__Spy__Notes_1, cls_analz__image__freshK_2, 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_synth__synthD_0, cls_order__eq__refl_0, cls_msg_Osimps_I7_J_0, cls_rangeI_0, cls_parts__subset__iff_1, cls_rev__image__eqI_0, cls_inj__on__insert_0, cls_privateKey__notin__image__publicKey_0, cls_distinct_Osimps_I2_J_1, cls_le__supE_1, cls_ns__shared_ONS4_0, cls_shrK__notin__image__publicKey_0, cls_analz__cut_0, cls_in__parts__UnE_0, cls_le__iff__sup_0, cls_publicKey__inject_0, cls_distinct_Osimps_I1_J_0, cls_insert__ident_0, cls_in__set__conv__decomp__last_2, cls_synth_OMPair_0, cls_fun__Compl__def__raw_0, cls_Un__UNIV__right_0, cls_Un__absorb2_0, cls_used__nil__subset_0, clsarity_bool__Orderings_Oorder, cls_inf__sup__aci_I8_J_0, cls_lemma1_0, cls_Key__not__used_0, cls_parts__mono_0, cls_parts__insert__MPair_0, cls_symKeys__invKey__iff_1, cls_append__Nil2_0, cls_Un__upper2_0, cls_remdups_Osimps_I2_J_0, cls_remdups__id__iff__distinct_0, cls_Nil__is__append__conv_0, cls_le__minus__iff_0, cls_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_analz__subset__iff_0, cls_append__self__conv2_0, cls_privateKey__notin__image__shrK_0, cls_self__append__conv2_0, cls_msg_Osimps_I40_J_0, cls_Spy__spies__bad__shrK_0, cls_subset__iff_0, cls_insert__code_2, cls_parts_OSnd_0, clsarity_fun__HOL_Oord, cls_remdups__eq__nil__iff_1, cls_inj__shrK_0, cls_event_Osimps_I6_J_0, 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_rangeE_0, cls_distinct__append_0, cls_parts__Un_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_A__trusts__NS4_0, cls_pushes_I8_J_0, cls_analz__conj__parts_0, cls_append__Nil_0, cls_in__lists__conv__set_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_event_Osimps_I3_J_0, cls_ns__shared_ONS1_0, cls_append__eq__append__conv2_5, cls_append__eq__Cons__conv_5, cls_Compl__partition2_0, cls_keysFor__mono_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_keysFor__insert__MPair_0, cls_le__minus__iff_1, 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, cls_Fake__analz__insert_0, cls_inj__image__subset__iff_1, 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_sup__commute_0, cls_Compl__anti__mono_0, cls_analz_OFst_0, cls_set__eq__subset_2, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_privateKey__neq__publicKey_0, cls_analz_OInj_0, cls_linorder__linear_0, cls_Nonce__synth__eq_1, cls_parts__insertI_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, clsarity_fun__Lattices_Olattice, cls_msg_Osimps_I1_J_0, cls_analz__parts_0, cls_order__antisym_0, cls_order__trans_0, cls_ns__sharedp__ns__shared__eq_0, cls_pushes_I12_J_0, cls_subset__trans_0, cls_analz__image__freshK__lemma_3, cls_Compl__eq__Compl__iff_0, cls_msg_Osimps_I4_J_0, cls_self__append__conv_1, cls_Compl__subset__Compl__iff_0, clsarity_bool__HOL_Ouminus, 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, clsarity_bool__Orderings_Opreorder, cls_parts__cut__eq_0, cls_MPair__synth_1, cls_sup__assoc_0, cls_list__inter_Osimps_I1_J_0, cls_analz__Crypt__if_0, cls_le__sup__iff_1, 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_analz__image__freshK_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_Un__absorb1_0, cls_sup__top__right_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_ODecrypt_0, cls_top__greatest_0, cls_analz__Un_0, cls_append__in__lists__conv_0, cls_not__symKeys__priK_0, cls_Spy__in__bad_0, cls_image__Un_0, cls_publicKey__notin__image__shrK_0, cls_UNIV__I_0, cls_sup1CI_1, cls_insertCI_0, cls_Notes__imp__knows__Spy_0, cls_msg_Osimps_I42_J_0, clsarity_fun__Lattices_Oboolean__algebra, cls_Spy__not__see__encrypted__key_0, cls_Crypt__synth__eq_0, cls_spies__pubK_0, cls_invKey__K_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_Crypt__synth__analz_1, clsarity_nat__Lattices_Olattice, cls_msg_Osimps_I13_J_0, cls_image__iff_2, cls_analz__spies__pubK_0, cls_order__eq__iff_2, cls_Fake__analz__eq_0, cls_event_Osimps_I1_J_1, cls_Notes__imp__used_0, cls_analz__mono__contra_I2_J_0, cls_insert__mono_0, cls_priK__in__initState_0, cls_list__inter_Osimps_I2_J_0, cls_distinct__append_1, cls_unique__session__keys_3, cls_top1I_0, cls_event_Osimps_I7_J_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_inf__sup__ord_I4_J_0, cls_distinct__remdups__id_0, cls_synth_OInj_0, cls_synth__idem_0, cls_publicKey__image__eq_2, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_shrK__injective_0, cls_remdups__eq__nil__right__iff_1, cls_inj__on__def_0, cls_Un__absorb_0, cls_MPair__used_1, cls_order__antisym__conv_0, cls_msg_Osimps_I18_J_0, cls_distinct_Osimps_I2_J_2, cls_event_Osimps_I2_J_0, cls_neq__shrK_0, cls_usedI_0, cls_parts__insert__Key_0, cls_analz__analzD_0, cls_invKey__eq_0, cls_parts__trans_0, cls_set__remdups_0, clsarity_bool__Lattices_Olattice, cls_keysFor__insert__Agent_0, cls_parts__analz_0, cls_le__imp__neg__le_0, cls_event_Osimps_I4_J_0, cls_Spy__see__shrK_1, cls_injD_0, cls_Crypt__notin__used__empty_0, cls_publicKey__image__eq_0, cls_pubK__neq__shrK_0, cls_MPair__synth__analz_2, cls_analz__insert__MPair_0, cls_msg_Osimps_I30_J_0, cls_list_Osimps_I3_J_0, clsarity_bool__Lattices_Obounded__lattice, cls_knows__Spy__imp__Says__Notes__initState_0, 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_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_Spy__analz__shrK_0, cls_subsetD_0, cls_Key__synth_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_xt1_I6_J_0, cls_double__compl_0, cls_event_Osimps_I8_J_0, cls_ComplI_0, cls_analz__mono__contra_I1_J_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_analz__synth_0, cls_event_Osimps_I1_J_2, cls_minus__le__iff_1, 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_Cons__eq__appendI_0, cls_event_Osimps_I1_J_0, cls_Crypt__notin__image__Key_0, cls_Crypt__synth_1, cls_ns__shared_ONS3_0, clsarity_bool__Lattices_Oboolean__algebra, clsarity_nat__Lattices_Oupper__semilattice, cls_inf__sup__ord_I3_J_0, cls_MPair__synth_0, cls_append__is__Nil__conv_0, cls_msg_Osimps_I17_J_0, cls_knows__subset__knows__Notes_0, cls_append__eq__appendI_0, cls_subset__inj__on_0, cls_neg__le__iff__le_0, cls_initState__into__used_0, cls_parts__Un__subset1_0, cls_subset__insert_0, cls_sup__idem_0, cls_msg_Osimps_I41_J_0, cls_Cons__eq__append__conv_4, cls_append__in__lists__conv_1, cls_inf__sup__aci_I5_J_0, cls_keysFor__parts__insert_0, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_msg_Osimps_I31_J_0, cls_analz__increasing_0, cls_distinct__remdups_0, clsarity_fun__Orderings_Opreorder, cls_unique__session__keys_1, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_analz__image__Key_0, cls_B__trusts__NS3_0, cls_Un__least_0, cls_double__complement_0, cls_ns__shared_ONS2_0, cls_inj__on__contraD_0, cls_sup1CI_0, cls_inj__onD_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_parts__idem_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_knows__Spy__subset__knows__Spy__Says_0, cls_invKey_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_insert__code_0, cls_subset__insertI_0, cls_analz__trans_0, cls_used__Gets_0, cls_Nonce__notin__initState_0, cls_msg_Osimps_I6_J_0, cls_length__unique_Osimps_I2_J_0, cls_Says__imp__knows_0, cls_analz__subset__cong_0, cls_analz__insert__freshK_2, cls_insert__image_0, cls_shrK__image__eq_0, cls_list__inter_Osimps_I2_J_1, cls_msg_Osimps_I10_J_0, cls_inj__on__Un_1, cls_analz__Decrypt_H_0, cls_compl__sup__top_0, cls_insert__commute_0, cls_insert__iff_2, cls_keysFor__insert__Key_0, cls_gen__analz__insert__eq_0, 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_imageI_0, cls_event_Osimps_I5_J_0, cls_sup__absorb1_0, cls_parts__insert__Crypt_0, cls_privateKey__into__used_0, cls_MPair__synth__analz_1, clsarity_nat__Orderings_Oorder, cls_remdups__eq__nil__iff_0, cls_Nonce__Key__image__eq_0, cls_knows__Spy__Notes_0, cls_priK__neq__shrK_0, clsarity_fun__HOL_Ouminus, cls_parts__synth_0, cls_analz__image__freshK__lemma_1, cls_equalityE_0, cls_msg_Osimps_I37_J_0, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_ns__sharedp_ONS1_0, cls_analz__image__freshK_1, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_synth__cut_0, cls_analz__insert__Nonce_0, cls_synth_OAgent_0, cls_Notes__imp__knows_0, cls_analz__insert_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_synth__mono_0, cls_remdups_Osimps_I2_J_1, cls_analz__into__parts_0, cls_predicate1D_0
% 15.68/7.34  % No. of inferences in proof: 1143
% 15.68/7.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6724 ms resp. 5638 ms w/o parsing
% 16.89/7.79  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.19/7.81  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------