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

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV730-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n016.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 09:00:19 AM UTC 2026

% Result   : Unsatisfiable 28.22s 6.86s
% Output   : Refutation 29.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  546
% Syntax   : Number of formulae    : 1093 ( 475 unt;   0 typ;   0 def)
%            Number of atoms       : 2047 ( 562 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 16068 (1008   ~; 954   |;   0   &;14106   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   78 (  76 usr;  24 con; 0-4 aty)
%            Number of variables   : 3112 (   0   ^;3112   !;   0   ?;3112   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Message_Osynthp_decl,type,
    c_Message_Osynthp: $i > $i > $o ).

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

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

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

thf(c_Message_Oagent_OFriend_decl,type,
    c_Message_Oagent_OFriend: $i > $i ).

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

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

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_Message_OkeysFor_decl,type,
    c_Message_OkeysFor: $i > $i ).

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

thf(v_sko__List__Xlists__Xcases__2_decl,type,
    v_sko__List__Xlists__Xcases__2: $i > $i > $i ).

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

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

thf(v_sko__List__Xlists__Xinduct__2_decl,type,
    v_sko__List__Xlists__Xinduct__2: $i > $i > $i ).

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

thf(v_sko__List__Xlists__Xcases__1_decl,type,
    v_sko__List__Xlists__Xcases__1: $i > $i > $i ).

thf(c_NS__Shared__Mirabelle_Ons__sharedp_decl,type,
    c_NS__Shared__Mirabelle_Ons__sharedp: $i > $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(v_sko__List__Xlists__Xinduct__1_decl,type,
    v_sko__List__Xlists__Xinduct__1: $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__List__Xlists__Xinducts__2_decl,type,
    v_sko__List__Xlists__Xinducts__2: $i > $i > $i ).

thf(v_sko__List__Xlists__Xinducts__1_decl,type,
    v_sko__List__Xlists__Xinducts__1: $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(c_List_Osko__List__Xin__lists__conv__set__1__1_decl,type,
    c_List_Osko__List__Xin__lists__conv__set__1__1: $i > $i > $i > $i ).

thf(151,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Osynth )
      = ( A @ c_Message_Osynth ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__idem_0) ).

thf(892,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Osynth )
      = ( A @ c_Message_Osynth ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_0) ).

thf(1036,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)],[215]) ).

thf(430,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_1) ).

thf(1501,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(530,axiom,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__emptyE_0) ).

thf(1718,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Message_Oparts @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(490,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).

thf(1633,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)],[490]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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)],[246]) ).

thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(628,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)],[36]) ).

thf(237,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/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(1083,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)],[237]) ).

thf(171,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( A @ c_Message_Oagent_OFriend ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I7_J_0) ).

thf(941,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(279,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).

thf(1179,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)],[279]) ).

thf(98,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).

thf(777,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)],[98]) ).

thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(666,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)],[53]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
     != ( C @ ( c_Public_OshrK @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).

thf(1549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
     != ( C @ ( c_Public_OshrK @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(367,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/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1369,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)],[367]) ).

thf(285,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_4) ).

thf(1190,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)],[285]) ).

thf(454,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/sandbox2/benchmark/theBenchmark.p',cls_parts__synth_0) ).

thf(1554,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)],[454]) ).

thf(248,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/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).

thf(1110,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)],[248]) ).

thf(290,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).

thf(1200,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)],[290]) ).

thf(185,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ tc_List_Olist @ ( t_a @ ( A @ c_List_Olists ) @ ( B @ ( A @ v_sko__List__Xlists__Xcases__2 ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Ocases_2) ).

thf(977,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ tc_List_Olist @ ( t_a @ ( A @ c_List_Olists ) @ ( B @ ( A @ v_sko__List__Xlists__Xcases__2 ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(473,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS5_0) ).

thf(1596,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)],[473]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Event_Oknows ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__knows__A_0) ).

thf(1068,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( B @ c_Event_Oknows ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(440,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I36_J_0) ).

thf(1522,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)],[440]) ).

thf(404,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/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1443,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)],[404]) ).

thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(994,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)],[193]) ).

thf(383,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey_0) ).

thf(1401,plain,
    ! [A: $i] :
      ( ( A @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(535,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).

thf(1728,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)],[535]) ).

thf(292,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/sandbox2/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).

thf(1205,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)],[292]) ).

thf(471,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).

thf(1591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(320,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 @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).

thf(1269,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 @ hAPP ) @ ( 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)],[320]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(401,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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(1437,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)],[401]) ).

thf(137,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/sandbox2/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).

thf(861,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)],[137]) ).

thf(85,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/sandbox2/benchmark/theBenchmark.p',cls_synth__Un_0) ).

thf(741,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)],[85]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1073,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)],[232]) ).

thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(878,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)],[144]) ).

thf(47,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(655,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(31,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/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).

thf(614,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)],[31]) ).

thf(518,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/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1692,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)],[518]) ).

thf(524,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Notes_0) ).

thf(1705,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)],[524]) ).

thf(509,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 @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__publicKey_0) ).

thf(1671,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 @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(479,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/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth__eq_1) ).

thf(1608,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)],[479]) ).

thf(502,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oset ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_0) ).

thf(1655,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_List_Olist_ONil ) )
      | ( ( B @ ( A @ c_List_Oset ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(4,negated_conjecture,
    ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_X @ ( 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 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(550,plain,
    ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evs @ c_List_Oset ) @ ( v_X @ ( 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 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(538,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/sandbox2/benchmark/theBenchmark.p',cls_in__lists__conv__set_0) ).

thf(1735,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)],[538]) ).

thf(347,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OHash_0) ).

thf(1327,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).

thf(1260,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)],[317]) ).

thf(160,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 @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__notin__image__shrK_0) ).

thf(913,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 @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(494,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I13_J_0) ).

thf(1640,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(360,axiom,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(1354,plain,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(410,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(1458,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)],[410]) ).

thf(55,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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(670,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)],[55]) ).

thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).

thf(1078,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)],[235]) ).

thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_Nonce__Key__image__eq_0) ).

thf(1426,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)],[396]) ).

thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_0) ).

thf(1507,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)],[433]) ).

thf(301,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/sandbox2/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).

thf(1222,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)],[301]) ).

thf(123,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I57_J_0) ).

thf(829,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)],[123]) ).

thf(288,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp__ns__shared__eq_0) ).

thf(1196,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)],[288]) ).

thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).

thf(1001,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)],[197]) ).

thf(310,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKeys__invKey__iff_0) ).

thf(1243,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(463,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).

thf(1576,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)],[463]) ).

thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(709,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)],[73]) ).

thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono_0) ).

thf(841,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)],[128]) ).

thf(362,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/sandbox2/benchmark/theBenchmark.p',cls_parts__Un_0) ).

thf(1359,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)],[362]) ).

thf(533,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).

thf(1724,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)],[533]) ).

thf(523,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lists__conv__set_1) ).

thf(1703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(45,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/sandbox2/benchmark/theBenchmark.p',cls_synth__mono_0) ).

thf(651,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)],[45]) ).

thf(101,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/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(782,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)],[101]) ).

thf(403,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Nonce_0) ).

thf(1441,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)],[403]) ).

thf(499,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/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(1650,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)],[499]) ).

thf(497,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS3_0) ).

thf(1645,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)],[497]) ).

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

thf(565,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1366,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(485,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__notin__image__shrK_0) ).

thf(1623,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)],[485]) ).

thf(421,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/sandbox2/benchmark/theBenchmark.p',cls_parts__mono_0) ).

thf(1482,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)],[421]) ).

thf(488,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinducts_3) ).

thf(1628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__2 ) @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(329,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/sandbox2/benchmark/theBenchmark.p',cls_Key__not__used_0) ).

thf(1287,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)],[329]) ).

thf(526,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/sandbox2/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).

thf(1709,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)],[526]) ).

thf(13,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/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(570,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)],[13]) ).

thf(334,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend @ c_Event_OinitState )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Message_Oagent_OFriend @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Oagent_OFriend @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Oagent_OFriend @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__Friend_0) ).

thf(1298,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend @ c_Event_OinitState )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Message_Oagent_OFriend @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Oagent_OFriend @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Oagent_OFriend @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(102,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/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(785,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)],[102]) ).

thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(802,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)],[110]) ).

thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_1) ).

thf(1313,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)],[341]) ).

thf(168,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/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).

thf(934,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)],[168]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) )
     != ( C @ ( B @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).

thf(949,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) )
     != ( C @ ( B @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_1) ).

thf(1055,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)],[224]) ).

thf(78,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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(724,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)],[78]) ).

thf(345,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/sandbox2/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).

thf(1323,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)],[345]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(838,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(435,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/sandbox2/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).

thf(1511,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)],[435]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_1) ).

thf(917,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( A @ c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(412,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 @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).

thf(1462,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 @ 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)],[412]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ ( A @ ( B @ ( A @ v_sko__List__Xlists__Xcases__1 ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Ocases_1) ).

thf(1059,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ( B
        = ( t_a @ c_List_Olist_ONil ) )
      | ( t_a @ ( A @ ( B @ ( A @ v_sko__List__Xlists__Xcases__1 ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__idem_0) ).

thf(1132,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(450,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/sandbox2/benchmark/theBenchmark.p',cls_new__keys__not__used_0) ).

thf(1545,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)],[450]) ).

thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(817,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)],[118]) ).

thf(7,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(559,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(372,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).

thf(1379,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)],[372]) ).

thf(312,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/sandbox2/benchmark/theBenchmark.p',cls_lists_ONil_0) ).

thf(1247,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)],[312]) ).

thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(606,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)],[28]) ).

thf(95,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(770,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)],[95]) ).

thf(146,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/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(881,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)],[146]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(1568,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).

thf(1494,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__spies_0) ).

thf(1100,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(414,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/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(1465,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)],[414]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Event_Oused @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Notes_0) ).

thf(1302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Event_Oused @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(406,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/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).

thf(1450,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)],[406]) ).

thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_0) ).

thf(1040,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)],[217]) ).

thf(43,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(646,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(1383,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)],[374]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
      = ( A @ ( c_Public_OshrK @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).

thf(1677,plain,
    ! [A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
      = ( A @ ( c_Public_OshrK @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(466,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).

thf(1581,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)],[466]) ).

thf(327,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/sandbox2/benchmark/theBenchmark.p',cls_pushes_I1_J_0) ).

thf(1283,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)],[327]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).

thf(905,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)],[156]) ).

thf(424,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(1489,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(390,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/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).

thf(1415,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)],[390]) ).

thf(514,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( B @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I15_J_0) ).

thf(1682,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( B @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).

thf(1136,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)],[260]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(26,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/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(602,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)],[26]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).

thf(1169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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)],[275]) ).

thf(297,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).

thf(1215,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).

thf(1072,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)],[231]) ).

thf(252,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).

thf(1119,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)],[252]) ).

thf(380,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS2_0) ).

thf(1394,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)],[380]) ).

thf(50,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/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).

thf(660,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)],[50]) ).

thf(385,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insertI_0) ).

thf(1405,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)],[385]) ).

thf(475,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_1) ).

thf(1600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( B @ ( D @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_Message_Oagent @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(849,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)],[132]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
      = ( A @ c_Event_OinitState ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).

thf(1696,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)],[520]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_2) ).

thf(1564,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Oagent @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( A @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(233,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/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_2) ).

thf(1074,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)],[233]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(678,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS1_0) ).

thf(1306,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)],[338]) ).

thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_analz__Un_0) ).

thf(810,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)],[113]) ).

thf(416,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Hash_0) ).

thf(1470,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(340,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/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).

thf(1311,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)],[340]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(714,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(267,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__priK_0) ).

thf(1153,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(91,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(761,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(220,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symKey__neq__priEK_0) ).

thf(1047,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(108,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(798,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(225,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_OOops_0) ).

thf(1057,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)],[225]) ).

thf(272,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_3) ).

thf(1163,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)],[272]) ).

thf(152,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(894,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(240,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/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).

thf(1091,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)],[240]) ).

thf(355,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I12_J_0) ).

thf(1343,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(439,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I2_J_0) ).

thf(1519,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(465,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/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).

thf(1580,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)],[465]) ).

thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(1123,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)],[254]) ).

thf(506,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).

thf(1666,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)],[506]) ).

thf(423,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/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Nonce_0) ).

thf(1487,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)],[423]) ).

thf(483,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oset ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty_1) ).

thf(1619,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oset ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(116,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(815,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(80,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/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(729,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)],[80]) ).

thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Key_0) ).

thf(1238,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)],[308]) ).

thf(376,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/sandbox2/benchmark/theBenchmark.p',cls_synth__trans_0) ).

thf(1387,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)],[376]) ).

thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(910,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)],[158]) ).

thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_analz_OFst_0) ).

thf(1021,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)],[207]) ).

thf(99,axiom,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Osimps_I2_J_0) ).

thf(778,plain,
    c_Public_Okeymode_OEncryption != c_Public_Okeymode_OSignature,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(218,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).

thf(1042,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)],[218]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I6_J_0) ).

thf(952,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(277,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_2) ).

thf(1174,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)],[277]) ).

thf(511,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).

thf(1676,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)],[511]) ).

thf(544,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Public_OshrK @ hAPP ) )
       != ( B @ ( c_Public_OshrK @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__injective_0) ).

thf(1751,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)],[544]) ).

thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).

thf(820,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)],[120]) ).

thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(693,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)],[65]) ).

thf(37,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).

thf(630,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)],[37]) ).

thf(394,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Agent_0) ).

thf(1423,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)],[394]) ).

thf(134,axiom,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Osimps_I1_J_0) ).

thf(852,plain,
    c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(333,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 @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).

thf(1296,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 @ hAPP ) @ ( 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)],[333]) ).

thf(516,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/sandbox2/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).

thf(1687,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)],[516]) ).

thf(18,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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(583,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)],[18]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).

thf(889,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)],[150]) ).

thf(270,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/sandbox2/benchmark/theBenchmark.p',cls_initState__into__used_0) ).

thf(1159,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)],[270]) ).

thf(294,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/sandbox2/benchmark/theBenchmark.p',cls_analz__Decrypt_H_0) ).

thf(1210,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)],[294]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__notin__image__privateKey_0) ).

thf(1027,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( C @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(386,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/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).

thf(1407,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)],[386]) ).

thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1128,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)],[256]) ).

thf(325,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/sandbox2/benchmark/theBenchmark.p',cls_neq__shrK_0) ).

thf(1281,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)],[325]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( C @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__1 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinducts_0) ).

thf(1392,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( C @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__1 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).

thf(1012,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)],[203]) ).

thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(847,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)],[131]) ).

thf(11,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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(566,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)],[11]) ).

thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_1) ).

thf(1032,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)],[213]) ).

thf(476,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Message_OinvKey @ hAPP ) )
       != ( B @ ( c_Message_OinvKey @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__eq_0) ).

thf(1602,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Message_OinvKey @ hAPP ) )
       != ( B @ ( c_Message_OinvKey @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__2 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinducts_1) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( A @ ( C @ v_sko__List__Xlists__Xinducts__2 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OFst_0) ).

thf(1121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(395,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONil_0) ).

thf(1425,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)],[395]) ).

thf(241,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/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(1096,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)],[241]) ).

thf(200,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_0) ).

thf(1006,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)],[200]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Message_Oparts @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert2_0) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ c_Message_Oparts @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(22,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(593,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)],[22]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OSnd_0) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Oanalzp ) )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(742,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

thf(578,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__symKeys__pubK_0) ).

thf(1234,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)],[306]) ).

thf(448,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/sandbox2/benchmark/theBenchmark.p',cls_shrK__image__eq_1) ).

thf(1541,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)],[448]) ).

thf(142,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(874,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).

thf(1143,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Hash_0) ).

thf(980,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(429,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
       != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).

thf(1498,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)],[429]) ).

thf(469,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/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).

thf(1587,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)],[469]) ).

thf(426,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).

thf(1493,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)],[426]) ).

thf(363,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/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1361,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)],[363]) ).

thf(331,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).

thf(1292,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)],[331]) ).

thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).

thf(753,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)],[89]) ).

thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__keysFor_0) ).

thf(1182,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)],[281]) ).

thf(540,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
     != ( B @ ( c_Public_OshrK @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priEK__noteq__shrK_0) ).

thf(1739,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) )
     != ( B @ ( c_Public_OshrK @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(41,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/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(642,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)],[41]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(637,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(496,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OAgent_0) ).

thf(1644,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)],[496]) ).

thf(71,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/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(706,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)],[71]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_OInj_0) ).

thf(1419,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(884,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)],[148]) ).

thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).

thf(1329,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)],[348]) ).

thf(205,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I45_J_0) ).

thf(1016,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(293,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_OHash ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I38_J_0) ).

thf(1207,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_OHash ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(590,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(481,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_Event_Oused )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ c_Event_Oused @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Says_0) ).

thf(1612,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_Event_Oused )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( D @ c_Event_Oused @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(182,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/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).

thf(970,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)],[182]) ).

thf(268,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__imp__Says__Notes__initState_0) ).

thf(1155,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)],[268]) ).

thf(1,negated_conjecture,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(547,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(126,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(837,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(250,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).

thf(1114,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)],[250]) ).

thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(701,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)],[69]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__lists__conv__set_2) ).

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( C @ ( A @ ( B @ c_List_Osko__List__Xin__lists__conv__set__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).

thf(1552,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)],[453]) ).

thf(286,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/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_0) ).

thf(1192,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)],[286]) ).

thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).

thf(984,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)],[188]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing__imp__Un_0) ).

thf(1002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( 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)],[198]) ).

thf(529,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ c_Message_Omsg_OHash ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I14_J_0) ).

thf(1715,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ c_Message_Omsg_OHash ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(531,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).

thf(1720,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)],[531]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__image__eq_0) ).

thf(1263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( B @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlists__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinduct_2) ).

thf(997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlists__Xinduct__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(443,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/sandbox2/benchmark/theBenchmark.p',cls_Spy__see__shrK_1) ).

thf(1530,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)],[443]) ).

thf(447,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).

thf(1539,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)],[447]) ).

thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I56_J_0) ).

thf(1456,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)],[409]) ).

thf(319,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).

thf(1266,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)],[319]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).

thf(1231,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)],[305]) ).

thf(12,axiom,
    tc_nat @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(569,plain,
    tc_nat @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(1429,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)],[398]) ).

thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).

thf(1627,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)],[487]) ).

thf(441,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/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(1525,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)],[441]) ).

thf(350,axiom,
    ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Message_Oparts )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__empty_0) ).

thf(1333,plain,
    ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Message_Oparts )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Public_Okeymode_OSignature @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Public_Okeymode_OEncryption @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keymode_Oinduct_0) ).

thf(1318,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Public_Okeymode_OSignature @ ( A @ hAPP ) @ hBOOL )
      | ~ ( c_Public_Okeymode_OEncryption @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(105,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/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(792,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)],[105]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I47_J_0) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(309,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/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).

thf(1241,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)],[309]) ).

thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).

thf(921,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)],[164]) ).

thf(458,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(1563,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)],[458]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ c_Message_Omsg_OHash ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I32_J_0) ).

thf(765,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ c_Message_Omsg_OHash ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(505,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Public_OshrK @ hAPP ) )
     != ( C @ ( B @ c_Public_OpublicKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).

thf(1663,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)],[505]) ).

thf(437,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).

thf(1515,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)],[437]) ).

thf(51,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(662,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I44_J_0) ).

thf(926,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I17_J_0) ).

thf(1278,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)],[324]) ).

thf(498,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1648,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)],[498]) ).

thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth__eq_0) ).

thf(1251,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)],[314]) ).

thf(322,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).

thf(1273,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(745,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)],[87]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(63,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/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(689,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)],[63]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( C @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__1 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinduct_0) ).

thf(1374,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ ( C @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__1 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I46_J_0) ).

thf(965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(750,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)],[88]) ).

thf(265,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/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Agent_0) ).

thf(1146,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)],[265]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I34_J_0) ).

thf(1754,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)],[545]) ).

thf(521,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A
        = ( t_a @ c_List_Olist_ONil ) )
      | ( A
        = ( t_a @ ( A @ ( B @ v_sko__List__Xlists__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlists__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Ocases_0) ).

thf(1698,plain,
    ! [B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A
        = ( t_a @ c_List_Olist_ONil ) )
      | ( A
        = ( t_a @ ( A @ ( B @ v_sko__List__Xlists__Xcases__2 ) @ ( A @ ( B @ v_sko__List__Xlists__Xcases__1 ) @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(245,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/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).

thf(1103,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)],[245]) ).

thf(119,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(819,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(184,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 @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).

thf(975,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 @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(694,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)],[66]) ).

thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).

thf(1389,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)],[377]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(772,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(500,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OHash @ 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_OHash @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I11_J_0) ).

thf(1652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ c_Message_Omsg_OHash @ 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_OHash @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).

thf(875,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)],[143]) ).

thf(445,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 @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_1) ).

thf(1535,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 @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(522,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/sandbox2/benchmark/theBenchmark.p',cls_analz__analzD_0) ).

thf(1701,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)],[522]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).

thf(1226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
     != ( D @ ( C @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(129,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/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(843,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)],[129]) ).

thf(255,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/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(1125,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)],[255]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__notin__image__privateKey_0) ).

thf(958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( D @ ( C @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Public_OpublicKey @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(384,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 @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_keysFor__parts__insert_0) ).

thf(1403,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 @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(397,axiom,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__shrK_0) ).

thf(1428,plain,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ ( c_Public_OshrK @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(431,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/sandbox2/benchmark/theBenchmark.p',cls_parts__insertI_0) ).

thf(1503,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)],[431]) ).

thf(508,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/sandbox2/benchmark/theBenchmark.p',cls_analz__trans_0) ).

thf(1669,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)],[508]) ).

thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(936,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)],[169]) ).

thf(525,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/sandbox2/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).

thf(1707,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)],[525]) ).

thf(321,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/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).

thf(1271,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)],[321]) ).

thf(103,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(787,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)],[103]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1464,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)],[413]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I19_J_0) ).

thf(1356,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)],[361]) ).

thf(56,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(672,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1635,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)],[491]) ).

thf(537,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/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1733,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)],[537]) ).

thf(163,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(919,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)],[163]) ).

thf(111,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/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

thf(804,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)],[111]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinduct_3) ).

thf(1258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_a @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__2 ) @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__1 ) @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(70,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/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(704,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)],[70]) ).

thf(493,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).

thf(1638,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)],[493]) ).

thf(302,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/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).

thf(1224,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)],[302]) ).

thf(27,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/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).

thf(604,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)],[27]) ).

thf(287,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/sandbox2/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).

thf(1194,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)],[287]) ).

thf(155,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Oinject_0) ).

thf(900,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(124,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(326,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Agent__synth_0) ).

thf(1282,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)],[326]) ).

thf(251,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/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_0) ).

thf(1117,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)],[251]) ).

thf(83,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(737,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(32,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).

thf(616,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)],[32]) ).

thf(138,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(863,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)],[138]) ).

thf(61,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(681,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)],[61]) ).

thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).

thf(1408,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)],[387]) ).

thf(470,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 @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing_0) ).

thf(1589,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 @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(194,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/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).

thf(996,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)],[194]) ).

thf(532,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/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).

thf(1722,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)],[532]) ).

thf(264,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/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(1144,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)],[264]) ).

thf(145,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__increasing_0) ).

thf(880,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)],[145]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(649,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(462,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).

thf(1571,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)],[462]) ).

thf(370,axiom,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).

thf(1376,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(402,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/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(1439,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)],[402]) ).

thf(507,axiom,
    ( ( c_Message_Oagent_OSpy @ c_Event_OinitState )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__Spy_0) ).

thf(1667,plain,
    ( ( c_Message_Oagent_OSpy @ c_Event_OinitState )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_OshrK @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

thf(811,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)],[114]) ).

thf(117,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/sandbox2/benchmark/theBenchmark.p',cls_synth__insert_0) ).

thf(816,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)],[117]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(609,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(489,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I37_J_0) ).

thf(1630,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)],[489]) ).

thf(536,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).

thf(1731,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)],[536]) ).

thf(79,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/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(726,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)],[79]) ).

thf(33,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/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

thf(621,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)],[33]) ).

thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).

thf(1325,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)],[346]) ).

thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_pushes_I2_J_0) ).

thf(1112,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)],[249]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != ( C @ c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

thf(758,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)],[90]) ).

thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).

thf(1339,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)],[353]) ).

thf(211,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(1029,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)],[211]) ).

thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(895,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)],[153]) ).

thf(35,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/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(626,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)],[35]) ).

thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(915,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)],[161]) ).

thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).

thf(1556,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)],[455]) ).

thf(411,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/sandbox2/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).

thf(1460,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)],[411]) ).

thf(332,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).

thf(1293,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)],[332]) ).

thf(54,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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(668,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)],[54]) ).

thf(278,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/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1177,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)],[278]) ).

thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_Oops__parts__spies_0) ).

thf(1381,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)],[373]) ).

thf(159,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).

thf(912,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)],[159]) ).

thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_OFake_0) ).

thf(1474,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)],[418]) ).

thf(472,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/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).

thf(1594,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)],[472]) ).

thf(311,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS4_0) ).

thf(1245,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)],[311]) ).

thf(495,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).

thf(1643,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)],[495]) ).

thf(204,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/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).

thf(1015,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)],[204]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(563,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)],[9]) ).

thf(400,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/sandbox2/benchmark/theBenchmark.p',cls_analz_OInj_0) ).

thf(1435,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)],[400]) ).

thf(428,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/sandbox2/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).

thf(1496,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)],[428]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(653,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(519,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 @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).

thf(1694,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 @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).

thf(658,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)],[49]) ).

thf(289,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/sandbox2/benchmark/theBenchmark.p',cls_Key__image__eq_1) ).

thf(1198,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)],[289]) ).

thf(381,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( ( A @ ( c_Message_OinvKey @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__K_0) ).

thf(1396,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) @ hBOOL )
      | ( ( A @ ( c_Message_OinvKey @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(296,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_OHash @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__notin__image__Key_0) ).

thf(1213,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_OHash @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Message_Osynthp ) )
      | ( B @ c_Message_Omsg_OHash @ ( A @ c_Message_Osynthp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthp_OHash_0) ).

thf(768,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Message_Osynthp ) )
      | ( B @ c_Message_Omsg_OHash @ ( A @ c_Message_Osynthp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(827,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)],[122]) ).

thf(140,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(868,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(405,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/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).

thf(1445,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)],[405]) ).

thf(442,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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(1528,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)],[442]) ).

thf(534,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__parts_0) ).

thf(1726,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(365,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/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_1) ).

thf(1364,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)],[365]) ).

thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert_0) ).

thf(851,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)],[133]) ).

thf(244,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).

thf(1102,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)],[244]) ).

thf(389,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS2_0) ).

thf(1413,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)],[389]) ).

thf(214,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/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_0) ).

thf(1034,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)],[214]) ).

thf(337,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/sandbox2/benchmark/theBenchmark.p',cls_parts_OBody_0) ).

thf(1304,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)],[337]) ).

thf(274,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).

thf(1166,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)],[274]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(1203,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(172,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/sandbox2/benchmark/theBenchmark.p',cls_Nonce__notin__initState_0) ).

thf(944,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)],[172]) ).

thf(415,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/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(1467,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)],[415]) ).

thf(106,axiom,
    tc_bool @ class_Orderings_Otop,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(795,plain,
    tc_bool @ class_Orderings_Otop,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Event_Oused @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__parts__subset__parts_0) ).

thf(1134,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Event_Oused @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(434,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(1509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_parts__trans_0) ).

thf(1081,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)],[236]) ).

thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).

thf(1472,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)],[417]) ).

thf(5,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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(553,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)],[5]) ).

thf(181,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).

thf(968,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)],[181]) ).

thf(221,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I10_J_0) ).

thf(1049,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( B @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(58,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(675,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OHash @ 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_OHash @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I4_J_0) ).

thf(1583,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Message_Omsg_OHash @ 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_OHash @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_analz__cong_0) ).

thf(663,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)],[52]) ).

thf(2,negated_conjecture,
    tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_evs @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(548,plain,
    tc_Event_Oevent @ tc_List_Olist @ ( c_NS__Shared__Mirabelle_Ons__shared @ ( v_evs @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).

thf(712,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)],[74]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I5_J_0) ).

thf(855,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(474,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/sandbox2/benchmark/theBenchmark.p',cls_parts_OFst_0) ).

thf(1598,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)],[474]) ).

thf(209,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__2 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinduct_1) ).

thf(1025,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( A @ ( C @ v_sko__List__Xlists__Xinduct__2 ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_parts_OInj_0) ).

thf(1070,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)],[230]) ).

thf(460,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_2) ).

thf(1566,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)],[460]) ).

thf(477,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1605,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(422,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).

thf(1484,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(242,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/sandbox2/benchmark/theBenchmark.p',cls_Nonce__synth_0) ).

thf(1098,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)],[242]) ).

thf(192,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/sandbox2/benchmark/theBenchmark.p',cls_spies__pubK_0) ).

thf(993,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)],[192]) ).

thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1547,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)],[451]) ).

thf(543,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).

thf(1748,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)],[543]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(673,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(399,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/sandbox2/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).

thf(1432,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)],[399]) ).

thf(513,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).

thf(1679,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)],[513]) ).

thf(257,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/sandbox2/benchmark/theBenchmark.p',cls_Nonce__notin__used__empty_0) ).

thf(1130,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)],[257]) ).

thf(352,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/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).

thf(1336,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)],[352]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1220,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(527,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 @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth__analz_0) ).

thf(1711,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 @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_used__Gets_0) ).

thf(1053,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)],[223]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Hash__synth_0) ).

thf(1300,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) @ hBOOL )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(492,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__increasing_0) ).

thf(1637,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)],[492]) ).

thf(284,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/sandbox2/benchmark/theBenchmark.p',cls_synth_OInj_0) ).

thf(1188,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)],[284]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_lemma2_0) ).

thf(1186,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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)],[283]) ).

thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_shrK__notin__image__publicKey_0) ).

thf(1038,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)],[216]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_List_Olist_ONil )
     != ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).

thf(585,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)],[19]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I16_J_0) ).

thf(1085,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)],[238]) ).

thf(15,axiom,
    ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Message_Oanalz )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__empty_0) ).

thf(576,plain,
    ( ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Message_Oanalz )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(328,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONS1_0) ).

thf(1285,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)],[328]) ).

thf(299,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/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1218,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)],[299]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Message_Osynthp ) )
      | ~ ( C @ ( A @ c_Message_Osynthp ) )
      | ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Osynthp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthp_OMPair_0) ).

thf(1543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Message_Osynthp ) )
      | ~ ( C @ ( A @ c_Message_Osynthp ) )
      | ( C @ ( B @ c_Message_Omsg_OMPair ) @ ( A @ c_Message_Osynthp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(600,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(222,axiom,
    ! [B: $i,A: $i] : ( B @ c_Message_Omsg_OAgent @ ( A @ c_Message_Osynthp ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthp_OAgent_0) ).

thf(1052,plain,
    ! [B: $i,A: $i] : ( B @ c_Message_Omsg_OAgent @ ( A @ c_Message_Osynthp ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(30,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/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(612,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)],[30]) ).

thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_parts__cut_0) ).

thf(991,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)],[191]) ).

thf(48,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/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(656,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)],[48]) ).

thf(208,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).

thf(1023,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)],[208]) ).

thf(468,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/sandbox2/benchmark/theBenchmark.p',cls_Key__synth_0) ).

thf(1585,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)],[468]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey @ hAPP ) )
     != ( C @ ( c_Public_OshrK @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).

thf(1140,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)],[262]) ).

thf(368,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/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).

thf(1372,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)],[368]) ).

thf(23,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
      = ( A @ c_Message_Oanalz ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).

thf(845,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
      = ( A @ c_Message_Oanalz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(393,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/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_1) ).

thf(1421,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)],[393]) ).

thf(342,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1316,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)],[342]) ).

thf(280,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/sandbox2/benchmark/theBenchmark.p',cls_parts__image__Key_0) ).

thf(1180,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)],[280]) ).

thf(6,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/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(556,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)],[6]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__image__eq_1) ).

thf(1157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(581,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)],[17]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1654,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)],[501]) ).

thf(438,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert_0) ).

thf(1517,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
      = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(298,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/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(1216,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)],[298]) ).

thf(247,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/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__Key_0) ).

thf(1108,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)],[247]) ).

thf(167,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).

thf(931,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)],[167]) ).

thf(515,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS4_0) ).

thf(1685,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)],[515]) ).

thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).

thf(1010,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)],[202]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(330,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I30_J_0) ).

thf(1289,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I39_J_0) ).

thf(1453,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( B @ ( c_Message_Omsg_OKey @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(323,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1276,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(179,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/sandbox2/benchmark/theBenchmark.p',cls_keysFor__insert__MPair_0) ).

thf(963,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)],[179]) ).

thf(419,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I1_J_0) ).

thf(1476,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)],[419]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1341,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).

thf(1062,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)],[227]) ).

thf(420,axiom,
    ! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).

thf(1481,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)],[420]) ).

thf(173,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS3_0) ).

thf(946,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)],[173]) ).

thf(542,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).

thf(1745,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)],[542]) ).

thf(81,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/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(731,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)],[81]) ).

thf(100,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/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

thf(781,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)],[100]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I18_J_0) ).

thf(1558,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)],[456]) ).

thf(20,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/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(588,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)],[20]) ).

thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).

thf(1253,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)],[315]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(699,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(813,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)],[115]) ).

thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).

thf(1385,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)],[375]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Message_Osynthp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthp_OInj_0) ).

thf(1030,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Message_Osynthp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(517,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I11_J_0) ).

thf(1689,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( B @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).

thf(929,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)],[166]) ).

thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_publicKey__image__eq_0) ).

thf(1308,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)],[339]) ).

thf(234,axiom,
    tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).

thf(1077,plain,
    tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(295,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/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).

thf(1212,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)],[295]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(436,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Message_Osynthp ) )
      | ~ ( B @ ( c_Message_Omsg_OKey @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Osynthp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthp_OCrypt_0) ).

thf(1513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Message_Osynthp ) )
      | ~ ( B @ ( c_Message_Omsg_OKey @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( B @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Osynthp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(504,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/sandbox2/benchmark/theBenchmark.p',cls_Spy__analz__shrK_0) ).

thf(1661,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)],[504]) ).

thf(62,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).

thf(684,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)],[62]) ).

thf(3,negated_conjecture,
    tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ ( 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 ) @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(549,plain,
    tc_Message_Omsg @ ( v_evs @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_X @ ( 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 ) @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Nonce_0) ).

thf(1045,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)],[219]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I3_J_0) ).

thf(716,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)],[76]) ).

thf(271,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OOops_0) ).

thf(1161,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)],[271]) ).

thf(482,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).

thf(1614,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)],[482]) ).

thf(357,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/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).

thf(1348,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)],[357]) ).

thf(196,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Hash_0) ).

thf(999,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(464,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/sandbox2/benchmark/theBenchmark.p',cls_ns__shared_ONS5_0) ).

thf(1578,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)],[464]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_lemma1_0) ).

thf(1229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ ( c_Message_OinvKey @ hAPP ) @ ( 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)],[304]) ).

thf(486,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1625,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)],[486]) ).

thf(313,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/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1248,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)],[313]) ).

thf(546,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1757,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)],[546]) ).

thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(865,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)],[139]) ).

thf(266,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/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).

thf(1148,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)],[266]) ).

thf(510,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).

thf(1673,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)],[510]) ).

thf(109,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(801,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(364,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/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).

thf(1363,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)],[364]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(807,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).

thf(1335,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)],[351]) ).

thf(457,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/sandbox2/benchmark/theBenchmark.p',cls_analz__cut_0) ).

thf(1561,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)],[457]) ).

thf(228,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).

thf(1065,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)],[228]) ).

thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(696,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)],[67]) ).

thf(273,axiom,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).

thf(1165,plain,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I3_J_0) ).

thf(955,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(107,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).

thf(796,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)],[107]) ).

thf(276,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/sandbox2/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).

thf(1172,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)],[276]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_1) ).

thf(1410,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)],[388]) ).

thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

thf(960,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)],[178]) ).

thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(635,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)],[38]) ).

thf(356,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/sandbox2/benchmark/theBenchmark.p',cls_Nonce__supply1_0) ).

thf(1346,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)],[356]) ).

thf(480,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/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).

thf(1610,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)],[480]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(541,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__lemma_5) ).

thf(1742,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)],[541]) ).

thf(34,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/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

thf(624,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)],[34]) ).

thf(359,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/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).

thf(1352,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)],[359]) ).

thf(446,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__image__eq_0) ).

thf(1537,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( c_Message_OinvKey @ c_Set_Oimage ) ) ) @ ( A @ ( c_Message_OinvKey @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( tc_nat @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(371,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/sandbox2/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).

thf(1378,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)],[371]) ).

thf(206,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/sandbox2/benchmark/theBenchmark.p',cls_synth__cut_0) ).

thf(1019,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)],[206]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).

thf(644,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)],[42]) ).

thf(157,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/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(908,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)],[157]) ).

thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(822,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)],[121]) ).

thf(528,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/sandbox2/benchmark/theBenchmark.p',cls_pushes_I8_J_0) ).

thf(1713,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)],[528]) ).

thf(64,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/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(691,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)],[64]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( B @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I33_J_0) ).

thf(871,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( B @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(307,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/sandbox2/benchmark/theBenchmark.p',cls_pushes_I9_J_0) ).

thf(1236,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)],[307]) ).

thf(189,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/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).

thf(987,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)],[189]) ).

thf(444,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I31_J_0) ).

thf(1532,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Message_Omsg_OKey @ hAPP ) )
     != ( B @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(136,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(860,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)],[136]) ).

thf(187,axiom,
    ( ( c_Message_Oagent_OServer @ c_Event_OinitState )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( 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_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Message_Oagent_OServer @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( c_Message_Oagent_OServer @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__Server_0) ).

thf(982,plain,
    ( ( c_Message_Oagent_OServer @ c_Event_OinitState )
    = ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( 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_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_nat @ ( tc_nat @ ( tc_Message_Oagent @ ( tc_bool @ ( tc_Message_Oagent @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ c_Set_Oimage ) ) ) @ ( c_Message_Omsg_OKey @ c_Set_Oimage ) ) ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( c_Message_Oagent_OServer @ ( c_Public_Okeymode_OSignature @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ ( c_Message_Oagent_OServer @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey @ hAPP ) @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__image__Key_0) ).

thf(1004,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)],[199]) ).

thf(432,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/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).

thf(1505,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)],[432]) ).

thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_analz__image__Key_0) ).

thf(1399,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)],[382]) ).

thf(484,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/sandbox2/benchmark/theBenchmark.p',cls_parts__partsD_0) ).

thf(1621,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)],[484]) ).

thf(344,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I35_J_0) ).

thf(1320,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)],[344]) ).

thf(201,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/sandbox2/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).

thf(1009,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)],[201]) ).

thf(539,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/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Agent_0) ).

thf(1737,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)],[539]) ).

thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).

thf(1184,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)],[282]) ).

thf(40,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(639,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)],[40]) ).

thf(59,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/sandbox2/benchmark/theBenchmark.p',cls_analz__synth_0) ).

thf(676,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)],[59]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).

thf(1088,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)],[239]) ).

thf(72,axiom,
    tc_nat @ class_Orderings_Obot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(708,plain,
    tc_nat @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(882,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)],[147]) ).

thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_synth__synthD_0) ).

thf(1331,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)],[349]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Oanalzp ) )
      | ~ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ ( A @ c_Message_Oanalzp ) )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analzp_ODecrypt_0) ).

thf(1606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Message_Omsg_OCrypt ) @ ( A @ c_Message_Oanalzp ) )
      | ~ ( C @ ( c_Message_OinvKey @ hAPP ) @ ( c_Message_Omsg_OKey @ hAPP ) @ ( A @ c_Message_Oanalzp ) )
      | ( B @ ( A @ c_Message_Oanalzp ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(425,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( B @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty2_0) ).

thf(1490,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_List_Olist_ONil ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( B @ c_List_Oset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(97,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/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).

thf(775,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)],[97]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(560,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)],[8]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlists__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists_Oinducts_2) ).

thf(1417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ tc_List_Olist @ ( t_a @ ( C @ c_List_Olists ) @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
      | ( A @ ( C @ v_sko__List__Xlists__Xinducts__2 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(972,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)],[183]) ).

thf(2845,plain,
    $false,
    inference(e,[status(thm)],[892,1036,1501,1718,1633,1105,628,1083,941,1179,777,666,1549,1369,1190,1554,1110,1200,977,1596,1068,1522,1443,994,1401,1728,1205,1591,1269,597,1437,861,741,1073,878,655,614,1692,1705,1671,1608,1655,550,1735,1327,1260,913,1640,1354,1458,670,1078,1426,1507,1222,829,1196,1001,1243,1576,709,841,1359,1724,1703,651,782,1441,1650,1645,565,1366,1623,1482,1628,1287,1709,570,1298,785,802,1313,934,949,1055,724,1323,838,1511,917,1462,1059,1132,1545,817,559,1379,1247,606,770,881,1568,1494,1100,1465,1302,789,1450,1040,646,1383,1677,1581,1283,905,1489,1415,1682,1136,834,602,1169,1215,734,1072,1119,1394,660,1405,1600,849,1696,1564,1074,678,1306,810,1470,1311,714,1153,761,1047,798,1057,1163,894,1091,1343,1519,1580,1123,1666,1487,1619,815,729,1238,1387,910,1021,778,1042,952,1174,1676,1751,820,693,630,1423,852,1296,1687,583,889,1159,1210,1027,1407,1128,1281,1392,1012,847,566,1032,1602,1350,1121,1425,1096,1006,1138,593,989,742,578,1234,1541,874,1143,980,1498,1587,1493,1361,1292,753,1182,1739,642,637,1644,706,1419,884,1329,1016,1207,590,1612,970,1155,547,837,1114,701,1451,1552,1192,984,721,1002,1715,1720,1263,997,1530,1539,1456,1266,1231,569,1429,1627,1525,1333,1318,792,938,1241,921,1563,765,1663,1515,662,926,1278,1648,1251,1273,745,573,689,1374,965,750,1146,1754,1698,1103,819,975,694,1389,772,1652,875,1535,1701,1226,843,1125,958,1403,1428,1503,1669,936,1707,1271,787,1464,1356,672,1635,1733,919,804,1258,704,1638,1224,604,1194,900,831,1282,1117,737,616,863,681,1408,1589,996,1722,1144,880,649,1571,1376,1439,1667,811,816,609,1630,1731,726,621,1325,1112,758,1339,1029,895,626,915,1556,1460,1293,668,1177,1381,912,1474,1594,1245,1643,1015,563,1435,1496,653,1694,658,1198,1396,1213,768,827,868,1445,1528,1726,1364,851,1102,1413,1034,1304,1166,1203,944,1467,795,1134,1509,1081,1472,553,968,1049,675,1583,663,548,712,855,1598,1025,1070,1566,1605,739,1484,1098,993,1547,1748,673,1432,1679,1130,1336,1220,1711,1053,1300,1637,1188,1186,1038,585,1085,576,1658,1285,1218,1543,600,1052,612,991,656,1023,1585,1140,1372,595,845,1421,1316,1180,556,1157,581,1654,1517,1216,1108,931,1685,1010,1390,1289,1453,1276,963,1476,1341,1062,1481,946,1745,731,781,1558,588,1253,699,813,1385,1030,1689,929,1308,1077,1212,763,1513,1661,684,549,1045,716,1161,1614,1348,999,1578,1229,1625,1248,1757,865,1148,1673,801,1363,807,1335,1561,1065,696,1165,955,796,1172,897,1410,960,635,1346,1610,886,1742,624,1352,1537,1378,1019,644,908,822,1713,691,871,1236,987,1532,860,982,1004,1505,1399,1621,1320,1009,1737,1184,639,676,1088,708,882,1331,1606,1490,775,560,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV730-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39  % Computer : n016.cluster.edu
% 0.13/0.39  % Model    : x86_64 x86_64
% 0.13/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39  % Memory   : 8046.5625MB
% 0.13/0.39  % OS       : Linux 6.8.0-71-generic
% 0.13/0.40  % CPULimit : 300
% 0.13/0.40  % WCLimit  : 300
% 0.13/0.40  % DateTime : Sat Sep 26 14:56:30 UTC 2026
% 0.13/0.40  % CPUTime  : 
% 0.13/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.83/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.83/1.33  % [INFO] 	 Parsing done (342ms). 
% 1.83/1.34  % [INFO] 	 Running in sequential loop mode. 
% 3.05/1.73  % [INFO] 	 eprover registered as external prover. 
% 3.05/1.73  % [INFO] 	 Scanning for conjecture ... 
% 3.59/1.95  % [INFO] 	 Found a conjecture (or negated_conjecture) and 557 axioms. Running axiom selection ... 
% 4.62/2.19  % [INFO] 	 Axiom selection finished. Selected 542 axioms (removed 15 axioms). 
% 5.61/2.42  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.61/2.44  % [INFO] 	 Type checking passed. 
% 5.61/2.44  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 28.22/6.85  % External prover 'e' found a proof!
% 28.22/6.85  % [INFO] 	 Killing All external provers ... 
% 28.22/6.85  % Time passed: 6311ms (effective reasoning time: 5504ms)
% 28.22/6.86  % Axioms used in derivation (542): clsarity_nat__HOL_Oord, cls_Key__image__eq_0, cls_Crypt__notin__initState_0, cls_synth_OHash_0, cls_shrK__in__initState_0, cls_subset__insert_1, cls_bot__fun__eq_0, cls_analz__image__freshK__lemma_5, cls_not__parts__not__analz_0, cls_top__fun__eq_0, cls_set__subset__Cons_0, cls_parts_OBody_0, cls_msg_Osimps_I47_J_0, cls_MPair__synth__analz_0, cls_symKeys__invKey__iff_0, cls_sup__ge1_0, cls_privateKey__image__eq_1, cls_Un__subset__iff_0, cls_parts__partsD_0, cls_MPair__used_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_knows__Notes_0, cls_subset__image__iff_2, cls_set__ConsD_0, cls_synth__analz__mono_0, cls_set__empty2_1, cls_initState__subset__knows_0, cls_used__Says_0, cls_empty__is__image_1, cls_image__mono_0, cls_Un__empty__left_0, cls_agent_Oinject_0, cls_le__funD_0, cls_subset__empty_1, cls_pushes_I9_J_0, cls_sup__bot__right_0, cls_insert__code_1, cls_list_Oinject_0, cls_analz__subset__iff_1, cls_Says__imp__used_0, cls_knows__Says_0, cls_analz__image__freshK__simps_I56_J_0, cls_Agent__synth_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_lists_Oinducts_0, cls_Un__commute_0, cls_ns__sharedp_ONS3_0, cls_analz__cong_0, cls_agent_Osimps_I6_J_0, cls_UnCI_1, cls_set__empty_1, cls_parts__image__Key_0, cls_initState__Friend_0, cls_insert__absorb_0, cls_lists_Ocases_2, cls_analz__subset__parts_0, cls_used__Notes_0, cls_ns__sharedp_ONS4_0, cls_msg_Osimps_I34_J_0, cls_mem__def_1, cls_msg_Osimps_I49_J_0, clsarity_nat__Orderings_Olinorder, cls_msg_Osimps_I6_J_1, cls_Says__imp__parts__knows__Spy_0, cls_empty__iff_0, cls_not__Cons__self2_0, cls_Fake__parts__insert_0, cls_ns__shared_OOops_0, cls_synthp_OMPair_0, cls_msg_Osimps_I45_J_0, cls_msg_Osimps_I12_J_0, cls_insert__iff_1, cls_Crypt__synth__eq_1, cls_Crypt__synth__analz_0, cls_knows__subset__knows__Says_0, clsarity_fun__Lattices_Oupper__semilattice, cls_Nonce__supply1_0, cls_Gets__imp__knows__agents_0, cls_le__sup__iff_0, cls_set__rev__mp_0, cls_knows__subset__knows__Cons_0, cls_analz__idem_0, cls_insert__subset_0, cls_lists_Oinduct_2, cls_msg_Osimps_I3_J_0, cls_ns__sharedp_ONS2_0, cls_analz__image__freshK__lemma_4, cls_subset__insert__iff_2, cls_publicKey__into__used_0, cls_Key__synth__eq_1, cls_parts__empty_0, cls_NS3__msg__in__parts__spies_0, cls_shrK__in__knows_0, cls_shrK__image__eq_1, cls_agent_Osimps_I5_J_0, cls_analz__image__freshK__lemma_2, cls_lists_ONil_0, cls_ns__sharedp_OOops_0, cls_analz__image__freshK__simps_I61_J_0, clsarity_fun__Orderings_Otop, cls_ns__sharedp_OFake_0, cls_initState__Spy_0, cls_synth__insert_0, cls_Un__left__commute_0, cls_Key__image__eq_1, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_privateKey__image__eq_2, cls_keysFor__insert__Hash_0, cls_synth_OCrypt_0, cls_knows__Nil_0, cls_analz__insert__Hash_0, cls_Says__imp__spies_0, cls_parts__increasing_0, cls_Server__not__bad_0, cls_analz__image__freshK__simps_I65_J_0, cls_analz__Crypt__if_1, cls_pushes_I11_J_0, cls_invKey__image__eq_1, cls_le__supI_0, cls_Un__subset__iff_1, cls_Un__empty_2, cls_le__iff__sup_1, cls_knows__Spy__Notes_1, cls_Hash__notin__image__Key_0, cls_msg_Osimps_I7_J_0, cls_rangeI_0, cls_parts__subset__iff_1, cls_initState__Server_0, cls_rev__image__eqI_0, cls_privateKey__notin__image__publicKey_0, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_ns__shared_ONS4_0, cls_empty__is__image_0, cls_synth__synthD_0, cls_shrK__notin__image__publicKey_0, cls_analz__cut_0, cls_in__parts__UnE_0, cls_keymode_Oinduct_0, cls_le__iff__sup_0, cls_publicKey__inject_0, cls_Fake__parts__sing__imp__Un_0, cls_synth_OMPair_0, cls_Un__UNIV__right_0, cls_Un__absorb2_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_lemma1_0, cls_Key__not__used_0, cls_parts__mono_0, cls_parts__emptyE_0, cls_used__nil__subset_0, cls_parts__insert__MPair_0, cls_symKeys__invKey__iff_1, cls_pushes_I4_J_0, cls_sup__eq__bot__eq2_0, cls_Un__upper2_0, cls_msg_Osimps_I44_J_0, cls_analz__subset__iff_0, cls_analz__empty_0, cls_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_msg_Osimps_I40_J_0, cls_subset__iff_0, cls_insert__code_2, cls_msg_Osimps_I38_J_0, cls_parts__Un_0, cls_parts_OSnd_0, clsarity_fun__HOL_Oord, cls_pushes_I5_J_0, cls_analz__mono__contra_I3_J_0, cls_event_Osimps_I9_J_0, cls_Spy__spies__bad__privateKey_0, cls_ns__shared_ONil_0, cls_privateKey__notin__image__shrK_0, cls_singleton__iff_1, cls_lists_Oinducts_3, cls_Spy__spies__bad__shrK_0, cls_symKey__neq__priEK_0, cls_event_Osimps_I6_J_0, cls_subset__empty_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_pushes_I8_J_0, cls_parts__insert_0, cls_msg_Osimps_I14_J_0, cls_synth__analz__insert__eq_0, cls_analz__conj__parts_0, cls_in__lists__conv__set_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_ns__shared_ONS1_0, cls_lists_Ocases_1, cls_doubleton__eq__iff_2, cls_set__empty2_0, cls_Spy__analz__shrK_1, cls_image__insert_0, cls_shrK__in__used_0, cls_event_Osimps_I3_J_0, cls_UNIV__not__empty_0, cls_keysFor__insert__MPair_0, cls_Nonce__notin__used__empty_0, cls_parts__insert__Agent_0, cls_synth__trans_0, cls_Un__insert__left_0, cls_Says__imp__analz__Spy_0, clsarity_nat__Orderings_Obot, cls_Fake__analz__insert_0, cls_sym__shrK_0, cls_msg_Osimps_I7_J_1, cls_Says__Server__message__form_2, cls_knows__Gets_0, cls_agent_Osimps_I4_J_0, cls_insert__subset_1, cls_Spy__see__shrK_0, cls_new__keys__not__used_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_analz_OFst_0, cls_set__eq__subset_2, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_analz_OInj_0, cls_Nonce__synth__eq_1, cls_parts__insertI_0, cls_msg_Osimps_I46_J_0, cls_shrK__neq__priK_0, cls_synth__increasing_0, cls_ns__sharedp_ONil_0, cls_Un__subset__iff_2, cls_msg_Osimps_I19_J_0, clsarity_fun__Lattices_Olattice, cls_analzp_OFst_0, cls_msg_Osimps_I1_J_0, cls_publicKey__notin__image__privateKey_0, cls_privateKey__neq__publicKey_0, cls_linorder__linear_0, cls_Un__empty_0, cls_msg_Osimps_I4_J_0, cls_analz__parts_0, cls_ns__sharedp__ns__shared__eq_0, cls_pushes_I12_J_0, cls_image__empty_0, cls_lists_Oinduct_1, cls_subset__trans_0, cls_agent_Osimps_I3_J_0, cls_analz__image__freshK__lemma_3, cls_insert__is__Un_0, cls_pushes_I2_J_0, cls_not__Cons__self_0, cls_insertI1_0, cls_msg_Osimps_I36_J_0, cls_analz__insert__Crypt__subset_0, cls_analzp_ODecrypt_0, cls_MPair__synth_1, cls_empty__not__insert_0, cls_sup__assoc_0, cls_msg_Osimps_I16_J_0, cls_analz__Crypt__if_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_le__supE_0, cls_analz__insert__cong_0, cls_msg_Osimps_I48_J_0, cls_msg_Osimps_I39_J_0, cls_parts__cut__eq_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_msg_Osimps_I35_J_0, cls_event_Osimps_I2_J_1, cls_ns__shared_OFake_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup1E_0, cls_synth__Un_0, cls_Un__UNIV__left_0, cls_parts__cut_0, cls_analz__image__freshK__simps_I57_J_0, cls_sup__least_0, cls_subset__refl_0, cls_analz__shrK__Decrypt_0, cls_analz__insert__Agent_0, cls_synth__subset__iff_1, cls_analz__Un_0, cls_analz_ODecrypt_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_sup__top__right_0, cls_shrK__notin__image__privateKey_0, cls_synthp_OAgent_0, cls_parts__subset__iff_0, cls_not__symKeys__priK_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_Crypt__synth__eq_0, cls_invKey__K_0, cls_Spy__in__bad_0, cls_singletonE_0, cls_parts__insert__knows__A_0, cls_Crypt__synth__analz_1, clsarity_nat__Lattices_Olattice, cls_msg_Osimps_I13_J_0, cls_image__iff_2, cls_lists_Oinducts_2, cls_msg_Osimps_I42_J_0, cls_spies__pubK_0, cls_analzp_OSnd_0, cls_analz__spies__pubK_0, cls_Fake__analz__eq_0, cls_parts__insert__Hash_0, cls_Notes__imp__used_0, cls_analz__mono__contra_I2_J_0, cls_priK__in__initState_0, cls_parts__insert2_0, cls_bex__empty_0, cls_top1I_0, cls_event_Osimps_I7_J_0, cls_bot1E_0, cls_synthp_OCrypt_0, cls_event_Osimps_I1_J_1, cls_lists_Ocases_0, cls_insert__mono_0, cls_analzp_OInj_0, cls_le__supI2_0, cls_synth__analz__insert__eq_1, cls_analz__image__freshK__lemma_0, cls_Un__assoc_0, cls_publicKey__neq__privateKey_0, cls_in__lists__conv__set_1, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_shrK__injective_0, cls_synth_OInj_0, cls_synth__idem_0, cls_msg_Osimps_I15_J_0, cls_publicKey__image__eq_2, cls_msg_Osimps_I18_J_0, cls_UnE_0, cls_subset__insertI2_0, cls_Un__absorb_0, cls_MPair__used_1, cls_parts__trans_0, cls_parts__analz_0, cls_event_Osimps_I2_J_0, cls_Crypt__notin__used__empty_0, cls_neq__shrK_0, cls_usedI_0, cls_parts__insert__Key_0, cls_analz__analzD_0, cls_invKey__eq_0, clsarity_bool__Lattices_Olattice, cls_keysFor__insert__Agent_0, cls_event_Osimps_I4_J_0, cls_Spy__see__shrK_1, cls_publicKey__image__eq_0, cls_pubK__neq__shrK_0, cls_MPair__synth__analz_2, cls_bot__empty__eq_0, cls_analz__insert__MPair_0, cls_msg_Osimps_I30_J_0, cls_list_Osimps_I3_J_0, clsarity_bool__Lattices_Obounded__lattice, cls_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_insert__not__empty_0, cls_keymode_Osimps_I2_J_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_Spy__analz__shrK_0, cls_subsetD_0, cls_Key__synth_0, cls_Hash__synth__analz_0, cls_keysFor__insert__Nonce_0, cls_analz__synth__Un_0, cls_sup__fun__eq_0, cls_pushes_I1_J_0, cls_Crypt__synth_0, cls_subset__singletonD_0, cls_Nonce__synth__eq_0, cls_event_Osimps_I8_J_0, cls_priEK__noteq__shrK_0, cls_insert__absorb2_0, cls_analz__mono_0, cls_analz_OSnd_0, cls_Crypt__imp__keysFor_0, cls_doubleton__eq__iff_1, cls_analz__mono__contra_I1_J_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_Nonce__synth_0, cls_analz__insert__eq_0, cls_parts__insert__Nonce_0, cls_synth__subset__iff_0, cls_Un__left__absorb_0, cls_msg_Osimps_I5_J_0, cls_keymode_Osimps_I1_J_0, cls_event_Osimps_I1_J_0, cls_Crypt__notin__image__Key_0, cls_agent_Osimps_I7_J_0, cls_analz__analz__Un_0, cls_Crypt__synth_1, cls_ns__shared_ONS3_0, cls_MPair__synth_0, cls_msg_Osimps_I17_J_0, cls_inf__sup__aci_I5_J_0, cls_singleton__inject_0, cls_privateKey__image__eq_0, cls_initState__into__used_0, cls_Hash__synth_0, cls_lists_Oinduct_0, cls_subset__insert_0, cls_sup__idem_0, cls_msg_Osimps_I41_J_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_msg_Osimps_I32_J_0, cls_knows__subset__knows__Notes_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_keysFor__parts__insert_0, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_msg_Osimps_I31_J_0, cls_analz__increasing_0, cls_Un__empty_1, cls_parts__Un__subset1_0, cls_lists_Oinducts_1, cls_Fake__parts__sing_0, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_analz__image__Key_0, cls_Un__least_0, cls_set__empty_0, cls_sup1CI_0, cls_Oops__parts__spies_0, cls_shrK__neq__pubK_0, cls_not__symKeys__pubK_0, cls_sup__ge2_0, cls_lists_Oinduct_3, cls_ns__shared_ONS2_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_ns__shared_ONS5_0, cls_parts__idem_0, cls_in__lists__conv__set_2, cls_lemma2_0, cls_ns__sharedp_ONS5_0, cls_image__eqI_0, cls_subset__UNIV_0, cls_analz__insertI_0, cls_image__subset__iff_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_knows__Spy__subset__knows__Spy__Says_0, cls_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_msg_Osimps_I6_J_0, cls_Nonce__notin__initState_0, cls_Says__imp__knows_0, cls_analz__subset__cong_0, cls_sup__bot__left_0, cls_insert__image_0, cls_shrK__image__eq_0, cls_Hash__synth__analz_1, cls_msg_Osimps_I10_J_0, cls_analz__Decrypt_H_0, cls_used__parts__subset__parts_0, cls_insert__commute_0, cls_insert__iff_2, cls_keysFor__insert__Key_0, cls_gen__analz__insert__eq_0, cls_Fake__parts__insert__in__Un_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_list_Osimps_I2_J_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, cls_synthp_OInj_0, cls_knows__imp__Says__Gets__Notes__initState_0, cls_agent_Osimps_I2_J_0, cls_Nonce__Key__image__eq_0, cls_knows__Spy__Notes_0, cls_priK__neq__shrK_0, cls_parts__synth_0, cls_invKey__image__eq_0, cls_image__is__empty_0, cls_analz__image__freshK__lemma_1, cls_equalityE_0, cls_msg_Osimps_I37_J_0, cls_ns__sharedp_ONS1_0, cls_msg_Osimps_I33_J_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_ball__empty_0, cls_synth__mono_0, cls_synthp_OHash_0, cls_synth__cut_0, cls_analz__insert__Nonce_0, cls_synth_OAgent_0, cls_Notes__imp__knows_0, cls_msg_Osimps_I11_J_0, cls_subset__insert__iff_1, cls_Crypt__imp__invKey__keysFor_0, cls_pushes_I6_J_0, clsarity_bool__Orderings_Otop, cls_publicKey__in__initState_0, cls_publicKey__image__eq_1, cls_analz__into__parts_0, cls_predicate1D_0, cls_analz__insert_0, cls_parts__insert__spies_0
% 28.22/6.86  % No. of inferences in proof: 1093
% 28.22/6.86  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6311 ms resp. 5504 ms w/o parsing
% 29.95/7.10  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.95/7.12  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------