TSTP Solution File: SWV333-1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV333-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:15:11 EDT 2023

% Result   : Unsatisfiable 9.59s 3.12s
% Output   : Refutation 10.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  589
% Syntax   : Number of formulae    : 1070 ( 479 unt; 109 typ;   0 def)
%            Number of atoms       : 1573 ( 874 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 9350 ( 630   ~; 612   |;   0   &;8108   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  187 ( 187   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  111 ( 109 usr;  26 con; 0-4 aty)
%            Number of variables   : 2570 (   0   ^;2570   !;   0   ?;2570   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_in_type,type,
    c_in: $i > $i > $i > $o ).

thf(v_evs4_type,type,
    v_evs4: $i ).

thf(c_Yahalom_Oyahalom_type,type,
    c_Yahalom_Oyahalom: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_Xa_type,type,
    v_Xa: $i ).

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

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

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

thf(c_0_type,type,
    c_0: $i ).

thf(c_List_Odrop_type,type,
    c_List_Odrop: $i > $i > $i > $i ).

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

thf(c_Nat_Osize_type,type,
    c_Nat_Osize: $i > $i > $i ).

thf(c_less_type,type,
    c_less: $i > $i > $i > $o ).

thf(c_plus_type,type,
    c_plus: $i > $i > $i > $i ).

thf(c_List_Ohd_type,type,
    c_List_Ohd: $i > $i > $i ).

thf(c_List_Oreplicate_type,type,
    c_List_Oreplicate: $i > $i > $i > $i ).

thf(c_Wellfounded__Recursion_Owf_type,type,
    c_Wellfounded__Recursion_Owf: $i > $i > $o ).

thf(c_insert_type,type,
    c_insert: $i > $i > $i > $i ).

thf(c_Pair_type,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(tc_prod_type,type,
    tc_prod: $i > $i > $i ).

thf(c_List_Oupt_type,type,
    c_List_Oupt: $i > $i > $i ).

thf(c_List_Otake_type,type,
    c_List_Otake: $i > $i > $i > $i ).

thf(c_Divides_Oop_Amod_type,type,
    c_Divides_Oop_Amod: $i > $i > $i > $i ).

thf(c_Numeral_Onumber__of_type,type,
    c_Numeral_Onumber__of: $i > $i > $i ).

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

thf(c_List_Obutlast_type,type,
    c_List_Obutlast: $i > $i > $i ).

thf(c_List_Onth_type,type,
    c_List_Onth: $i > $i > $i > $i ).

thf(c_List_Olist__update_type,type,
    c_List_Olist__update: $i > $i > $i > $i > $i ).

thf(c_append_type,type,
    c_append: $i > $i > $i > $i ).

thf(c_List_Ozip_type,type,
    c_List_Ozip: $i > $i > $i > $i > $i ).

thf(c_List_Otl_type,type,
    c_List_Otl: $i > $i > $i ).

thf(c_List_Orev_type,type,
    c_List_Orev: $i > $i > $i ).

thf(c_List_Olast_type,type,
    c_List_Olast: $i > $i > $i ).

thf(c_Wellfounded__Relations_Oless__than_type,type,
    c_Wellfounded__Relations_Oless__than: $i ).

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

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

thf(c_union_type,type,
    c_union: $i > $i > $i > $i ).

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

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

thf(c_List_Oremove1_type,type,
    c_List_Oremove1: $i > $i > $i > $i ).

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

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

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

thf(v_sko__uhi_type,type,
    v_sko__uhi: $i > $i > $i ).

thf(c_emptyset_type,type,
    c_emptyset: $i ).

thf(c_List_Oconcat_type,type,
    c_List_Oconcat: $i > $i > $i ).

thf(c_Message_Omsg_ONumber_type,type,
    c_Message_Omsg_ONumber: $i > $i ).

thf(c_List_Orotate_type,type,
    c_List_Orotate: $i > $i > $i > $i ).

thf(c_List_Osublist_type,type,
    c_List_Osublist: $i > $i > $i > $i ).

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

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

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

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

thf(c_List_Orotate1_type,type,
    c_List_Orotate1: $i > $i > $i ).

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

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

thf(c_Main_ONil__eq__concat__conv__1_type,type,
    c_Main_ONil__eq__concat__conv__1: $i > $i > $i ).

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

thf(c_SetInterval_OatMost_type,type,
    c_SetInterval_OatMost: $i > $i > $i ).

thf(c_Datatype_Ooption_ONone_type,type,
    c_Datatype_Ooption_ONone: $i ).

thf(tc_Datatype_Ooption_type,type,
    tc_Datatype_Ooption: $i > $i ).

thf(c_List_Olexn_type,type,
    c_List_Olexn: $i > $i > $i > $i ).

thf(c_Yahalom_OKeyWithNonce_type,type,
    c_Yahalom_OKeyWithNonce: $i > $i > $i > $o ).

thf(c_Set_Ocontents_type,type,
    c_Set_Ocontents: $i > $i > $i ).

thf(c_List_Olistset_type,type,
    c_List_Olistset: $i > $i > $i ).

thf(c_Main_Oconcat__eq__Nil__conv__1_type,type,
    c_Main_Oconcat__eq__Nil__conv__1: $i > $i > $i ).

thf(c_Map_Omap__of_type,type,
    c_Map_Omap__of: $i > $i > $i > $i > $i ).

thf(v_sko__2VZ_type,type,
    v_sko__2VZ: $i > $i > $i > $i > $i ).

thf(v_sko__2Va_type,type,
    v_sko__2Va: $i > $i > $i > $i > $i ).

thf(v_sko__2Vb_type,type,
    v_sko__2Vb: $i > $i > $i > $i > $i ).

thf(c_Main_Oin__listsI__1_type,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $i ).

thf(class_Nat_Opower_type,type,
    class_Nat_Opower: $i > $o ).

thf(class_Wellfounded__Recursion_Owellorder_type,type,
    class_Wellfounded__Recursion_Owellorder: $i > $o ).

thf(c_Infinite__Set_Oatmost__one_type,type,
    c_Infinite__Set_Oatmost__one: $i > $i > $o ).

thf(class_Parity_Oeven__odd_type,type,
    class_Parity_Oeven__odd: $i > $o ).

thf(c_Relation_Otrans_type,type,
    c_Relation_Otrans: $i > $i > $o ).

thf(c_Main_Oall__not__in__conv__1_type,type,
    c_Main_Oall__not__in__conv__1: $i > $i > $i ).

thf(v_sko__wPE_type,type,
    v_sko__wPE: $i > $i > $i > $i ).

thf(v_sko__2ji_type,type,
    v_sko__2ji: $i > $i > $i > $i > $i ).

thf(v_sko__2jj_type,type,
    v_sko__2jj: $i > $i > $i > $i > $i ).

thf(c_List_Olenlex_type,type,
    c_List_Olenlex: $i > $i > $i ).

thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

thf(class_Divides_Odiv_type,type,
    class_Divides_Odiv: $i > $o ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).

thf(1411,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).

thf(1469,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSays__imp__knows__Spy_0) ).

thf(1190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_append @ A @ B @ C ) @ C )
      = ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_append @ A @ B @ C ) @ C )
      = ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).

thf(893,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_1) ).

thf(1315,plain,
    ! [A: $i] :
      ( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olist__update @ B @ A @ ( c_List_Onth @ B @ A @ C ) @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).

thf(962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olist__update @ B @ A @ ( c_List_Onth @ B @ A @ C ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Otake @ B @ C @ D ) @ A @ D )
        = ( c_List_Onth @ C @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).

thf(941,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Otake @ B @ C @ D ) @ A @ D )
        = ( c_List_Onth @ C @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Otl @ A @ B ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).

thf(777,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Otl @ A @ B ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
      = ( c_insert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).

thf(666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ ( c_insert @ A @ B @ C ) @ C )
      = ( c_insert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(448,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OCrypt__notin__used__empty_0) ).

thf(1549,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(5,negated_conjecture,
    c_in @ v_K @ c_Message_OsymKeys @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(481,plain,
    c_in @ v_K @ c_Message_OsymKeys @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(466,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).

thf(1586,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(427,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).

thf(1501,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriK__neq__shrK_0) ).

thf(809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(283,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_Map_Omap__of @ ( c_List_Ozip @ B @ D @ C @ E ) @ A @ C @ E )
       != c_Datatype_Ooption_ONone )
      | ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
       != ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).

thf(1168,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_Map_Omap__of @ ( c_List_Ozip @ B @ D @ C @ E ) @ A @ C @ E )
       != c_Datatype_Ooption_ONone )
      | ( ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) )
       != ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_OinitState @ A ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OkeysFor__parts__initState_0) ).

thf(760,plain,
    ! [A: $i] :
      ( ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_OinitState @ A ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(314,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( D = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_1) ).

thf(1237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( D = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ D )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_0) ).

thf(846,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ D )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_insert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).

thf(909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_insert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Otl @ ( c_append @ A @ B @ C ) @ C )
        = ( c_append @ ( c_List_Otl @ A @ C ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).

thf(628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Otl @ ( c_append @ A @ B @ C ) @ C )
        = ( c_append @ ( c_List_Otl @ A @ C ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ A ) @ B ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OCrypt__Spy__analz__bad_0) ).

thf(1211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ A ) @ B ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(91,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).

thf(683,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(108,axiom,
    ( ( c_Message_Oanalz @ c_emptyset )
    = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).

thf(730,plain,
    ( ( c_Message_Oanalz @ c_emptyset )
    = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OpublicKey @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).

thf(1068,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OpublicKey @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).

thf(994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).

thf(1401,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(468,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).

thf(1591,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).

thf(655,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
      = ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(62,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( c_List_Onth @ ( c_List_Olist__update @ C @ A @ D @ E ) @ B @ E )
        = ( c_List_Onth @ C @ B @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).

thf(614,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( c_List_Onth @ ( c_List_Olist__update @ C @ A @ D @ E ) @ B @ E )
        = ( c_List_Onth @ C @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
      | ~ ( c_in @ C @ A @ B )
      | ~ ( c_in @ D @ A @ B )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(1305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Infinite__Set_Oatmost__one @ A @ B )
      | ~ ( c_in @ C @ A @ B )
      | ~ ( c_in @ D @ A @ B )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(279,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_List_Oremdups @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).

thf(1158,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_List_Oremdups @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).

thf(582,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(120,axiom,
    c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).

thf(762,plain,
    c_Wellfounded__Recursion_Owf @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(425,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).

thf(1497,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(394,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3_0) ).

thf(1426,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(271,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ E @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Notes_0) ).

thf(1137,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ E @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Odrop @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_0) ).

thf(533,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Odrop @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Olast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
        = ( c_List_Olast @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).

thf(797,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Olast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
        = ( c_List_Olast @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ B @ A @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).

thf(814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ B @ A @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(325,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_Oconcat__eq__Nil__conv__1 @ A @ B ) @ ( c_List_Oset @ A @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) )
      | ( ( c_List_Oconcat @ A @ B )
        = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).

thf(1260,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_Oconcat__eq__Nil__conv__1 @ A @ B ) @ ( c_List_Oset @ A @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) )
      | ( ( c_List_Oconcat @ A @ B )
        = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).

thf(1063,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(364,axiom,
    ! [A: $i] : ( c_in @ ( c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).

thf(1354,plain,
    ! [A: $i] : ( c_in @ ( c_Public_OshrK @ A ) @ c_Message_OsymKeys @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(306,axiom,
    ! [A: $i] :
      ~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).

thf(1222,plain,
    ! [A: $i] :
      ~ ( c_in @ A @ ( c_Message_Oparts @ c_emptyset ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(407,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).

thf(1458,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(85,axiom,
    ~ ( c_less @ c_0 @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).

thf(670,plain,
    ~ ( c_less @ c_0 @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_0) ).

thf(829,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).

thf(782,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( C
        = ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).

thf(709,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( C
        = ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(205,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_append @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ c_List_Olist_ONil @ B ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).

thf(973,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_append @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ c_List_Olist_ONil @ B ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(477,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).

thf(1613,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orev @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(415,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_1) ).

thf(1475,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).

thf(565,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_Divides_Oop_Amod @ A @ B @ tc_nat )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(440,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_3) ).

thf(1529,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(327,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).

thf(1265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(317,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_1) ).

thf(1243,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ( c_List_Oconcat @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).

thf(1127,plain,
    ! [A: $i] :
      ( ( c_List_Oconcat @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_1) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(461,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(309,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ F @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ F )
      | ( E
        = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ ( v_sko__2VZ @ D @ A @ B @ E ) ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OMPair @ ( v_sko__2Va @ D @ A @ B @ E ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) ) @ ( v_sko__2Vb @ D @ A @ B @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_1) ).

thf(1228,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ F @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ F )
      | ( E
        = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ ( v_sko__2VZ @ D @ A @ B @ E ) ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OMPair @ ( v_sko__2Va @ D @ A @ B @ E ) @ ( c_Message_Omsg_ONonce @ B ) ) ) ) ) @ ( v_sko__2Vb @ D @ A @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(418,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).

thf(1482,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(322,axiom,
    class_Nat_Opower @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).

thf(1254,plain,
    class_Nat_Opower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).

thf(1055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_append @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).

thf(570,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_append @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(340,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
      | ( c_in @ D @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(1298,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ A @ C ) @ C )
      | ( c_in @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(14,axiom,
    c_lessequals @ c_0 @ c_0 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).

thf(504,plain,
    c_lessequals @ c_0 @ c_0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).

thf(1330,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_append @ D @ A @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__HPair_0) ).

thf(838,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__wPE @ B @ C @ A ) @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__Says_0) ).

thf(1511,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ ( v_sko__wPE @ B @ C @ A ) @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(409,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState_0) ).

thf(1462,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).

thf(542,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).

thf(1545,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ A @ c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).

thf(817,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ A @ c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).

thf(638,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate1 @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).

thf(1379,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate1 @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONumber @ A )
       != ( c_Message_Omsg_ONumber @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).

thf(1087,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONumber @ A )
       != ( c_Message_Omsg_ONumber @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).

thf(1247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
      | ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ B @ A ) ) @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).

thf(1319,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
      | ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ B @ A ) ) @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(475,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).

thf(1609,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).

thf(1115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_1) ).

thf(1568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).

thf(1100,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orotate1 @ A @ B )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).

thf(1232,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(382,axiom,
    class_Parity_Oeven__odd @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_47) ).

thf(1398,plain,
    class_Parity_Oeven__odd @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ c_emptyset @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).

thf(881,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ c_emptyset @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(4,negated_conjecture,
    ! [A: $i] :
      ( ( A != v_X )
      | ( v_B != v_Ba )
      | ( v_A != v_Aa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_11) ).

thf(492,plain,
    ! [A: $i] :
      ( ( A != v_X )
      | ( v_B != v_Ba )
      | ( v_A != v_Aa ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).

thf(1040,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ D @ B ) )
      | ( C = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( ( c_List_Otake @ B @ ( c_List_Oupt @ A @ C ) @ tc_nat )
        = ( c_List_Oupt @ A @ ( c_plus @ A @ B @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).

thf(623,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( ( c_List_Otake @ B @ ( c_List_Oupt @ A @ C ) @ tc_nat )
        = ( c_List_Oupt @ A @ ( c_plus @ A @ B @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).

thf(574,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ B @ C )
     != c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_insert @ A @ B @ C )
     != c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(334,axiom,
    ( ( c_Nat_Osize @ c_Message_Oagent_OSpy @ tc_Message_Oagent )
    = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).

thf(1283,plain,
    ( ( c_Nat_Osize @ c_Message_Oagent_OSpy @ tc_Message_Oagent )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(179,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_OinvKey @ A )
       != ( c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).

thf(905,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_OinvKey @ A )
       != ( c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(356,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_1) ).

thf(1334,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Odrop @ A @ C @ D ) @ B @ D )
        = ( c_List_Onth @ C @ ( c_plus @ A @ B @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).

thf(646,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Odrop @ A @ C @ D ) @ B @ D )
        = ( c_List_Onth @ C @ ( c_plus @ A @ B @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(9,negated_conjecture,
    ~ ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(485,plain,
    ~ ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).

thf(834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_insert @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(277,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ D @ A @ B )
       != ( c_append @ E @ C @ B ) )
      | ( D = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).

thf(1151,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ D @ A @ B )
       != ( c_append @ E @ C @ B ) )
      | ( D = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(191,axiom,
    ! [B: $i,A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_1) ).

thf(937,plain,
    ! [B: $i,A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_union @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Notes_0) ).

thf(1051,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_union @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_1) ).

thf(821,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OHash @ A )
       != ( c_Message_Omsg_OHash @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).

thf(687,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OHash @ A )
       != ( c_Message_Omsg_OHash @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(166,axiom,
    ! [A: $i] :
      ~ ( c_less @ A @ c_0 @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).

thf(877,plain,
    ! [A: $i] :
      ~ ( c_less @ A @ c_0 @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( c_insert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( c_insert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(380,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK_0) ).

thf(1394,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) @ c_Message_OsymKeys @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(439,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1_0) ).

thf(1526,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).

thf(660,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ A @ C @ tc_nat ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_1) ).

thf(998,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(385,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).

thf(1405,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(296,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).

thf(1201,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).

thf(1521,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).

thf(527,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
      | ( c_less @ c_0 @ B @ tc_nat )
      | ( c_less @ c_0 @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).

thf(1215,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).

thf(634,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(402,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ C )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ D @ E ) @ C @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Gets_1) ).

thf(1447,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ C )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ D @ E ) @ C @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_union @ ( c_Message_Oparts @ ( c_insert @ C @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Says_0) ).

thf(956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_union @ ( c_Message_Oparts @ ( c_insert @ C @ c_emptyset @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(316,axiom,
    ! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__initState_0) ).

thf(1242,plain,
    ! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5_0) ).

thf(849,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OHash @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(298,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( J = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys_2) ).

thf(1206,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( J = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_append @ A @ B @ C ) @ ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ tc_nat ) @ C )
      = ( c_List_Onth @ B @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).

thf(920,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_append @ A @ B @ C ) @ ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ tc_nat ) @ C )
      = ( c_List_Onth @ B @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).

thf(678,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).

thf(529,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OKey @ D ) ) ) ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OA__trusts__YM3_0) ).

thf(1438,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OKey @ D ) ) ) ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(186,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).

thf(925,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(357,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( I = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys_1) ).

thf(1338,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( I = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(345,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OAgent @ A )
       != ( c_Message_Omsg_OAgent @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).

thf(1311,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OAgent @ A )
       != ( c_Message_Omsg_OAgent @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ c_0 @ A @ tc_nat )
      | ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
        = ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).

thf(1074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ c_0 @ A @ tc_nat )
      | ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
        = ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
      = ( c_Public_OshrK @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__shrK_0) ).

thf(1604,plain,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
      = ( c_Public_OshrK @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Oupt @ A @ C ) @ B @ tc_nat )
        = ( c_plus @ A @ B @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).

thf(546,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Oupt @ A @ C ) @ B @ tc_nat )
        = ( c_plus @ A @ B @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(133,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).

thf(793,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ c_emptyset @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).

thf(1047,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ c_emptyset @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_in @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).

thf(1387,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( c_in @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_union @ A @ ( c_union @ B @ A @ C ) @ C )
      = ( c_union @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).

thf(825,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_union @ A @ ( c_union @ B @ A @ C ) @ C )
      = ( c_union @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(435,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OKey @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ ( v_sko__2ji @ C @ B @ D @ A ) ) @ ( c_Message_Omsg_ONonce @ ( v_sko__2jj @ C @ B @ D @ A ) ) ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OKey @ D ) ) ) ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OB__trusts__YM4__shrK_0) ).

thf(1519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OKey @ D ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ ( v_sko__2ji @ C @ B @ D @ A ) ) @ ( c_Message_Omsg_ONonce @ ( v_sko__2jj @ C @ B @ D @ A ) ) ) ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OKey @ D ) ) ) ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(323,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OCrypt @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0) ).

thf(1255,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OCrypt @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_List_Oset @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).

thf(862,plain,
    ! [B: $i,A: $i] :
      ( ( c_emptyset
       != ( c_List_Oset @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(56,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).

thf(598,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(428,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).

thf(1502,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(421,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( H = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys_0) ).

thf(1487,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( H = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(453,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).

thf(1560,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).

thf(746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orotate @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_ONumber @ A ) @ tc_Message_Omsg )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).

thf(1091,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_ONumber @ A ) @ tc_Message_Omsg )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(365,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4_0) ).

thf(1355,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(463,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).

thf(1580,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(458,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).

thf(1570,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).

thf(1174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).

thf(1619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(370,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_1) ).

thf(1370,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(392,axiom,
    c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).

thf(1423,plain,
    c_Relation_Otrans @ c_Wellfounded__Relations_Oless__than @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(6,negated_conjecture,
    c_in @ ( c_Event_Oevent_OGets @ v_Aa @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NA ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(484,plain,
    c_in @ ( c_Event_Oevent_OGets @ v_Aa @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Aa ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NA ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) ) @ v_X ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(472,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).

thf(1602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(167,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_OKey @ A ) @ tc_Message_Omsg )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).

thf(879,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_OKey @ A ) @ tc_Message_Omsg )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Osublist @ c_List_Olist_ONil @ A @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).

thf(852,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Osublist @ c_List_Olist_ONil @ A @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(287,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).

thf(1178,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Ohd @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).

thf(1296,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(22,axiom,
    ( ( c_plus @ c_0 @ c_0 @ tc_nat )
    = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).

thf(522,plain,
    ( ( c_plus @ c_0 @ c_0 @ tc_nat )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(172,axiom,
    ( ( c_Message_OkeysFor @ c_emptyset )
    = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).

thf(889,plain,
    ( ( c_Message_OkeysFor @ c_emptyset )
    = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).

thf(757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(386,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_1) ).

thf(1407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ tc_nat )
      | ( ( c_List_Odrop @ C @ A @ B )
        = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).

thf(551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ tc_nat )
      | ( ( c_List_Odrop @ C @ A @ B )
        = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ c_emptyset @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(1012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ c_emptyset @ B )
       != ( c_insert @ C @ c_emptyset @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).

thf(1079,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(227,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != B )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_0) ).

thf(1027,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != B )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Main_Oconcat__eq__Nil__conv__1 @ A @ B )
       != c_List_Olist_ONil )
      | ( ( c_List_Oconcat @ A @ B )
        = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Main_Oconcat__eq__Nil__conv__1 @ A @ B )
       != c_List_Olist_ONil )
      | ( ( c_List_Oconcat @ A @ B )
        = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).

thf(1270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ C @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).

thf(1328,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq_0) ).

thf(1111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ c_List_Olist_ONil @ A @ B @ C )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).

thf(980,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ c_List_Olist_ONil @ A @ B @ C )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ A @ c_List_Olist_ONil @ B @ C )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).

thf(1096,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ A @ c_List_Olist_ONil @ B @ C )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ c_List_Olist_ONil @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_1) ).

thf(1006,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_append @ c_List_Olist_ONil @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(163,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).

thf(869,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(262,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(1118,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ c_emptyset @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(212,axiom,
    ( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
    = ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).

thf(989,plain,
    ( ( c_SetInterval_OatMost @ c_0 @ tc_nat )
    = ( c_insert @ c_0 @ c_emptyset @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(367,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).

thf(1360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_2) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ D @ B @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).

thf(742,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ D @ B @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( c_List_Oupt @ A @ c_0 )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).

thf(578,plain,
    ! [A: $i] :
      ( ( c_List_Oupt @ A @ c_0 )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
      | ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
      | ( A
        = ( c_Message_OinvKey @ ( v_sko__uhi @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).

thf(697,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
      | ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
      | ( A
        = ( c_Message_OinvKey @ ( v_sko__uhi @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(312,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) ) @ tc_nat )
      | ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).

thf(1234,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) ) @ tc_nat )
      | ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(442,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).

thf(1534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_append @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(223,axiom,
    ! [A: $i] :
      ( ( c_List_Orev @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).

thf(1017,plain,
    ! [A: $i] :
      ( ( c_List_Orev @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(423,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4_0) ).

thf(1493,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(353,axiom,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).

thf(1329,plain,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(7,negated_conjecture,
    c_in @ ( c_Event_Oevent_OSays @ v_Aa @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_ONonce @ v_NA ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(488,plain,
    c_in @ ( c_Event_Oevent_OSays @ v_Aa @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_ONonce @ v_NA ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( c_plus @ c_0 @ A @ tc_nat )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).

thf(554,plain,
    ! [A: $i] :
      ( ( c_plus @ c_0 @ A @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).

thf(1424,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).

thf(642,plain,
    ! [B: $i,A: $i] :
      ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).

thf(1414,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_10) ).

thf(489,plain,
    ! [A: $i] :
      ~ ( c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ A @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_2) ).

thf(590,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(204,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).

thf(1419,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(337,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Public_OpublicKey @ A @ B ) @ c_Message_OsymKeys @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK_0) ).

thf(1292,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Public_OpublicKey @ A @ B ) @ c_Message_OsymKeys @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_append @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).

thf(933,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_append @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_plus @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(1324,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_Main_Oin__listsI__1 @ B @ A @ C ) @ ( c_List_Oset @ A @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_0) ).

thf(1263,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).

thf(515,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
      = ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(404,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_union @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(310,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_ONonce @ B ) ) ) ) ) @ F ) ) @ G @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_2) ).

thf(1231,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ C @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ D ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Omsg_OMPair @ E @ ( c_Message_Omsg_ONonce @ B ) ) ) ) ) @ F ) ) @ G @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).

thf(1131,plain,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( c_insert @ A @ c_emptyset @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).

thf(1192,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olast @ ( c_List_Odrop @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).

thf(1060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olast @ ( c_List_Odrop @ A @ B @ C ) @ C )
        = ( c_List_Olast @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).

thf(911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).

thf(1002,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
      | ( c_in @ A @ C @ D )
      | ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ( ( c_Message_Oparts @ ( c_insert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).

thf(1429,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ( ( c_Message_Oparts @ ( c_insert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).

thf(1525,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(467,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).

thf(1588,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_List_Olast @ A @ B ) @ ( c_List_Oset @ A @ B ) @ B )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(210,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).

thf(985,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
      = ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(444,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_insert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).

thf(1539,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_insert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_1) ).

thf(1456,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).

thf(508,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).

thf(657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( B = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).

thf(765,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_union @ A @ B @ C )
       != c_emptyset )
      | ( B = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olist__update @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ E @ C )
        = ( c_List_Olist__update @ B @ A @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).

thf(1035,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Olist__update @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ E @ C )
        = ( c_List_Olist__update @ B @ A @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(87,axiom,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).

thf(674,plain,
    ! [B: $i,A: $i] :
      ( ( c_union @ A @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_0) ).

thf(1515,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(171,axiom,
    ! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(888,plain,
    ! [B: $i,A: $i] : ( c_in @ c_List_Olist_ONil @ ( c_List_Olists @ A @ B ) @ ( tc_List_Olist @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).

thf(558,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ c_0 @ A @ tc_nat )
      | ( c_lessequals @ ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(245,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_1) ).

thf(1071,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oremdups @ A @ B )
       != A )
      | ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
        = ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Olast @ ( c_append @ B @ A @ C ) @ C )
        = ( c_List_Olast @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).

thf(773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Olast @ ( c_append @ B @ A @ C ) @ C )
        = ( c_List_Olast @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( c_List_Otl @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).

thf(586,plain,
    ! [A: $i] :
      ( ( c_List_Otl @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(332,axiom,
    ! [A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__notin__used__empty_0) ).

thf(1278,plain,
    ! [A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ c_List_Olist_ONil ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(270,axiom,
    ( ( c_Message_Oparts @ c_emptyset )
    = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).

thf(1135,plain,
    ( ( c_Message_Oparts @ c_emptyset )
    = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).

thf(965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_append @ A @ B @ C ) @ C )
      = ( c_union @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).

thf(1103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_append @ A @ B @ C ) @ C )
      = ( c_union @ ( c_List_Oset @ A @ C ) @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(419,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).

thf(1483,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_ONumber @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0) ).

thf(856,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_ONumber @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(470,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_in @ E @ ( c_List_Oset @ A @ B ) @ B )
      | ( ( c_Map_Omap__of @ ( c_List_Ozip @ A @ C @ B @ D ) @ E @ B @ D )
        = c_Datatype_Ooption_ONone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).

thf(1595,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( c_in @ E @ ( c_List_Oset @ A @ B ) @ B )
      | ( ( c_Map_Omap__of @ ( c_List_Ozip @ A @ C @ B @ D ) @ E @ B @ D )
        = c_Datatype_Ooption_ONone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).

thf(1374,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).

thf(513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ ( c_insert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
      | ( c_Wellfounded__Recursion_Owf @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(275,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
      = ( c_Message_OHPair @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_2) ).

thf(1146,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B )
      = ( c_Message_OHPair @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).

thf(819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(95,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_0) ).

thf(694,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ c_0 @ A @ tc_nat )
      | ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
        = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).

thf(732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ c_0 @ A @ tc_nat )
      | ( ( c_List_Osublist @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ A @ C )
        = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(165,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_append @ ( c_append @ A @ B @ C ) @ D @ C )
      = ( c_append @ A @ ( c_append @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).

thf(875,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_append @ ( c_append @ A @ B @ C ) @ D @ C )
      = ( c_append @ A @ ( c_append @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(199,axiom,
    ! [A: $i] :
      ( ( c_List_Oset @ c_List_Olist_ONil @ A )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).

thf(958,plain,
    ! [A: $i] :
      ( ( c_List_Oset @ c_List_Olist_ONil @ A )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).

thf(1226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(49,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
      = ( c_List_Olist_OCons @ ( c_Pair @ A @ D @ C @ F ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).

thf(584,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Ozip @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olist_OCons @ D @ E @ F ) @ C @ F )
      = ( c_List_Olist_OCons @ ( c_Pair @ A @ D @ C @ F ) @ ( c_List_Ozip @ B @ E @ C @ F ) @ ( tc_prod @ C @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_1) ).

thf(1154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oused__Gets_0) ).

thf(1615,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).

thf(1389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_List_Ohd @ ( c_List_Oupt @ A @ B ) @ tc_nat )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).

thf(843,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_List_Ohd @ ( c_List_Oupt @ A @ B ) @ tc_nat )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( c_Event_Oknows @ A @ c_List_Olist_ONil )
      = ( c_Event_OinitState @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows_Oknows__Nil_0) ).

thf(1125,plain,
    ! [A: $i] :
      ( ( c_Event_Oknows @ A @ c_List_Olist_ONil )
      = ( c_Event_OinitState @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).

thf(572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_lessequals @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(131,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ~ ( c_less @ A @ ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Ozip @ D @ B @ E @ C ) @ A @ ( tc_prod @ E @ C ) )
        = ( c_Pair @ ( c_List_Onth @ D @ A @ E ) @ ( c_List_Onth @ B @ A @ C ) @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).

thf(787,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ~ ( c_less @ A @ ( c_Nat_Osize @ D @ ( tc_List_Olist @ E ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Ozip @ D @ B @ E @ C ) @ A @ ( tc_prod @ E @ C ) )
        = ( c_Pair @ ( c_List_Onth @ D @ A @ E ) @ ( c_List_Onth @ B @ A @ C ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(355,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__HPair_0) ).

thf(1332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_0) ).

thf(1258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).

thf(1224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ~ ( c_in @ ( c_Pair @ C @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).

thf(540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ~ ( c_in @ ( c_Pair @ C @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( c_List_Oremdups @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).

thf(672,plain,
    ! [A: $i] :
      ( ( c_List_Oremdups @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).

thf(1139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_append @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) @ B )
      = ( c_List_Olist_OCons @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__pubK_0) ).

thf(1503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Public_OshrK @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(240,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olexn @ A @ c_0 @ B )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).

thf(1058,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olexn @ A @ c_0 @ B )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oagent_OFriend @ A )
       != ( c_Message_Oagent_OFriend @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).

thf(1107,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oagent_OFriend @ A )
       != ( c_Message_Oagent_OFriend @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2_0) ).

thf(1464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_0) ).

thf(947,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(294,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_0) ).

thf(1194,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).

thf(1209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Main_ONil__eq__concat__conv__1 @ A @ B )
       != c_List_Olist_ONil )
      | ( c_List_Olist_ONil
        = ( c_List_Oconcat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).

thf(900,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Main_ONil__eq__concat__conv__1 @ A @ B )
       != c_List_Olist_ONil )
      | ( c_List_Olist_ONil
        = ( c_List_Oconcat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_List_Oset @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = ( c_insert @ B @ c_emptyset @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).

thf(784,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_List_Oset @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = ( c_insert @ B @ c_emptyset @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__HPair_0) ).

thf(1574,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_OHPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_OHPair @ A @ B ) @ ( c_insert @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(215,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_append @ A @ c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olast @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendL_0) ).

thf(996,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_append @ A @ c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olast @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(445,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ F @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ F )
      | ( c_Message_Oagent_OServer = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_0) ).

thf(1542,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ F @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ F )
      | ( c_Message_Oagent_OServer = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Oreplicate @ B @ C @ D ) @ A @ D )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Oreplicate @ B @ C @ D ) @ A @ D )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_0) ).

thf(1122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( c_append @ A @ B @ C ) )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oupt @ A @ B )
       != c_List_Olist_ONil )
      | ( c_lessequals @ B @ A @ tc_nat )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).

thf(649,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oupt @ A @ B )
       != c_List_Olist_ONil )
      | ( c_lessequals @ B @ A @ tc_nat )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(1043,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ B @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(459,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( c_Message_Oagent_OFriend @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).

thf(1571,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( c_Message_Oagent_OFriend @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(373,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__2_0) ).

thf(1376,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).

thf(1471,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_OinvKey @ A ) @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).

thf(631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_0 )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).

thf(609,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Otake @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_0 )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oupt @ B @ C ) @ tc_nat )
      = ( c_List_Oupt @ ( c_plus @ B @ A @ tc_nat ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).

thf(594,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Oupt @ B @ C ) @ tc_nat )
      = ( c_List_Oupt @ ( c_plus @ B @ A @ tc_nat ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).

thf(726,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Orev @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(1,negated_conjecture,
    c_in @ v_evs4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(483,plain,
    c_in @ v_evs4 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(175,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_List_Oremdups @ c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).

thf(895,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_List_Oremdups @ c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).

thf(626,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ A @ c_0 @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_0) ).

thf(1344,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(225,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ D @ A @ B )
       != ( c_append @ E @ C @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).

thf(1022,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ D @ A @ B )
       != ( c_append @ E @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ D @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ ( c_List_Olist_OCons @ A @ D @ C ) @ ( c_List_Olists @ B @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(375,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_2) ).

thf(1381,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(97,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oset @ A @ B )
       != c_emptyset )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).

thf(700,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_List_Oset @ A @ B )
       != c_emptyset )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ c_0 @ A @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_1) ).

thf(520,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Otake @ c_0 @ A @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(451,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_0) ).

thf(1556,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ B ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).

thf(1460,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
      = ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).

thf(983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
      = ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(128,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_2) ).

thf(780,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ C )
        = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).

thf(883,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
      | ( ( c_List_Onth @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ C )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(222,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_List_Orev @ c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).

thf(1015,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( c_List_Orev @ c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).

thf(1176,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(39,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ c_List_Olist_ONil @ A @ B @ C )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).

thf(563,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ c_List_Olist_ONil @ A @ B @ C )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(397,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3_0) ).

thf(1435,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
      | ( ( c_List_Oconcat @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_0) ).

thf(1477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
      | ( ( c_List_Oconcat @ B @ C )
       != c_List_Olist_ONil )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(424,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).

thf(1496,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( c_lessequals @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).

thf(505,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Odrop @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( c_lessequals @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ A @ D @ B )
       != ( c_append @ C @ E @ B ) )
      | ( D = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).

thf(922,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ A @ D @ B )
       != ( c_append @ C @ E @ B ) )
      | ( D = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(454,axiom,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OSpy ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5_0) ).

thf(1562,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OSpy ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).

thf(685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(284,axiom,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( K = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ounique__session__keys_3) ).

thf(1171,plain,
    ! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ H @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ H ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ I ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ D ) @ ( c_Message_Omsg_OMPair @ J @ K ) ) ) ) @ L ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( K = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(295,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Oremdups @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).

thf(1198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Oremdups @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
        = ( c_List_Oremdups @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).

thf(1396,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(301,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

thf(1213,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(768,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_insert @ B @ c_emptyset @ C ) @ C )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).

thf(827,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
      | ( c_less @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).

thf(636,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) )
      | ( c_less @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
      | ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(1245,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Main_Oin__listsI__1 @ A @ B @ C ) @ A @ C )
      | ( c_in @ B @ ( c_List_Olists @ A @ C ) @ ( tc_List_Olist @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
      | ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_2) ).

thf(1066,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
      | ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(401,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).

thf(1445,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(368,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( c_Message_Oagent_OFriend @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).

thf(1364,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( c_Message_Oagent_OFriend @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ A ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ A ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(342,axiom,
    class_Wellfounded__Recursion_Owellorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).

thf(1304,plain,
    class_Wellfounded__Recursion_Owellorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).

thf(1166,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_insert @ A @ ( c_insert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
        = ( c_List_Olist__inter @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).

thf(1203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
        = ( c_List_Olist__inter @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_1) ).

thf(1467,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_OHPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ tc_nat )
      | ( ( c_List_Otake @ C @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ tc_nat )
      | ( ( c_List_Otake @ C @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(12,negated_conjecture,
    ~ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).

thf(487,plain,
    ~ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
        = ( c_List_Olist_OCons @ B @ ( c_List_Obutlast @ A @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).

thf(617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ B @ A @ C ) @ C )
        = ( c_List_Olist_OCons @ B @ ( c_List_Obutlast @ A @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).

thf(939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(117,axiom,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).

thf(754,plain,
    ! [B: $i,A: $i] :
      ( ( c_less @ c_0 @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).

thf(1049,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(11,negated_conjecture,
    c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).

thf(490,plain,
    c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(465,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_ONil__eq__concat__conv__1 @ A @ B ) @ ( c_List_Oset @ A @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) )
      | ( c_List_Olist_ONil
        = ( c_List_Oconcat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).

thf(1583,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_ONil__eq__concat__conv__1 @ A @ B ) @ ( c_List_Oset @ A @ ( tc_List_Olist @ B ) ) @ ( tc_List_Olist @ B ) )
      | ( c_List_Olist_ONil
        = ( c_List_Oconcat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(26,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ C @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).

thf(531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
      | ( c_less @ B @ C @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( c_List_Olist_OCons @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).

thf(944,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( c_List_Olist_OCons @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(134,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).

thf(795,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orotate @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ D @ B ) )
      | ( A
        = ( c_append @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).

thf(680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ D @ B ) )
      | ( A
        = ( c_append @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_2) ).

thf(812,plain,
    ! [A: $i] :
      ( ( c_append @ c_List_Olist_ONil @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(431,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ C )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ D @ E @ F ) @ C @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Says_3) ).

thf(1509,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ C )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ D @ E @ F ) @ C @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_List_Orev @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).

thf(1081,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
       != ( c_List_Orev @ A @ B ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != A )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != A )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_append @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_append @ B @ D @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).

thf(968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_append @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
      = ( c_List_Olist_OCons @ A @ ( c_append @ B @ D @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_insert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_0) ).

thf(1181,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_insert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).

thf(836,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).

thf(1551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(102,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONumber @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3_0) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONumber @ A )
     != ( c_Message_OHPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).

thf(580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OKey @ A )
       != ( c_Message_Omsg_OKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).

thf(1598,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OKey @ A )
       != ( c_Message_Omsg_OKey @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).

thf(640,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ c_List_Olist_ONil @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
      = ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_1) ).

thf(1025,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B )
      = ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).

thf(872,plain,
    ! [A: $i] :
      ( ( c_less @ c_0 @ A @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat @ ( c_List_Olist_OCons @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
      = ( c_append @ A @ ( c_List_Oconcat @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).

thf(707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat @ ( c_List_Olist_OCons @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
      = ( c_append @ A @ ( c_List_Oconcat @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).

thf(1566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Public_OpublicKey @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpubK__neq__shrK_0) ).

thf(1267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Public_OpublicKey @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ D @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).

thf(1531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( ( c_List_Olist__inter @ ( c_List_Olist_OCons @ A @ D @ C ) @ B @ C )
        = ( c_List_Olist_OCons @ A @ ( c_List_Olist__inter @ D @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(255,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).

thf(1098,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olast @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(447,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

thf(1547,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Wellfounded__Recursion_Owf @ A @ B )
      | ( c_Wellfounded__Recursion_Owf @ ( c_List_Olenlex @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(126,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).

thf(776,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat @ ( c_append @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
      = ( c_append @ ( c_List_Oconcat @ A @ C ) @ ( c_List_Oconcat @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).

thf(705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oconcat @ ( c_append @ A @ B @ ( tc_List_Olist @ C ) ) @ C )
      = ( c_append @ ( c_List_Oconcat @ A @ C ) @ ( c_List_Oconcat @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(476,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).

thf(1611,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(197,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
      = ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).

thf(954,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
      = ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).

thf(1252,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
      = ( c_List_Oset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(396,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).

thf(1432,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).

thf(1300,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).

thf(1038,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) @ B )
      = ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).

thf(717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_Orev @ A @ B )
       != ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) )
      | ( A
        = ( c_List_Olist_OCons @ C @ c_List_Olist_ONil @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OHash @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).

thf(840,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_OHash @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(347,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ E @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Gets_0) ).

thf(1317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ E @ tc_Event_Oevent ) )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).

thf(576,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) @ B @ tc_nat )
      = ( c_Divides_Oop_Amod @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( B = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != c_List_Olist_ONil )
      | ( B = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).

thf(1220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( c_plus @ A @ c_0 @ tc_nat )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(544,plain,
    ! [A: $i] :
      ( ( c_plus @ A @ c_0 @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ c_Datatype_Ooption_ONone @ ( tc_Datatype_Ooption @ A ) )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).

thf(1053,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ c_Datatype_Ooption_ONone @ ( tc_Datatype_Ooption @ A ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Gets_0) ).

thf(1499,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(291,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).

thf(1188,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Event_Oevent_OGets @ A @ B ) @ tc_Event_Oevent )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__2_0) ).

thf(1186,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Event_Oevent_OGets @ A @ B ) @ tc_Event_Oevent )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(335,axiom,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OServer ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2_0) ).

thf(1285,plain,
    ! [A: $i] :
      ( ( c_Message_Oagent_OFriend @ A )
     != c_Message_Oagent_OServer ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).

thf(1218,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Oset @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).

thf(1358,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Orotate @ A @ B @ C ) @ C )
      = ( c_List_Oset @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(98,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
      = ( c_append @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).

thf(703,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__update @ ( c_append @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
      = ( c_append @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).

thf(600,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(220,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).

thf(1008,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).

thf(1372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption @ A ) )
     != ( c_Public_OshrK @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpriEK__noteq__shrK_0) ).

thf(859,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ c_Public_Okeymode_OEncryption @ A ) )
     != ( c_Public_OshrK @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(273,axiom,
    ! [A: $i] :
      ( ( c_List_Olistset @ c_List_Olist_ONil @ A )
      = ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).

thf(1141,plain,
    ! [A: $i] :
      ( ( c_List_Olistset @ c_List_Olist_ONil @ A )
      = ( c_insert @ c_List_Olist_ONil @ c_emptyset @ ( tc_List_Olist @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(443,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__4_0) ).

thf(1536,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(420,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_1) ).

thf(1485,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_1) ).

thf(1506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_OHPair @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(330,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONonce @ A )
       != ( c_Message_Omsg_ONonce @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).

thf(1272,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONonce @ A )
       != ( c_Message_Omsg_ONonce @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( c_List_Obutlast @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).

thf(612,plain,
    ! [A: $i] :
      ( ( c_List_Obutlast @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(315,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).

thf(1240,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).

thf(991,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(479,axiom,
    ~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).

thf(1617,plain,
    ~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OpublicKey__neq__privateKey_0) ).

thf(1084,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat )
      = ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).

thf(556,plain,
    ! [B: $i,A: $i] :
      ( ( c_Divides_Oop_Amod @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat )
      = ( c_Divides_Oop_Amod @ B @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ c_0 @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).

thf(931,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ c_0 @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(450,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5_0) ).

thf(1553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(10,negated_conjecture,
    c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ v_Xa @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).

thf(482,plain,
    c_in @ ( c_Event_Oevent_OSays @ v_A @ v_B @ ( c_Message_Omsg_OMPair @ v_Xa @ ( c_Message_Omsg_OCrypt @ v_K @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(349,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
        = ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
        = ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(23,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).

thf(524,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != c_0 )
      | ( B = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).

thf(1412,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(405,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).

thf(1453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Event_Oevent_ONotes @ A @ B ) @ tc_Event_Oevent )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__3_0) ).

thf(771,plain,
    ! [B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Event_Oevent_ONotes @ A @ B ) @ tc_Event_Oevent )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(206,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).

thf(976,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).

thf(903,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_append @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ c_List_Olist_ONil @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(303,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).

thf(1216,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_ONonce @ A ) @ tc_Message_Omsg )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).

thf(891,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_ONonce @ A ) @ tc_Message_Omsg )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).

thf(1276,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_union @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).

thf(1326,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Oreplicate @ c_0 @ A @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).

thf(588,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Oreplicate @ c_0 @ A @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).

thf(1385,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(20,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_List_Oupt @ B @ A )
        = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).

thf(517,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( ( c_List_Oupt @ B @ A )
        = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(358,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__6_0) ).

thf(1341,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ tc_nat )
      | ( ( c_List_Olist__update @ A @ C @ D @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).

thf(652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ tc_nat )
      | ( ( c_List_Olist__update @ A @ C @ D @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(437,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).

thf(1523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_2) ).

thf(1558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ C @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_OHPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Ohd @ ( c_append @ A @ B @ C ) @ C )
        = ( c_List_Ohd @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( c_List_Ohd @ ( c_append @ A @ B @ C ) @ C )
        = ( c_List_Ohd @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).

thf(568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ A @ D @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).

thf(914,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ B @ C )
       != ( c_append @ A @ D @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).

thf(510,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_0) ).

thf(1294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(399,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSpy__see__shrK_1) ).

thf(1440,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ B @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(344,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat )
      | ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
        = ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).

thf(1308,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Oanalz @ B ) ) @ tc_nat )
      | ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
        = ( c_insert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( c_List_Orotate1 @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).

thf(1077,plain,
    ! [A: $i] :
      ( ( c_List_Orotate1 @ c_List_Olist_ONil @ A )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(121,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__inter @ c_List_Olist_ONil @ A @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).

thf(763,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist__inter @ c_List_Olist_ONil @ A @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(433,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).

thf(1513,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
      = ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).

thf(832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
      = ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(28,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).

thf(536,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(234,axiom,
    ! [A: $i] :
      ~ ( c_less @ A @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(1045,plain,
    ! [A: $i] :
      ~ ( c_less @ A @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(33,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ c_0 @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).

thf(549,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Odrop @ c_0 @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(400,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
      | ( A = c_emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).

thf(1442,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Main_Oall__not__in__conv__1 @ A @ B ) @ A @ B )
      | ( A = c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(280,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).

thf(1161,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ( c_in @ B @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(136,axiom,
    ! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(800,plain,
    ! [A: $i] : ( c_Wellfounded__Recursion_Owf @ c_emptyset @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

thf(1133,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ c_emptyset @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_insert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Says_0) ).

thf(1348,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_insert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ C @ B @ tc_nat ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).

thf(620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_plus @ A @ B @ tc_nat )
       != ( c_plus @ C @ B @ tc_nat ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).

thf(752,plain,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ( ( c_Message_OinvKey @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).

thf(1280,plain,
    ! [A: $i] :
      ( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ( ( c_Message_OinvKey @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
      | ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_0) ).

thf(1578,plain,
    ! [A: $i] :
      ( ~ ( c_in @ ( c_Message_OinvKey @ A ) @ c_Message_OsymKeys @ tc_nat )
      | ( c_in @ A @ c_Message_OsymKeys @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).

thf(1593,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONumber @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ tc_Event_Oevent )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__1_0) ).

thf(854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Nat_Osize @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ tc_Event_Oevent )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( C
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_0) ).

thf(1148,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_OHPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( C
        = ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(132,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ A @ D @ B )
       != ( c_append @ C @ E @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).

thf(790,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ B ) ) )
      | ( ( c_append @ A @ D @ B )
       != ( c_append @ C @ E @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(58,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).

thf(603,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Pair @ A @ B @ C @ D )
       != ( c_Pair @ E @ F @ C @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Oagent_OFriend @ A ) @ tc_Message_Oagent )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).

thf(735,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Oagent_OFriend @ A ) @ tc_Message_Oagent )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_0) ).

thf(865,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(417,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).

thf(1480,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(176,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).

thf(897,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_insert @ A @ B @ C )
       != ( c_insert @ D @ c_emptyset @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).

thf(720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(360,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ D ) ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__not__shrK_0) ).

thf(1346,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ B @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ D ) ) @ ( c_Message_Omsg_OMPair @ E @ F ) ) ) ) @ G ) ) @ ( c_List_Oset @ A @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( c_append @ A @ c_List_Olist_ONil @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).

thf(918,plain,
    ! [B: $i,A: $i] :
      ( ( c_append @ A @ c_List_Olist_ONil @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).

thf(801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_OAgent @ A ) @ tc_Message_Omsg )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).

thf(1033,plain,
    ! [A: $i] :
      ( ( c_Nat_Osize @ ( c_Message_Omsg_OAgent @ A ) @ tc_Message_Omsg )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(336,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__injective_0) ).

thf(1288,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(960,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_List_Olists @ D @ C ) @ ( tc_List_Olist @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(414,axiom,
    ( ( c_Nat_Osize @ c_Message_Oagent_OServer @ tc_Message_Oagent )
    = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).

thf(1473,plain,
    ( ( c_Nat_Osize @ c_Message_Oagent_OServer @ tc_Message_Oagent )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Osublist @ A @ c_emptyset @ B )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).

thf(886,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Osublist @ A @ c_emptyset @ B )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).

thf(928,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_append @ A @ ( c_List_Olist_OCons @ B @ c_List_Olist_ONil @ C ) @ C )
       != ( c_append @ D @ ( c_List_Olist_OCons @ E @ c_List_Olist_ONil @ C ) @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__neq__priK_0) ).

thf(1093,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OshrK @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(112,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).

thf(740,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( c_List_Oset @ c_List_Olist_ONil @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
      = ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).

thf(1352,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
      = ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ C )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ D @ E ) @ C @ tc_Event_Oevent ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OKeyWithNonce__Notes_1) ).

thf(1129,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Yahalom_OKeyWithNonce @ A @ B @ C )
      | ( c_Yahalom_OKeyWithNonce @ A @ B @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ D @ E ) @ C @ tc_Event_Oevent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
      = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).

thf(596,plain,
    ! [A: $i] :
      ( ( c_Divides_Oop_Amod @ c_0 @ A @ tc_nat )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).

thf(644,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_less @ A @ B @ tc_nat )
      | ( c_in @ ( c_Pair @ A @ B @ tc_nat @ tc_nat ) @ c_Wellfounded__Relations_Oless__than @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
       != c_0 )
      | ( ( c_List_Orotate @ A @ B @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Divides_Oop_Amod @ A @ ( c_Nat_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat )
       != c_0 )
      | ( ( c_List_Orotate @ A @ B @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) )
      | ( ( c_List_Oremdups @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).

thf(691,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) ) )
      | ( ( c_List_Oremdups @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(383,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).

thf(1399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).

thf(501,plain,
    ! [A: $i] :
      ( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
      = ( c_List_Oreplicate @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).

thf(607,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
      = ( c_List_Oreplicate @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(313,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).

thf(1236,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(211,axiom,
    ! [A: $i] :
      ( ( c_union @ c_emptyset @ c_emptyset @ A )
      = c_emptyset ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).

thf(987,plain,
    ! [A: $i] :
      ( ( c_union @ c_emptyset @ c_emptyset @ A )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(464,axiom,
    class_Divides_Odiv @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_44) ).

thf(1582,plain,
    class_Divides_Odiv @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != c_0 )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).

thf(1019,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != c_0 )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

thf(982,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(218,axiom,
    ! [A: $i] :
      ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_0) ).

thf(1004,plain,
    ! [A: $i] :
      ~ ( c_less @ c_0 @ ( c_Nat_Osize @ c_List_Olist_ONil @ ( tc_List_Olist @ A ) ) @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(474,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
      | ( c_List_Olist_ONil
       != ( c_List_Oconcat @ B @ C ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).

thf(1606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ B @ ( tc_List_Olist @ C ) ) @ ( tc_List_Olist @ C ) )
      | ( c_List_Olist_ONil
       != ( c_List_Oconcat @ B @ C ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(2,negated_conjecture,
    v_Aa != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(486,plain,
    v_Aa != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(138,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( ( c_List_Ozip @ ( c_append @ E @ A @ B ) @ ( c_append @ F @ C @ D ) @ B @ D )
        = ( c_append @ ( c_List_Ozip @ E @ F @ B @ D ) @ ( c_List_Ozip @ A @ C @ B @ D ) @ ( tc_prod @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).

thf(803,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Nat_Osize @ A @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ C @ ( tc_List_Olist @ D ) ) )
      | ( ( c_Nat_Osize @ E @ ( tc_List_Olist @ B ) )
       != ( c_Nat_Osize @ F @ ( tc_List_Olist @ D ) ) )
      | ( ( c_List_Ozip @ ( c_append @ E @ A @ B ) @ ( c_append @ F @ C @ D ) @ B @ D )
        = ( c_append @ ( c_List_Ozip @ E @ F @ B @ D ) @ ( c_List_Ozip @ A @ C @ B @ D ) @ ( tc_prod @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
        = ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ ( c_insert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).

thf(1367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( ( c_Message_Oanalz @ ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg ) )
        = ( c_insert @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Oanalz @ ( c_insert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).

thf(935,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OkeysFor @ ( c_insert @ ( c_Message_Omsg_OHash @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Message_OkeysFor @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(289,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).

thf(1184,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_insert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(88,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
      = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_2) ).

thf(676,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_OHPair @ A @ B )
      = ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OHash @ ( c_Message_Omsg_OMPair @ A @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(8,negated_conjecture,
    c_in @ v_X @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(491,plain,
    c_in @ v_X @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(403,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_OCrypt__imp__keysFor_0) ).

thf(1449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ c_Message_OsymKeys @ tc_nat )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_OkeysFor @ C ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(53,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).

thf(592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_lessequals @ A @ B @ tc_nat )
      | ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).

thf(1417,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(80,axiom,
    ! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(659,plain,
    ! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(455,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).

thf(1565,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_OHPair @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6_0) ).

thf(1490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_OHPair @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Otake @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_0) ).

thf(560,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
       != c_0 )
      | ( ( c_List_Otake @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(1621,plain,
    $false,
    inference(e,[status(thm)],[1411,1469,1190,1105,893,1315,962,941,777,666,1549,481,1586,1501,809,1168,760,1237,846,909,628,1211,683,730,1068,994,1401,1591,655,614,1305,1158,582,762,1497,1426,1137,533,797,715,814,1260,1063,1354,1222,1458,670,829,782,709,973,1613,1475,565,1529,1265,1243,1127,1391,1576,1228,1482,1254,1055,570,1298,504,1330,838,1511,1462,542,1545,817,638,1379,1087,1247,1319,1609,1115,1568,1100,1232,1398,881,492,1040,623,574,806,1283,905,1334,646,485,834,1151,937,1051,821,687,877,1119,1394,1526,660,998,1405,1201,1521,527,1215,634,1447,956,1242,849,1206,920,678,529,1438,925,1338,1311,1074,1604,546,793,1047,1163,1387,825,1519,1255,862,598,1502,1487,1560,746,1091,1355,1580,1570,1174,1619,1370,1423,484,1602,879,852,1178,1296,522,889,757,1407,551,1012,1079,1027,1143,1270,1328,1111,980,1096,1006,869,1118,989,1360,1350,742,578,697,1234,1534,1017,1493,1329,488,554,1424,642,1414,489,590,970,1419,1292,933,1324,1263,515,1451,1231,1131,1192,1060,911,1002,1429,1525,1588,985,1539,1456,508,657,765,1035,674,1515,888,558,1071,773,586,1278,1135,965,1103,1483,856,1595,1374,513,1146,819,694,732,875,958,1226,584,1154,1615,1389,843,1125,572,787,1332,1258,1224,540,672,1139,1503,1058,1107,1464,947,1194,1209,900,784,1574,996,1542,737,1122,649,1043,1571,1376,1471,631,609,594,726,483,895,626,1344,1022,668,1381,700,520,1556,1460,983,780,883,1015,1176,563,1435,1477,1496,505,922,1562,685,1171,1198,1396,1213,768,827,636,1245,1066,1445,1364,1250,1304,1166,1203,1467,663,487,617,939,754,1049,490,1583,531,944,795,680,812,1509,1081,749,968,1181,836,1551,712,580,1598,640,1025,872,707,1566,1267,1531,1098,1547,776,705,1611,954,1252,1432,1300,1038,717,840,1317,576,951,1220,544,1053,1499,1188,1186,1285,1218,1358,703,600,1008,1372,859,1141,1536,1485,1506,1272,612,1240,991,1617,1084,556,931,1553,482,1321,524,1412,1453,771,976,903,1216,891,1276,1326,588,1385,517,1341,652,1523,1558,1030,568,914,510,1294,1440,1308,1077,763,1513,832,536,1045,549,1442,1161,800,1133,1348,620,752,1280,1578,1593,854,1148,790,603,735,865,1480,897,720,1346,918,801,1033,1288,960,1473,886,928,1093,740,1352,1129,596,644,723,691,1399,501,607,1236,987,1582,1019,982,1004,1606,486,803,1367,935,1184,676,491,1449,592,1417,659,1565,1490,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWV333-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri May 19 02:51:40 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.90/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.18/1.16  % [INFO] 	 Parsing done (325ms). 
% 2.18/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.64/1.37  % [INFO] 	 eprover registered as external prover. 
% 2.64/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 2.64/1.37  % [INFO] 	 Scanning for conjecture ... 
% 3.31/1.53  % [INFO] 	 Found a conjecture and 2960 axioms. Running axiom selection ... 
% 4.28/1.77  % [INFO] 	 Axiom selection finished. Selected 468 axioms (removed 2492 axioms). 
% 4.64/1.88  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.64/1.89  % [INFO] 	 Type checking passed. 
% 4.64/1.89  % [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 ... 
% 9.59/3.11  % External prover 'e' found a proof!
% 9.59/3.11  % [INFO] 	 Killing All external provers ... 
% 9.59/3.12  % Time passed: 2603ms (effective reasoning time: 1939ms)
% 9.59/3.12  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.59/3.12  % Axioms used in derivation (468): cls_Event_Oevent_Oinject__3_0, cls_List_Onth__upt_0, cls_Message_Oanalz__synth__Un_0, cls_Nat_Onot__less0_0, cls_List_Oself__append__conv2_0, cls_Nat_Onot__gr0_0, cls_Message_Oanalz_OInj_0, cls_Nat_Onat__add__left__cancel__less_1, cls_List_Ohd__Cons__tl_0, cls_Set_Osingleton__insert__inj__eq_0, cls_Message_Oagent_Osize__3_0, cls_Event_OSays__imp__analz__Spy__dest_0, cls_SetInterval_OatMost__0_0, cls_Public_OpublicKey__into__used_0, cls_List_Olist__update__overwrite_0, cls_List_Onth__zip_0, cls_List_Otake__all_0, cls_List_Oremdups__eq__nil__iff_1, cls_List_Oappend__eq__append__conv_1, cls_Event_OkeysFor__synth_H_0, cls_List_Onth__append__length_0, cls_Message_Oparts__Un_0, cls_List_Olists_ONil_0, cls_Message_OHPair__neqs__2_0, cls_Message_Oanalz__analzD__dest_0, cls_Message_OCrypt__synth__eq_0, cls_Message_Omsg_Osize__2_0, cls_List_Olength__append_0, cls_Nat_Onat__add__right__cancel_0, cls_Event_Oused__Gets_0, cls_List_Olast__snoc_0, cls_List_Olength__remdups__eq_1, cls_Wellfounded__Recursion_Owf__insert_0, cls_List_Onotin__set__remove1_0, cls_Message_Oanalz__synth_0, cls_Message_Oparts__insert__Crypt_0, cls_List_Otake__Cons__number__of_0, cls_List_Olist__update_Osimps__1_0, cls_Message_OkeysFor__Un_0, cls_List_Orev__is__Nil__conv_0, cls_Message_Oparts__empty_0, cls_Message_OKey__synth__eq_1, cls_Message_Oanalz__conj__parts_0, cls_Message_Oanalz__idem_0, cls_Message_OHPair__synth__analz_1, cls_Public_OpubK__neq__shrK_0, cls_Message_Oagent_Oinject_0, cls_List_Olast_Osimps_0, cls_Message_Oanalz__empty_0, cls_Message_Oparts__insert__MPair_0, cls_List_Oappend__in__lists__conv_2, cls_Yahalom_Ounique__session__keys_0, cls_Set_Osingleton__inject__dest_0, cls_Message_Oanalz__insert__HPair_0, cls_List_Olength__0__conv_1, cls_Public_Onot__symKeys__priK_0, cls_List_Olist_Oinject_1, cls_Event_Oused__Notes_0, cls_List_Oappend__same__eq_0, cls_Message_Oparts__insert__Nonce_0, cls_Nat_Oadd__is__0_0, cls_List_Oupt__eq__Nil__conv_2, cls_Message_OHPair__neqs__5_0, cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0, cls_List_Oappend__eq__append__conv_0, cls_Message_Oanalz__Crypt__if_0, cls_Yahalom_OSpy__see__shrK_0, cls_List_Onth__Cons__number__of_0, cls_List_Onth__list__update__neq_0, cls_Event_Oevent_Odistinct__6_0, cls_Nat_Oless__irrefl_0, cls_Message_Omsg_Oinject__1_0, cls_Yahalom_OA__trusts__YM3_0, cls_Event_OkeysFor__synth_H_3, cls_List_Obutlast__snoc_0, cls_List_Orotate__is__Nil__conv_0, cls_List_Olast__in__set_0, cls_Message_OMPair__synth__analz_2, cls_List_Odrop__eq__Nil_1, cls_Public_OpriK__neq__shrK_0, cls_List_Oself__append__conv_1, cls_List_Otake__eq__Nil_1, cls_Divides_Omod__add__self1_0, cls_Message_OHash__synth_0, cls_Set_Osingleton__insert__inj__eq_H_0, clsarity_nat_47, cls_List_Onth__mem_0, cls_Nat_Onat__add__left__cancel__le_0, cls_List_Oappend__eq__append__conv_3, cls_Message_Oparts__insert__Agent_0, cls_Message_Osynth_OHash_0, cls_List_Oconcat_Osimps__2_0, cls_List_Oconcat__eq__Nil__conv_2, cls_List_Onth__drop_0, cls_Message_OHPair__eq_0, cls_List_Osame__append__eq_0, cls_Public_OCrypt__imp__keysFor_0, cls_List_ONil__is__rev__conv_0, cls_List_Olength__remdups__eq_0, cls_Event_Oevent_Osize__3_0, cls_List_Olength__replicate_0, cls_List_Olength__list__update_0, cls_List_Otl_Osimps__2_0, cls_Public_OCrypt__notin__used__empty_0, cls_Message_Oanalz__insert__Agent_0, cls_Message_Omsg_Oinject__6_0, cls_Nat_Onat__add__left__cancel__less_0, cls_Event_Oknows__Spy__Notes_1, cls_Yahalom_Ounique__session__keys_3, cls_Message_Oanalz__insert__Nonce_0, cls_List_Oremdups__eq__nil__iff_0, cls_List_Oremove1_Osimps__2_1, cls_List_Orev__rev__ident_0, cls_Nat_Oadd__gr__0_2, cls_Public_ONonce__notin__initState_0, cls_List_Olist__inter_Osimps__2_1, cls_List_Oset__empty2_1, cls_Public_OshrK__injective_0, cls_Message_Oagent_Odistinct__1_0, cls_Public_OMPair__used_1, cls_Message_Oparts_OInj_0, cls_List_Olength__remdups__leq_0, cls_List_Ohd_Osimps_0, cls_List_Odrop__Cons__number__of_0, cls_Message_Oparts__synth_0, cls_List_Otake__upt_0, cls_List_ONil__eq__concat__conv_1, cls_List_Olist__inter_Osimps__2_0, cls_List_Olast__replicate_0, cls_List_Obutlast_Osimps__2_0, cls_Message_OkeysFor__empty_0, cls_Message_Omsg_Oinject__5_0, cls_Message_OCrypt__synth_1, cls_List_Olength__rotate_0, cls_List_Oset__remdups_0, cls_List_OlistsE_0, cls_Message_OHPair__neqs__6_0, cls_List_Osingleton__rev__conv_0, cls_List_Oconcat__eq__Nil__conv_1, clsarity_nat_44, cls_Divides_Omod__le__divisor_0, cls_Public_OkeysFor__parts__initState_0, cls_Public_OinvKey__K_0, cls_Message_Omsg_Osize__4_0, cls_List_Orev__is__rev__conv_0, cls_Message_Oparts__insert__Key_0, cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0, cls_Message_OHPair__synth__analz_0, cls_Public_OsymKeys__invKey__iff_0, cls_Nat_Oadd__is__0_1, cls_Message_Osynth_OMPair_0, cls_Message_ONonce__synth__eq_1, cls_Event_Oevent_Odistinct__4_0, cls_Set_OUn__iff_0, cls_Message_Oparts__insert__HPair_0, cls_Set_OUn__empty_1, cls_List_Oappend1__eq__conv_1, cls_Yahalom_OKeyWithNonce__Notes_0, cls_Message_Omsg_Oinject__2_0, cls_Yahalom_OKeyWithNonce__Notes_1, cls_Message_Omsg_Oinject__7_1, cls_Set_Oinsert__iff_2, cls_List_Oremdups__eq__nil__right__iff_0, cls_List_Oappend__self__conv_0, cls_List_Orotate1__is__Nil__conv_0, cls_List_Orev__is__Nil__conv_1, cls_Event_Oevent_Oinject__2_0, cls_Message_Oagent_Odistinct__3_0, cls_List_Ozip__append_0, cls_Set_OsingletonD__dest_0, cls_Set_Oinsert__not__empty_0, cls_List_Otake__eq__Nil_2, cls_Yahalom_OB__trusts__YM4__shrK_0, cls_Event_Oknows__Spy__Says_0, cls_Message_OFake__analz__eq_0, cls_Nat_Ole__0__eq_0, cls_Event_Oevent_Odistinct__3_0, cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0, cls_List_Oappend__self__conv_1, cls_Map_Omap__of__zip__is__None_0, cls_List_Oupt__eq__Nil__conv_1, cls_List_Osublist__nil_0, cls_Divides_Omod__add__self2_0, cls_List_Oappend__in__lists__conv_1, cls_List_Olist_Oinject_0, cls_Set_Oempty__iff_0, cls_Wellfounded__Recursion_Owf__not__refl_0, cls_Message_OkeysFor__insert__HPair_0, cls_List_Odrop__0_0, cls_Public_OCrypt__Spy__analz__bad_0, cls_List_Oreplicate_Oreplicate__0_0, cls_Message_Omsg_Oinject__4_0, cls_Public_OpublicKey__neq__privateKey_0, cls_Event_Oevent_Oinject__3_1, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_Message_ONumber__synth_0, cls_Event_Oevent_Osize__2_0, cls_Event_Oknows__Spy__Notes_0, cls_Message_OAgent__synth_0, cls_List_Oin__listsI_1, cls_List_Oremdups_Osimps__2_0, cls_List_Olast_Osimps_1, cls_Set_OsingletonI_0, cls_Message_Oparts__partsD__dest_0, cls_Message_OHPair__eq__MPair_0, cls_List_Ohd__replicate_0, cls_Message_Oparts__insert__Hash_0, cls_Message_Omsg_Oinject__6_1, cls_List_Obutlast_Osimps__2_1, cls_Nat_Onat__add__left__cancel__le_1, cls_Divides_Omod__less__divisor_0, cls_Event_Oevent_Oinject__1_2, cls_Message_OkeysFor__insert__Agent_0, cls_Public_OshrK__neq__priK_0, cls_Yahalom_OKeyWithNonce__Says_2, cls_Message_Oparts__insert__Number_0, cls_Message_Oanalz__insert__Key_0, cls_List_Olength__greater__0__conv_1, cls_List_Orev__eq__Cons__iff_1, cls_Message_Oanalz__insert__Hash_0, cls_List_Ozip_Osimps__1_0, cls_Message_Oparts_OBody__dest_0, cls_Event_Oknows_Oknows__Nil_0, cls_List_Oappend__self__conv2_1, cls_Yahalom_OSpy__analz__shrK_1, cls_List_Otl__append2_0, cls_List_Olist__inter_Osimps__1_0, cls_List_Onth__append__length__plus_0, cls_List_Orev__singleton__conv_1, cls_Set_Oall__not__in__conv_0, cls_List_Orotate1__is__Nil__conv_1, cls_Set_Oinsert__iff_1, cls_Yahalom_Ounique__session__keys_2, cls_Public_OshrK__in__used_0, cls_Message_OHash__synth__analz_1, cls_Public_OMPair__used_0, cls_List_Obutlast_Osimps__1_0, cls_Public_OshrK__in__initState_0, cls_Public_OpublicKey__inject_0, cls_List_Oset__empty_0, cls_Yahalom_OSpy__analz__shrK_0, cls_Yahalom_OKeyWithNonce__Says_0, cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0, cls_Event_OkeysFor__synth_H_2, cls_List_Orev__replicate_0, cls_List_Olength__0__conv_0, cls_List_Oconcat_Osimps__1_0, cls_Wellfounded__Relations_Otrans__less__than_0, cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0, cls_Message_OMPair__analz_1, cls_Public_Onot__symKeys__pubK_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_List_ONil__is__rev__conv_1, cls_Message_Oin__parts__UnE_0, cls_List_Oappend1__eq__conv_0, cls_List_Oupt__eq__Nil__conv_0, cls_Message_OMPair__eq__HPair_0, cls_List_Oconcat__append_0, cls_List_Oop_A_64_Oappend__Cons_0, cls_Message_OkeysFor__insert__Nonce_0, cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0, cls_Message_OHPair__eq__MPair_1, cls_List_Olength__greater__0__conv_0, cls_Nat_Oadd__gr__0_0, cls_Datatype_Ooption_Osize__1_0, cls_List_Olist__update__beyond_0, cls_List_Oself__append__conv_0, cls_Set_OUn__insert__left_0, cls_List_Oappend__is__Nil__conv_0, cls_List_ONil__is__append__conv_1, cls_Set_OUn__insert__right_0, cls_Nat_Onot__add__less1_0, cls_Message_OkeysFor__insert__Crypt_0, cls_List_Olist_Odistinct__2_0, cls_Product__Type_OPair__eq_1, cls_Yahalom_OGets__imp__analz__Spy__dest_0, cls_Nat_Oadd__is__0_2, cls_List_Oset__replicate_0, cls_Public_Oanalz__spies__pubK_0, cls_List_Oappend__self__conv2_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_Message_OHPair__neqs__3_0, cls_List_Orev__append_0, cls_Event_OSays__imp__knows__Spy_0, cls_Message_Osynth_OCrypt_0, cls_Event_Oevent_Odistinct__2_0, cls_Message_OMPair__parts_1, cls_List_ONil__is__append__conv_2, cls_Public_OinvKey__shrK_0, cls_Message_ONonce__synth__eq_0, cls_Message_Osynth__synthD__dest_0, cls_Message_Omsg_Osize__1_0, clsarity_nat_12, cls_Message_OkeysFor__insert__Hash_0, cls_Public_OSpy__spies__bad__shrK_0, cls_List_Onot__Cons__self_0, cls_Set_OUn__iff_1, cls_Message_OkeysFor__insert__Number_0, cls_List_Orev__eq__Cons__iff_0, cls_Event_Oevent_Oinject__2_1, cls_Nat_Oadd__0__right_0, cls_Message_Oagent_Odistinct__4_0, cls_List_Osublist__singleton_1, cls_List_ONil__is__append__conv_0, cls_Message_Omsg_Osize__3_0, cls_List_OlistsE_1, cls_List_Olast__appendL_0, cls_Message_Oagent_Odistinct__6_0, cls_Event_Oevent_Oinject__1_1, cls_List_Onth__Cons__0_0, cls_List_Olist_Odistinct__1_0, cls_Set_Oempty__not__insert_0, cls_Wellfounded__Relations_Oless__than__iff_1, cls_List_Ohd__append2_0, cls_Nat_Onot__gr0_1, cls_Message_OHPair__neqs__1_0, cls_Yahalom_OKeyWithNonce__Says_1, cls_Nat_Onot__add__less2_0, cls_Message_Oagent_Osize__2_0, cls_Message_Oanalz__insert__MPair_0, cls_List_Ohd__upt_0, cls_List_Oset__append_0, cls_Public_OSpy__spies__bad__privateKey_0, cls_List_Onotin__set__sublistI_0, cls_Event_Oused__Says_0, cls_List_Onth__replicate_0, cls_List_Oappend__assoc_0, cls_Message_Oagent_Odistinct__2_0, cls_Message_Oanalz__insert__Number_0, cls_List_ONil__eq__concat__conv_2, cls_Yahalom_OKeyWithNonce__Gets_0, cls_Message_OinvKey__eq_0, cls_Yahalom_OKeyWithNonce__Says_3, cls_List_Olength__rev_0, cls_List_Ohd__in__set_0, cls_List_Oconcat__eq__Nil__conv_0, cls_List_Oappend__butlast__last__id_0, cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0, cls_Message_OHash__synth__analz_0, cls_List_Oappend__is__Nil__conv_1, cls_Set_OUn__empty__left_0, cls_Event_Oevent_Odistinct__1_0, cls_Set_OUn__empty__right_0, cls_Yahalom_Ounique__session__keys_1, cls_Message_Oanalz__parts_0, cls_Message_Oanalz__Crypt__if_1, cls_List_Olist__update__id_0, cls_Message_OMPair__synth_1, cls_Divides_Omod__less_0, cls_Public_OshrK__neq__pubK_0, cls_List_Olast__appendR_0, cls_Message_OCrypt__synth__eq_1, cls_List_Orev__singleton__conv_0, cls_List_Odrop_Odrop__Nil_0, cls_Event_Oevent_Odistinct__5_0, cls_List_Oset__rotate_0, cls_List_Oset__rev_0, cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0, cls_Divides_Omod__self_0, cls_Public_Ospies__pubK_0, cls_Message_Osynth_OInj_0, cls_List_Oset__empty_1, cls_List_Otl_Osimps__1_0, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Set_Ocontents__eq_0, cls_List_Ozip__Nil_0, cls_Message_OkeysFor__insert__MPair_0, cls_List_Osingleton__rev__conv_1, cls_Divides_ODIVISION__BY__ZERO__MOD_0, cls_Yahalom_OSays__Server__not__shrK_0, cls_List_Onth__list__update__eq_0, cls_List_Odrop__eq__Nil_0, cls_List_Oin__listsI_0, cls_Message_OMPair__analz_0, cls_Public_OprivateKey__into__used_0, cls_List_Oappend__in__lists__conv_0, cls_Message_OMPair__eq__HPair_1, cls_List_Oremove1_Osimps__1_0, cls_Message_Oanalz__analz__Un_0, cls_Public_OpublicKey__inject_1, cls_Event_OkeysFor__synth_H_1, cls_Yahalom_OKeyWithNonce__Gets_1, cls_Nat_Onat__add__left__cancel_0, cls_Message_Ostrange__Un__eq_0, cls_Map_Omap__of__zip__is__None_1, clsarity_nat_8, cls_Message_OkeysFor__insert__Key_0, cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0, cls_Message_OFake__parts__insert__in__Un__dest_0, cls_Message_Oparts__cut__eq_0, cls_Public_OpriEK__noteq__shrK_0, cls_Message_OKey__synth__eq_0, cls_Public_OpriK__in__initState_0, clsarity_nat_24, cls_Product__Type_OPair__eq_0, cls_List_Orev_Osimps__2_0, cls_List_Olexn_Osimps__1_0, cls_Message_Oanalz_ODecrypt__dest_0, cls_Message_OHPair__synth__analz_2, cls_List_Oin__listsD__dest_0, cls_List_Oself__append__conv2_1, cls_List_Olistset_Osimps__1_0, cls_List_Oappend__eq__append__conv_2, cls_List_Otake__eq__Nil_0, cls_Divides_Onat__mod__mod__trivial_0, cls_List_Oset__empty2_0, cls_Message_Oagent_Odistinct__5_0, cls_Public_OpublicKey__in__initState_0, cls_Message_OHPair__eq__MPair_2, cls_List_Osublist__empty_0, cls_Datatype_Oprod_Osize_0, cls_Event_Oevent_Osize__1_0, cls_Message_Omsg_Oinject__7_0, cls_List_Oremdups__eq__nil__right__iff_1, cls_Message_OMPair__parts_0, cls_Message_Omsg_Oinject__3_0, cls_Message_Oparts__analz_0, cls_Set_Oinsert__iff_0, cls_Nat_Oadd__gr__0_1, cls_Nat_Ole0_0, cls_List_Ozip__Cons__Cons_0, cls_List_Oset_Osimps__2_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__absorb2_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Set_OUn__empty_2, cls_Event_Oevent_Oinject__1_0, cls_Message_Oparts__emptyE_0, cls_Set_OUn__iff_2, cls_List_Olist__update__length_0, cls_Nat_Ole__0__eq_1, cls_Message_Oagent_Osize__1_0, cls_List_Owf__lenlex_0, cls_Yahalom_OSpy__see__shrK_1, cls_Public_ONonce__notin__used__empty_0, cls_Yahalom_Onew__keys__not__used_0, cls_List_Oremove1_Osimps__2_0, cls_Message_OMPair__eq__HPair_2, cls_Message_OMPair__synth__analz_0, cls_List_Oappend__take__drop__id_0, cls_List_Olength__rotate1_0, cls_List_ONil__eq__concat__conv_0, cls_List_Odrop__upt_0, cls_List_Oset__rotate1_0, cls_Public_OsymKeys__invKey__iff_1, cls_Divides_Omod__0_0, cls_Message_Oparts__idem_0, cls_Wellfounded__Relations_Oless__than__iff_0, cls_Yahalom_OGets__imp__Says_0, cls_Message_OMPair__synth_0, cls_Message_OHPair__neqs__4_0, cls_List_Orotate__id_0, cls_List_Oappend__is__Nil__conv_2, cls_List_Osublist__singleton_0, cls_Message_OHPair__eq_1, cls_Event_Oknows__Spy__Gets_0, cls_List_Odrop__drop_0, cls_Public_OshrK__in__knows_0, cls_List_Onth__take_0, cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0, cls_Set_OUn__absorb_0, cls_Message_OMPair__synth__analz_1, cls_List_Olists_OCons_0, cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0, cls_List_Oremdups_Osimps__2_1, cls_List_Orotate__is__Nil__conv_1, cls_List_Olast__drop_0
% 9.59/3.12  % No. of inferences in proof: 961
% 9.59/3.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2603 ms resp. 1939 ms w/o parsing
% 10.27/3.27  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.27/3.28  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------