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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV319-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:58:55 AM UTC 2026

% Result   : Unsatisfiable 15.08s 5.84s
% Output   : Refutation 16.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  435
% Syntax   : Number of formulae    :  871 ( 435 unt;   0 typ;   0 def)
%            Number of atoms       : 1389 ( 800 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 7694 ( 538   ~; 518   |;   0   &;6638   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   92 (  90 usr;  22 con; 0-4 aty)
%            Number of variables   : 2246 (   0   ^;2246   !;   0   ?;2246   :)

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

thf(v_evso_decl,type,
    v_evso: $i ).

thf(c_OtwayRees_Ootway_decl,type,
    c_OtwayRees_Ootway: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_0_decl,type,
    c_0: $i ).

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

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

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

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

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

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

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

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

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

thf(c_List_Orotate1_decl,type,
    c_List_Orotate1: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

thf(c_List_Oremove1_decl,type,
    c_List_Oremove1: $i > $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Main_ONil__eq__concat__conv__1_decl,type,
    c_Main_ONil__eq__concat__conv__1: $i > $i > $i ).

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

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

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

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

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

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

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

thf(c_Main_Oconcat__eq__Nil__conv__1_decl,type,
    c_Main_Oconcat__eq__Nil__conv__1: $i > $i > $i ).

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

thf(c_Main_Oin__listsI__1_decl,type,
    c_Main_Oin__listsI__1: $i > $i > $i > $i ).

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

thf(v_sko__usf_decl,type,
    v_sko__usf: $i > $i > $i > $i ).

thf(c_Main_Oall__not__in__conv__1_decl,type,
    c_Main_Oall__not__in__conv__1: $i > $i > $i ).

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

thf(188,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ( ( B @ ( D @ ( A @ c_append ) ) )
       != ( B @ ( E @ ( C @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).

thf(892,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ( ( B @ ( D @ ( A @ c_append ) ) )
       != ( B @ ( E @ ( C @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(359,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__2_0) ).

thf(1322,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(245,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).

thf(1036,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_0 @ ( A @ c_List_Olexn ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OKey )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__4_0) ).

thf(1411,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OKey )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).

thf(629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_append ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OKey ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AKey_AK2_A_61_61_AFalse_0) ).

thf(1369,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq_0) ).

thf(1105,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(356,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( A @ c_Message_Oagent_OFriend ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).

thf(1315,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OSpy
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
        = ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_insert ) ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_0) ).

thf(1179,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
        = ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_insert ) ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(144,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).

thf(777,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).

thf(1110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
        = B )
      | ( A = c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).

thf(481,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Ohd ) )
        = B )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(434,axiom,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OServer_A_58_Abad_A_61_61_AFalse_0) ).

thf(1501,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(156,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) )
      | ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).

thf(809,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) )
      | ( tc_nat @ ( B @ c_Message_Oanalz @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).

thf(909,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(243,axiom,
    ! [A: $i] :
      ( ( A @ tc_Datatype_Ooption @ ( c_Datatype_Ooption_ONone @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).

thf(1031,plain,
    ! [A: $i] :
      ( ( A @ tc_Datatype_Ooption @ ( c_Datatype_Ooption_ONone @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(215,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).

thf(962,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orev ) @ c_Nat_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).

thf(468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONumber )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__3_0) ).

thf(666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONumber )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_2) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(222,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) @ c_List_Olast ) )
      = ( B @ ( A @ c_List_Olast ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__appendL_0) ).

thf(977,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) @ c_List_Olast ) )
      = ( B @ ( A @ c_List_Olast ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_1) ).

thf(1406,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(124,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_append ) ) @ c_List_Olast ) )
        = ( C @ ( A @ c_List_Olast ) ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_append ) ) @ c_List_Olast ) )
        = ( C @ ( A @ c_List_Olast ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
        = ( B @ c_Message_Oanalz @ c_Message_Osynth ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__analz__eq_0) ).

thf(1068,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
        = ( B @ c_Message_Oanalz @ c_Message_Osynth ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(389,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).

thf(1401,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(400,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriK__in__initState_0) ).

thf(1422,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).

thf(873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).

thf(1269,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( C @ ( B @ ( D @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).

thf(1437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( C @ ( B @ ( D @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

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

thf(741,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize ) )
      = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(259,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__neq__privateKey_0) ).

thf(1073,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( D @ ( C @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(7,negated_conjecture,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
    | ( ( v_A @ c_Public_OshrK )
      = v_K ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(440,plain,
    ( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
    | ( ( v_A @ c_Public_OshrK )
      = v_K ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(96,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).

thf(655,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olist__update ) ) ) )
      = ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_insert ) ) @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_0) ).

thf(1305,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_insert ) ) @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).

thf(597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_2) ).

thf(1041,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONonce @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).

thf(861,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONonce @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(432,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).

thf(1497,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_1) ).

thf(1426,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).

thf(1310,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Otl ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).

thf(550,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Otl ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).

thf(500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts @ c_Message_OkeysFor )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OkeysFor__parts__initState_0) ).

thf(715,plain,
    ! [A: $i] :
      ( ( A @ c_Event_OinitState @ c_Message_Oparts @ c_Message_OkeysFor )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).

thf(472,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(325,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ACrypt_AK2_AX_H2_A_61_61_AFalse_0) ).

thf(1233,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_1) ).

thf(913,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(208,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_append ) ) )
        = A )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).

thf(945,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_append ) ) )
        = A )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(255,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).

thf(1063,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(371,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/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(1354,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).

thf(1222,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oanalz )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(416,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).

thf(1458,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OAgent @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).

thf(814,plain,
    ! [A: $i] :
      ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(361,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_2) ).

thf(1327,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).

thf(1196,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( C @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( D @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(190,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).

thf(898,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpubK__neq__shrK_0) ).

thf(1243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__2_0) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_ONonce )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).

thf(782,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize ) )
      = ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).

thf(709,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).

thf(1475,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(5,negated_conjecture,
    ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
    | ( tc_Message_Omsg @ ( v_evso @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(436,plain,
    ( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
    | ( tc_Message_Omsg @ ( v_evso @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(336,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).

thf(1265,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(427,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( E @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
        = c_Datatype_Ooption_ONone )
      | ( B @ ( B @ ( A @ c_List_Oset ) @ ( E @ c_in ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).

thf(1482,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( E @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
        = c_Datatype_Ooption_ONone )
      | ( B @ ( B @ ( A @ c_List_Oset ) @ ( E @ c_in ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
      = ( A @ c_Message_Oanalz ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).

thf(973,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
      = ( A @ c_Message_Oanalz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).

thf(885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( D @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(60,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( E @ ( A @ ( B @ c_List_Olist__update ) ) ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).

thf(565,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
        = ( C @ ( E @ ( A @ ( B @ c_List_Olist__update ) ) ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(375,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oparts )
        = ( B @ c_Message_Oparts ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).

thf(1366,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( A @ c_insert ) ) @ c_Message_Oparts )
        = ( B @ c_Message_Oparts ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Obutlast ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).

thf(570,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Obutlast ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_0) ).

thf(719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OAgent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).

thf(504,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(133,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).

thf(751,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_0) ).

thf(802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A
        = ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(415,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__5_0) ).

thf(1455,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OSpy ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(49,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).

thf(542,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orotate1 ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).

thf(1059,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orotate1 ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(281,axiom,
    ( ( c_emptyset @ c_Message_Oparts )
    = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).

thf(1132,plain,
    ( ( c_emptyset @ c_Message_Oparts )
    = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(91,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).

thf(638,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OHash )
       != ( B @ c_Message_Omsg_OHash ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).

thf(1087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(181,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
        = ( B @ ( A @ c_List_Oconcat ) ) )
      | ( ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).

thf(870,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
        = ( B @ ( A @ c_List_Oconcat ) ) )
      | ( ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

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

thf(770,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(388,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ c_List_Oconcat ) )
       != c_List_Olist_ONil )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_0) ).

thf(1398,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ c_List_Oconcat ) )
       != c_List_Olist_ONil )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).

thf(1100,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Oagent_OFriend )
       != ( B @ c_Message_Oagent_OFriend ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).

thf(606,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Osublist ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).

thf(1347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Osublist ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(396,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).

thf(1415,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(17,axiom,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).

thf(475,plain,
    tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(135,axiom,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).

thf(756,plain,
    ! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( A @ c_List_Osublist ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).

thf(591,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ ( A @ c_List_Osublist ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(84,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
      = ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_2) ).

thf(623,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
      = ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__MPair_0) ).

thf(1136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(289,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_1) ).

thf(1151,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(217,axiom,
    ( ( tc_nat @ ( c_0 @ c_SetInterval_OatMost ) )
    = ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).

thf(966,plain,
    ( ( tc_nat @ ( c_0 @ c_SetInterval_OatMost ) )
    = ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(343,axiom,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0) ).

thf(1283,plain,
    tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Oanalz @ c_union ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).

thf(821,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Oanalz @ c_union ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__priK_0) ).

thf(905,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).

thf(1334,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(93,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orev ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_0) ).

thf(646,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orev ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_1) ).

thf(1383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(238,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).

thf(1020,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
      = ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).

thf(634,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( tc_Message_Oagent @ ( A @ c_Message_Oagent_OFriend @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).

thf(692,plain,
    ! [A: $i] :
      ( ( tc_Message_Oagent @ ( A @ c_Message_Oagent_OFriend @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(411,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).

thf(1447,plain,
    ! [B: $i,A: $i] :
      ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(386,axiom,
    ( ( tc_Message_Oagent @ ( c_Message_Oagent_OServer @ c_Nat_Osize ) )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).

thf(1394,plain,
    ( ( tc_Message_Oagent @ ( c_Message_Oagent_OServer @ c_Nat_Osize ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).

thf(1351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(226,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_0) ).

thf(988,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).

thf(1201,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize ) )
      = ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).

thf(602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize ) )
      = ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(224,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq_1) ).

thf(981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_OHPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(296,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
       != ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) ) )
      | ( ( E @ ( C @ ( A @ ( E @ ( C @ ( D @ ( B @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
       != c_Datatype_Ooption_ONone )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).

thf(1169,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
       != ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) ) )
      | ( ( E @ ( C @ ( A @ ( E @ ( C @ ( D @ ( B @ c_List_Ozip ) ) ) @ c_Map_Omap__of ) ) ) )
       != c_Datatype_Ooption_ONone )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

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

thf(687,plain,
    ( ( c_emptyset @ c_Message_Oanalz )
    = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(311,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_0) ).

thf(1206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(2,negated_conjecture,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evso @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(439,plain,
    tc_Event_Oevent @ ( tc_Event_Oevent @ ( v_evso @ c_List_Oset ) @ ( v_K @ c_Message_Omsg_OKey @ ( v_NB @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( v_X @ c_Message_Omsg_OMPair ) @ ( v_NA @ c_Message_Omsg_ONonce @ c_Message_Omsg_OMPair ) @ ( v_B @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
      = ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).

thf(661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oconcat ) )
      = ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(138,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( D @ ( C @ ( F @ c_append ) ) @ ( B @ ( A @ ( E @ c_append ) ) @ c_List_Ozip ) ) ) )
        = ( D @ ( B @ tc_prod ) @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ ( D @ ( B @ ( F @ ( E @ c_List_Ozip ) ) ) @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
       != ( D @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).

thf(761,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( D @ ( C @ ( F @ c_append ) ) @ ( B @ ( A @ ( E @ c_append ) ) @ c_List_Ozip ) ) ) )
        = ( D @ ( B @ tc_prod ) @ ( D @ ( B @ ( C @ ( A @ c_List_Ozip ) ) ) @ ( D @ ( B @ ( F @ ( E @ c_List_Ozip ) ) ) @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
       != ( D @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( D @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).

thf(1470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).

thf(534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__MPair_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ ( A @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
      = ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).

thf(546,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) @ c_Divides_Oop_Amod ) ) )
      = ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(150,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).

thf(793,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).

thf(1274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ~ ( B @ ( A @ ( D @ c_in ) ) )
      | ~ ( B @ ( A @ ( C @ c_in ) ) )
      | ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).

thf(1387,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_union ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).

thf(957,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__2_0) ).

thf(1255,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oagent_OFriend )
     != c_Message_Oagent_OServer ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).

thf(1174,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(317,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).

thf(1217,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oconcat ) )
        = c_List_Olist_ONil )
      | ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).

thf(1238,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oconcat ) )
        = c_List_Olist_ONil )
      | ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(131,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( D @ ( A @ c_append ) ) )
       != ( B @ ( E @ ( C @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).

thf(746,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( D @ ( A @ c_append ) ) )
       != ( B @ ( E @ ( C @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_2) ).

thf(1091,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_OHPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( C @ c_Public_OshrK ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__neq__pubK_0) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) )
     != ( C @ c_Public_OshrK ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(85,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).

thf(625,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(172,axiom,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OKey @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).

thf(852,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OKey @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Obutlast ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).

thf(1027,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Obutlast ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(136,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_0) ).

thf(757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

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

thf(682,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(279,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).

thf(1128,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_ONumber @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__3_0) ).

thf(842,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
       != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(235,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_0) ).

thf(1012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(170,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).

thf(847,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
       != ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(21,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).

thf(484,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_List_Odistinct ) )
      | ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

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

thf(583,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Otl ) )
        = ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_append ) ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).

thf(522,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONumber ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANumber_AN2_A_61_61_AFalse_0) ).

thf(830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONumber ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(291,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( C @ c_Event_Oused ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oused__Gets_0) ).

thf(1159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( C @ c_Event_Oused ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(12,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).

thf(461,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(25,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).

thf(493,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
      | ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(313,axiom,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__emptyE_0) ).

thf(1210,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_emptyset @ c_Message_Oparts @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olast ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).

thf(1089,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Olast ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(286,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
      = ( B @ ( A @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__eq__HPair_2) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_Message_Omsg_OMPair ) )
      = ( B @ ( A @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).

thf(948,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oanalz @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(378,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).

thf(1375,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).

thf(1227,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).

thf(725,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Oset ) )
      = ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).

thf(1096,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Oset ) )
      = ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ c_List_Oset ) @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
      = ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).

thf(1138,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
      = ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(71,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).

thf(593,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(37,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).

thf(519,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).

thf(578,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(23,axiom,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).

thf(488,plain,
    ( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(373,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).

thf(1361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).

thf(933,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(301,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).

thf(1182,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_1) ).

thf(1461,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).

thf(669,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).

thf(1214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B )
      | ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).

thf(679,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
        = B )
      | ( ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_Divides_Oop_Amod ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Gets_0) ).

thf(1419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).

thf(554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
        = ( C @ ( A @ c_List_Olast ) ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).

thf(753,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
        = ( C @ ( A @ c_List_Olast ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_append ) ) @ c_Nat_Osize ) )
      = ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).

thf(901,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_append ) ) @ c_Nat_Osize ) )
      = ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).

thf(476,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(395,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__knows_0) ).

thf(1414,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_nat @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Onth ) ) )
      = ( C @ ( D @ ( B @ c_List_Onth ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).

thf(526,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_nat @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_plus ) ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Onth ) ) )
      = ( C @ ( D @ ( B @ c_List_Onth ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( C @ ( B @ ( A @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).

thf(1114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_emptyset
     != ( C @ ( B @ ( A @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).

thf(701,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(35,axiom,
    ! [A: $i] : ( A @ ( c_List_Olist_ONil @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).

thf(515,plain,
    ! [A: $i] : ( A @ ( c_List_Olist_ONil @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(349,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).

thf(1297,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).

thf(1231,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).

thf(457,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
      | ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).

thf(911,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).

thf(1002,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Orev ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(403,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_OkeysFor )
      = ( C @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).

thf(1429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_insert ) ) @ c_Message_OkeysFor )
      = ( C @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(330,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).

thf(1246,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONonce )
       != ( B @ c_Message_Omsg_ONonce ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Message_OinvKey )
        = A )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).

thf(779,plain,
    ! [A: $i] :
      ( ( ( A @ c_Message_OinvKey )
        = A )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(335,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz_0) ).

thf(1263,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).

thf(997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).

thf(1318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_append ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).

thf(938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_append ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).

thf(1241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).

thf(805,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(508,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_0 @ ( A @ c_plus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_0) ).

thf(921,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(48,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).

thf(541,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_append ) ) @ c_List_Oconcat ) )
      = ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( C @ ( A @ c_List_Oconcat ) @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).

thf(657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ tc_List_Olist @ ( B @ ( A @ c_append ) ) @ c_List_Oconcat ) )
      = ( C @ ( C @ ( B @ c_List_Oconcat ) @ ( C @ ( A @ c_List_Oconcat ) @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(345,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__1_0) ).

thf(1286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).

thf(1167,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( c_0 @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).

thf(530,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( c_0 @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onth ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

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

thf(586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Olast ) )
        = B )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).

thf(926,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__HPair_0) ).

thf(1466,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).

thf(558,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONumber @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).

thf(1071,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_ONumber @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(34,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).

thf(513,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D = B )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_1) ).

thf(1219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D = B )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_List_Osublist ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).

thf(856,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_List_Osublist ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

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

thf(689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Osublist ) ) )
        = c_List_Olist_ONil )
      | ( tc_nat @ ( A @ ( c_0 @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Oset ) @ ( C @ c_in ) ) )
      | ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).

thf(733,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Oset ) @ ( C @ c_in ) ) )
      | ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(331,axiom,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__notin__used__empty_0) ).

thf(1251,plain,
    ! [A: $i] :
      ~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(82,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ c_union ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).

thf(618,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ c_union ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(384,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__notin__initState_0) ).

thf(1389,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

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

thf(772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( A @ ( B @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

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

thf(743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oset ) )
        = ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
      | ( A = c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(390,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).

thf(1403,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONumber @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oconcat ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).

thf(1124,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oconcat ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(59,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).

thf(562,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).

thf(975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(233,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( D @ c_append ) ) )
       != ( B @ ( C @ ( E @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).

thf(1007,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ ( D @ c_append ) ) )
       != ( B @ ( C @ ( E @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(111,axiom,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).

thf(694,plain,
    ! [A: $i] :
      ( c_emptyset
      = ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_OinvKey )
       != ( B @ c_Message_OinvKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).

thf(875,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_OinvKey )
       != ( B @ c_Message_OinvKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Osublist ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).

thf(826,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Osublist ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(435,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).

thf(1503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(63,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( B @ ( E @ ( D @ ( A @ ( C @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
        = ( E @ ( B @ ( C @ c_List_Onth ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).

thf(572,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( B @ ( E @ ( D @ ( A @ ( C @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
        = ( E @ ( B @ ( C @ c_List_Onth ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).

thf(611,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
      = ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).

thf(498,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
      = ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).

thf(1332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(13,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).

thf(466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(320,axiom,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__initState_0) ).

thf(1224,plain,
    ! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).

thf(1356,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Public_OshrK )
       != ( B @ c_Public_OshrK ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__injective_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Public_OshrK )
       != ( B @ c_Public_OshrK ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).

thf(704,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__6_0) ).

thf(1408,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
     != ( D @ ( C @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(342,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__in__initState_0) ).

thf(1282,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(369,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__shrK_0) ).

thf(1349,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_1) ).

thf(990,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ c_List_Oconcat ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).

thf(1492,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ c_List_Oconcat ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ ( A @ c_List_Olist__update ) ) ) )
        = A )
      | ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).

thf(599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( C @ ( A @ c_List_Olist__update ) ) ) )
        = A )
      | ~ ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).

thf(863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

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

thf(764,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_insert ) ) )
     != c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_OkeysFor )
      = ( tc_nat @ ( C @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).

thf(979,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_OkeysFor )
      = ( tc_nat @ ( C @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).

thf(604,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( C @ c_List_Oremove1 ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Onot__symKeys__pubK_0) ).

thf(784,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( c_Message_OsymKeys @ ( B @ ( A @ c_Public_OpublicKey ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv_0) ).

thf(1117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( A
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__2_0) ).

thf(1048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Event_Oevent_OGets ) )
       != ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

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

thf(736,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_List_Otl ) @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) )
        = A )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
      = ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).

thf(880,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
      = ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).

thf(649,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).

thf(1043,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(81,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).

thf(616,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(276,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_0) ).

thf(1122,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(187,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).

thf(890,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(365,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).

thf(1339,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
       != ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_OkeysFor )
      = ( C @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__HPair_0) ).

thf(816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_OkeysFor )
      = ( C @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
      = ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).

thf(520,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Divides_Oop_Amod ) ) )
      = ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(360,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).

thf(1325,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).

thf(964,plain,
    ! [A: $i] :
      ( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
      = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(366,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).

thf(1344,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Says_0) ).

thf(1293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
      = ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(254,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_3) ).

thf(1061,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_Message_OinvKey @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(175,axiom,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).

thf(858,plain,
    ! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_0 @ c_List_Oreplicate ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).

thf(552,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_0 @ c_List_Oreplicate ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oused__Notes_0) ).

thf(1029,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).

thf(895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).

thf(943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).

thf(1022,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
       != ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

thf(959,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Onth ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).

thf(636,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) @ c_List_Onth ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).

thf(1445,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oparts @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).

thf(455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
      | ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Ohd ) )
        = ( C @ ( A @ c_List_Ohd ) ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).

thf(1015,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Ohd ) )
        = ( C @ ( A @ c_List_Ohd ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).

thf(986,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(272,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).

thf(1113,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(425,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).

thf(1477,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(6,negated_conjecture,
    ( ( ( v_A @ c_Public_OshrK )
     != v_K )
    | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(438,plain,
    ( ( ( v_A @ c_Public_OshrK )
     != v_K )
    | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( B @ ( D @ c_List_Olist__inter ) ) ) )
      | ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).

thf(1198,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
        = ( C @ ( B @ ( D @ c_List_Olist__inter ) ) ) )
      | ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_1) ).

thf(1396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Ohd ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).

thf(1176,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Ohd ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( A @ ( B @ c_List_Olist__update ) ) ) )
        = B )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).

thf(608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( A @ ( B @ c_List_Olist__update ) ) ) )
        = B )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(230,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).

thf(1000,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(406,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).

thf(1435,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONumber )
       != ( B @ c_Message_Omsg_ONumber ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).

thf(1076,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_ONumber )
       != ( B @ c_Message_Omsg_ONumber ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(24,axiom,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).

thf(490,plain,
    ! [B: $i,A: $i] :
      ( ( B = c_0 )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).

thf(795,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OAgent )
       != ( B @ c_Message_Omsg_OAgent ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(340,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__Crypt__if_1) ).

thf(1277,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) @ c_Message_Oanalz )
        = ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_insert ) ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_append ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).

thf(1134,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_append ) ) @ c_List_Orev ) )
      = ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).

thf(812,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
      | ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
        = D )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).

thf(516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( D @ ( A @ ( B @ c_List_Olist__update ) ) ) @ c_List_Onth ) ) )
        = D )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(423,axiom,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
        = ( B @ ( A @ c_List_Oconcat ) ) )
      | ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).

thf(1472,plain,
    ! [B: $i,A: $i] :
      ( ( c_List_Olist_ONil
        = ( B @ ( A @ c_List_Oconcat ) ) )
      | ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_Main_ONil__eq__concat__conv__1 ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(167,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__6_0) ).

thf(836,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Ospies__pubK_0) ).

thf(1203,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).

thf(1208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

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

thf(589,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_Divides_Oop_Amod ) ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
       != ( B @ ( C @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).

thf(548,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( C @ c_Public_OshrK ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__neq__priK_0) ).

thf(1081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( C @ c_Public_OshrK ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(132,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).

thf(749,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(287,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__eq__MPair_0) ).

thf(1145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash ) )
      | ( ( B @ ( A @ c_Message_OHPair ) )
       != ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OAgent @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).

thf(1018,plain,
    ! [A: $i] :
      ( ( tc_Message_Omsg @ ( A @ c_Message_Omsg_OAgent @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(218,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).

thf(968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
        = ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__5_0) ).

thf(823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OHash )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(117,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(240,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).

thf(1025,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( B @ ( A @ c_List_Oremdups ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).

thf(1156,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( B @ ( A @ c_List_Oremdups ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__synth__analz_1) ).

thf(971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_OHPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

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

thf(739,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).

thf(1267,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_in ) ) )
      | ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).

thf(1098,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_append ) ) @ c_List_Orev ) )
      = ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_1) ).

thf(1225,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(115,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).

thf(707,plain,
    ! [A: $i] :
      ( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).

thf(673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
      | ( ( B @ ( A @ c_List_Orev ) )
       != ( B @ ( c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(405,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__1_0) ).

thf(1432,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(351,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__4_0) ).

thf(1300,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
      = ( C @ ( A @ ( B @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).

thf(791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ ( B @ c_union ) ) @ ( A @ c_union ) ) )
      = ( C @ ( A @ ( B @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(3,negated_conjecture,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(441,plain,
    ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).

thf(1038,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__inter ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).

thf(717,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Olist__inter ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).

thf(502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(15,axiom,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).

thf(470,plain,
    ~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

thf(1130,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_1) ).

thf(1053,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
        = ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) )
      | ( ( B @ ( A @ c_List_Oremdups ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(433,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).

thf(1499,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Oset ) )
      = ( B @ ( A @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(304,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_0) ).

thf(1188,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).

thf(1186,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
      = ( A @ c_Message_Oparts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
        = ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows__Spy__Notes_1) ).

thf(1336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
        = ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) )
      | ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(92,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).

thf(643,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oremdups ) )
        = A )
      | ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).

thf(544,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_Divides_Oop_Amod ) ) @ c_less ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(194,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_1) ).

thf(907,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).

thf(1404,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).

thf(613,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).

thf(1284,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(428,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OKey )
       != ( B @ c_Message_Omsg_OKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).

thf(1485,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Message_Omsg_OKey )
       != ( B @ c_Message_Omsg_OKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oconcat ) )
        = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).

thf(1140,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_List_Oconcat ) )
        = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_Main_Oconcat__eq__Nil__conv__1 ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(176,axiom,
    ( ( c_emptyset @ c_Message_OkeysFor )
    = c_emptyset ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).

thf(859,plain,
    ( ( c_emptyset @ c_Message_OkeysFor )
    = c_emptyset ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(377,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3_0) ).

thf(1372,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).

thf(595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(399,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey__into__used_0) ).

thf(1421,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
      = ( C @ ( B @ ( A @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).

thf(627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
      = ( C @ ( B @ ( A @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).

thf(1459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).

thf(556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).

thf(671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).

thf(903,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OHash @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(26,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
        = ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
      | ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).

thf(495,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
        = ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
      | ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).

thf(759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(316,axiom,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK__in__used_0) ).

thf(1216,plain,
    ! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(278,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).

thf(1126,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(234,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
      = ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_1) ).

thf(1010,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
      = ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(414,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__partsD__dest_0) ).

thf(1453,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(8,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).

thf(450,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
       != ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__5_0) ).

thf(1084,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_OGets ) )
     != ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( C @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oused__Says_0) ).

thf(931,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
      = ( tc_Message_Omsg @ ( D @ c_Event_Oused @ ( tc_Message_Omsg @ ( c_emptyset @ ( C @ c_insert ) ) @ c_Message_Oparts @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).

thf(539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).

thf(524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ c_List_Odistinct ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

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

thf(581,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Amod ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(332,axiom,
    ( ( tc_Message_Oagent @ ( c_Message_Oagent_OSpy @ c_Nat_Osize ) )
    = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).

thf(1253,plain,
    ( ( tc_Message_Oagent @ ( c_Message_Oagent_OSpy @ c_Nat_Osize ) )
    = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(382,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).

thf(1385,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(95,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).

thf(652,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Oset ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).

thf(632,plain,
    ! [A: $i] :
      ( ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__inject_1) ).

thf(786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Public_OpublicKey ) )
       != ( D @ ( C @ c_Public_OpublicKey ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
      = ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).

thf(568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
      = ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).

thf(510,plain,
    ! [A: $i] :
      ( ( A = c_0 )
      | ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Oset ) )
      = ( C @ ( B @ c_List_Oset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).

thf(1308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Oset ) )
      = ( C @ ( B @ c_List_Oset ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( B @ c_List_Oremdups ) ) )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).

thf(1193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
        = ( C @ ( B @ c_List_Oremdups ) ) )
      | ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ c_List_Onth ) ) )
        = C )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).

thf(478,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ c_List_Onth ) ) )
        = C )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).

thf(1212,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(409,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__4_0) ).

thf(1442,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
     != ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(46,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
        = A )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).

thf(536,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Oop_Amod ) ) )
        = A )
      | ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(249,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OprivateKey_Ab1_AA1_A_61_ApublicKey_Ac1_AA_H1_A_61_61_AFalse_0) ).

thf(1045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( D @ ( C @ c_Public_OpublicKey ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).

thf(1440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
      = ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).

thf(929,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
      = ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).

thf(1161,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OsymKeys__invKey__iff_1) ).

thf(800,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Message_OinvKey @ c_in ) ) )
      | ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHPair__neqs__1_0) ).

thf(620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Message_Omsg_OAgent )
     != ( C @ ( B @ c_Message_OHPair ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(341,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).

thf(1280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
      | ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(166,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( B @ c_Public_OshrK ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpriEK__noteq__shrK_0) ).

thf(833,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( c_Public_Okeymode_OEncryption @ c_Public_OpublicKey ) @ c_Message_OinvKey )
     != ( B @ c_Public_OshrK ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(210,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).

thf(950,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OSpy__spies__bad__privateKey_0) ).

thf(1229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
      | ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_AHash_AZ2_A_61_61_AFalse_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_OHash ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash_91X2_93_AY2_A_61_ANonce_AN2_A_61_61_AFalse_0) ).

thf(1380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Message_OHPair ) )
     != ( C @ c_Message_Omsg_ONonce ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ( ( B @ ( A @ ( D @ c_append ) ) )
       != ( B @ ( C @ ( E @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).

thf(1148,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = E )
      | ( ( B @ ( A @ ( D @ c_append ) ) )
       != ( B @ ( C @ ( E @ c_append ) ) ) )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != ( B @ tc_List_Olist @ ( C @ c_Nat_Osize ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).

thf(867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_insert ) ) )
       != ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(126,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).

thf(735,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).

thf(854,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__usf ) ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OGets__imp__Says__dest_0) ).

thf(1303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ ( A @ ( C @ ( B @ v_sko__usf ) ) @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(179,axiom,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).

thf(865,plain,
    ! [A: $i] :
      ( c_List_Olist_ONil
      = ( A @ ( c_List_Olist_ONil @ c_List_Oremdups ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).

thf(1480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).

thf(918,plain,
    ! [C: $i,B: $i,A: $i] :
      ( c_List_Olist_ONil
     != ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(374,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Odistinct__3_0) ).

thf(1363,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
     != ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(431,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).

thf(1495,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_insert ) ) @ c_Message_OkeysFor )
      = ( B @ c_Message_OkeysFor ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).

thf(506,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(155,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).

thf(807,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(1,negated_conjecture,
    tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evso @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(437,plain,
    tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( v_evso @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(252,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Osublist ) ) )
        = ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).

thf(1056,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Osublist ) ) )
        = ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) ) )
      | ~ ( tc_nat @ ( A @ ( c_0 @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__HPair_0) ).

thf(828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_insert ) ) @ ( B @ ( A @ c_Message_OHPair ) @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).

thf(960,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).

thf(696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( C @ ( B @ ( A @ c_append ) ) )
       != ( C @ ( B @ ( D @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(294,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OOR2__parts__knows__Spy__dest_0) ).

thf(1165,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( E @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( A @ c_List_Oset ) @ ( E @ ( B @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OAgent @ c_Message_Omsg_OMPair ) @ ( C @ c_Message_Omsg_OMPair ) @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
      | ~ ( tc_Event_Oevent @ tc_List_Olist @ ( c_OtwayRees_Ootway @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).

thf(955,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
      = c_List_Olist_ONil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Oanalz__spies__pubK_0) ).

thf(1346,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).

thf(1172,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

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

thf(767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Public_OshrK )
     != ( C @ ( B @ c_Public_OpublicKey ) @ c_Message_OinvKey ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).

thf(1033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(346,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Oinject__1_1) ).

thf(1288,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
       != ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).

thf(532,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( B @ ( A @ c_List_Orev ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).

thf(1065,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( B @ ( A @ c_List_Orev ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(123,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__3_0) ).

thf(728,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OHash__synth__analz_0) ).

thf(1236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Message_Omsg_OHash @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
        = ( C @ ( C @ ( A @ c_List_Obutlast ) @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( A = c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).

thf(575,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
        = ( C @ ( C @ ( A @ c_List_Obutlast ) @ ( B @ c_List_Olist_OCons ) ) ) )
      | ( A = c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(379,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).

thf(1378,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).

thf(528,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ c_in ) ) )
      | ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(11,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).

thf(459,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
      = ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).

thf(992,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
       != ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_append ) ) @ c_append ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_append ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).

thf(850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ ( B @ ( A @ c_append ) ) @ c_append ) ) )
      = ( C @ ( C @ ( D @ ( B @ c_append ) ) @ ( A @ c_append ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(350,axiom,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OshrK_AX1_A_58_AsymKeys_A_61_61_ATrue_0) ).

thf(1299,plain,
    ! [A: $i] : ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_Public_OshrK @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(4,negated_conjecture,
    ( ~ ( tc_Message_Omsg @ ( v_evso @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
    | ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(442,plain,
    ( ~ ( tc_Message_Omsg @ ( v_evso @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( v_A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
    | ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(275,axiom,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
      = ( A @ c_Event_OinitState ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oknows_Oknows__Nil_0) ).

thf(1120,plain,
    ! [A: $i] :
      ( ( c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
      = ( A @ c_Event_OinitState ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(266,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orotate1 ) )
       != c_List_Olist_ONil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).

thf(1093,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ ( A @ c_List_Orotate1 ) )
       != c_List_Olist_ONil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).

thf(839,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( c_emptyset
       != ( B @ ( A @ c_List_Oset ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(404,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OpublicKey__into__used_0) ).

thf(1431,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Public_OpublicKey ) @ c_Message_Omsg_OKey @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(232,axiom,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).

thf(1004,plain,
    ! [B: $i,A: $i] :
      ( ( A = c_List_Olist_ONil )
      | ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
       != c_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).

thf(486,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
      | ~ ( B @ ( A @ c_List_Odistinct ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(358,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OMPair__used_1) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).

thf(940,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = c_List_Olist_ONil )
      | ( c_List_Olist_ONil
       != ( C @ ( B @ ( A @ c_append ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(302,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).

thf(1184,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) @ c_Message_Oparts )
      = ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OAgent @ c_insert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).

thf(676,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(421,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).

thf(1468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
      | ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).

thf(882,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = c_emptyset )
      | ( ( C @ ( B @ ( A @ c_union ) ) )
       != c_emptyset ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).

thf(1417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
      | ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(419,axiom,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).

thf(1463,plain,
    ! [A: $i] :
      ( c_Message_Oagent_OServer
     != ( A @ c_Message_Oagent_OFriend ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_Nat_Osize ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oevent_Osize__2_0) ).

thf(659,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Event_Oevent @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_Nat_Osize ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(429,axiom,
    ! [A: $i] :
      ( ( A @ c_Public_OshrK @ c_Message_OinvKey )
      = ( A @ c_Public_OshrK ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OinvKey__shrK_0) ).

thf(1490,plain,
    ! [A: $i] :
      ( ( A @ c_Public_OshrK @ c_Message_OinvKey )
      = ( A @ c_Public_OshrK ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__synth_0) ).

thf(775,plain,
    ! [A: $i] :
      ( ( A @ c_Message_Osynth @ c_Message_Oanalz )
      = ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_union ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
      = c_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).

thf(560,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Amod ) ) )
      = c_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(310,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__analzD__dest_0) ).

thf(1204,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
      | ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(412,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OCrypt__notin__used__empty_0) ).

thf(1449,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_Message_Omsg @ ( c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(1560,plain,
    $false,
    inference(e,[status(thm)],[892,1322,1036,1411,629,1369,1105,1315,1179,777,1110,481,1501,809,909,1031,962,468,666,1295,977,1406,730,1068,1401,1422,873,1269,1437,741,1073,440,655,1305,597,1041,861,1497,1426,1310,550,500,715,472,1233,913,945,1063,1354,1222,1458,814,1327,1196,898,1243,1391,782,709,1475,436,1265,1482,973,885,565,1366,570,719,504,751,802,1455,542,1059,1132,638,1087,870,770,1398,1100,606,1347,1415,475,756,591,623,1136,1151,966,1283,821,905,1334,646,1383,1020,634,692,1447,1394,1351,988,1201,602,981,1169,687,1206,439,661,761,1470,534,1163,546,793,1274,1387,957,1255,1174,1217,1238,746,1091,1423,625,852,1027,757,682,1128,842,1012,847,484,583,522,830,1159,461,493,1210,1089,1143,948,1375,1227,725,1096,1138,593,519,578,488,1361,933,1182,1461,669,1214,679,1419,554,753,901,476,1414,526,1114,701,515,1297,1451,1231,457,911,1002,1429,1246,779,1263,997,1318,938,1241,805,508,921,541,657,1286,1167,530,586,926,1466,558,1071,513,1219,856,689,733,1251,618,1389,772,743,1403,1124,562,975,1007,694,875,826,1503,572,611,498,1332,466,1224,1356,1258,704,1408,1282,1349,990,1492,599,863,764,979,604,784,1117,1048,736,880,649,1043,616,1122,890,1339,816,520,1325,964,1344,1293,1061,858,552,1029,895,943,1022,959,636,1445,455,1015,986,1113,1477,438,1198,1396,1176,608,1000,1435,1076,722,490,795,1277,1134,812,516,1472,836,1203,1208,589,663,548,1081,749,1145,1018,968,823,712,1025,1156,971,739,1267,1098,1225,707,673,1432,1300,791,441,1038,717,502,470,1130,1053,1499,1188,1186,1336,643,544,907,1404,613,1284,1485,1140,859,1372,595,1421,627,1459,556,671,903,495,759,1216,1126,1010,1453,450,1084,931,539,524,581,1253,1385,652,632,786,568,510,1308,1193,478,1212,1442,536,1045,1440,929,1161,800,620,1280,833,950,1229,818,1380,1148,867,735,854,1303,865,1480,918,1363,1495,506,807,437,1056,828,960,696,1165,955,1346,1172,767,1033,1288,532,1065,728,1236,575,1378,528,459,992,850,1299,442,1120,1093,839,1431,1004,486,1320,940,935,1184,676,1468,882,1417,1463,659,1490,775,560,1204,1449]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV319-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40  % Computer : n026.cluster.edu
% 0.14/0.40  % Model    : x86_64 x86_64
% 0.14/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40  % Memory   : 8046.5625MB
% 0.14/0.40  % OS       : Linux 6.8.0-71-generic
% 0.14/0.40  % CPULimit : 300
% 0.14/0.40  % WCLimit  : 300
% 0.14/0.40  % DateTime : Sat Sep 26 13:34:41 UTC 2026
% 0.14/0.40  % CPUTime  : 
% 0.14/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.72/0.70  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.04/1.06  % [INFO] 	 Parsing done (362ms). 
% 2.04/1.07  % [INFO] 	 Running in sequential loop mode. 
% 3.21/1.40  % [INFO] 	 eprover registered as external prover. 
% 3.21/1.41  % [INFO] 	 Scanning for conjecture ... 
% 3.96/1.67  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2937 axioms. Running axiom selection ... 
% 5.83/2.12  % [INFO] 	 Axiom selection finished. Selected 428 axioms (removed 2509 axioms). 
% 6.64/2.41  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 6.64/2.44  % [INFO] 	 Type checking passed. 
% 6.64/2.45  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 15.08/5.83  % External prover 'e' found a proof!
% 15.08/5.83  % [INFO] 	 Killing All external provers ... 
% 15.08/5.83  % Time passed: 5332ms (effective reasoning time: 4751ms)
% 15.08/5.84  % Axioms used in derivation (428): cls_Event_Oevent_Oinject__3_0, cls_Message_Oanalz__synth__Un_0, cls_Nat_Onot__less0_0, cls_List_Odistinct__remove1_0, cls_List_Oself__append__conv2_0, cls_OtwayRees_OOR2__parts__knows__Spy__dest_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_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_Message_Oparts__insert__Crypt_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_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_List_Oappend__in__lists__conv_2, 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_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_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_List_Onth__list__update__neq_0, cls_Event_Oevent_Odistinct__6_0, cls_Nat_Oless__irrefl_0, cls_Message_Omsg_Oinject__1_0, cls_List_Odistinct_Osimps__2_2, cls_Event_OkeysFor__synth_H_3, cls_List_Obutlast__snoc_0, cls_Divides_Omod__add__self1_0, cls_List_Orotate__is__Nil__conv_0, cls_List_Olast__in__set_0, cls_Message_OMPair__synth__analz_2, cls_List_Onth__mem_0, cls_Public_OpriK__neq__shrK_0, cls_List_Oself__append__conv_1, cls_Message_OHash__synth_0, cls_Set_Osingleton__insert__inj__eq_H_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_Message_OHPair__eq_0, cls_List_Osame__append__eq_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_List_Odistinct__append_0, cls_Message_Oanalz__insert__Nonce_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_Odistinct__rev_0, cls_List_Olist__inter_Osimps__2_1, cls_List_Oset__empty2_1, cls_List_Odistinct1__rotate_0, cls_List_Oremdups__eq__nil__iff_0, 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_Message_Oparts__synth_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_List_Oconcat__eq__Nil__conv_1, 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_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_Message_Omsg_Oinject__2_0, 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_List_Odistinct__append_1, cls_Message_Oagent_Odistinct__3_0, cls_List_Ozip__append_0, cls_Set_OsingletonD__dest_0, cls_Set_Oinsert__not__empty_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_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_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_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_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_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_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_OtwayRees_OGets__imp__Says__dest_0, cls_List_Oappend1__eq__conv_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_Odistinct__remdups_0, cls_Message_OHash_91X2_93_AY2_A_61_AAgent_AA2_A_61_61_AFalse_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_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_Nat_Oadd__gr__0_0, cls_List_Odistinct__sublistI_0, cls_Product__Type_OPair__eq_1, 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_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_Message_OHPair__neqs__3_0, cls_List_Orev__append_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, 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_Odistinct__rotate_1, cls_List_Olast__appendL_0, cls_Message_Oanalz__insert__MPair_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_List_Ohd__append2_0, cls_Nat_Onot__gr0_1, cls_Message_OHPair__neqs__1_0, cls_Nat_Onot__add__less2_0, cls_Message_Oagent_Osize__2_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_Message_OinvKey__eq_0, 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_Message_Oanalz__parts_0, cls_Message_Oanalz__Crypt__if_1, cls_Event_Oevent_Odistinct__5_0, 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_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_List_Onth__list__update__eq_0, cls_Message_OMPair__analz_0, cls_Public_OprivateKey__into__used_0, cls_Map_Omap__of__zip__is__None_1, 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_Nat_Onat__add__left__cancel_0, cls_Message_Ostrange__Un__eq_0, cls_List_Oin__listsI_0, cls_List_Odistinct_Osimps__2_0, cls_Message_OkeysFor__insert__Key_0, cls_Event_OSpy_A_58_Abad_A_61_61_ATrue_0, cls_List_Odistinct_Osimps__1_0, cls_Divides_Onat__mod__mod__trivial_0, cls_Message_OFake__parts__insert__in__Un__dest_0, cls_Message_Oparts__cut__eq_0, cls_Public_OpriEK__noteq__shrK_0, cls_List_Odistinct__rotate_0, cls_Message_OKey__synth__eq_0, cls_Public_OpriK__in__initState_0, 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_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_List_Odistinct_Osimps__2_1, 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_List_Olength__rotate1_0, cls_Public_ONonce__notin__used__empty_0, cls_List_Odistinct1__rotate_1, cls_List_Oremove1_Osimps__2_0, cls_Message_OMPair__eq__HPair_2, cls_Message_OMPair__synth__analz_0, cls_List_ONil__eq__concat__conv_0, cls_List_Oset__rotate1_0, cls_Public_OsymKeys__invKey__iff_1, cls_Divides_Omod__0_0, cls_Message_Oparts__idem_0, cls_Message_OMPair__synth_0, cls_Message_OHPair__neqs__4_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_Public_OshrK__in__knows_0, cls_List_Orotate__is__Nil__conv_1, 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_List_Odistinct__rev_1, cls_List_Orotate__id_0, cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0, cls_List_Oremdups_Osimps__2_1
% 15.08/5.84  % No. of inferences in proof: 871
% 15.08/5.84  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5332 ms resp. 4751 ms w/o parsing
% 16.21/6.22  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.21/6.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------