TSTP Solution File: SWV721-1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV721-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:18:02 EDT 2023

% Result   : Unsatisfiable 9.77s 3.03s
% Output   : Refutation 10.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  516
% Syntax   : Number of formulae    :  939 ( 293 unt;  94 typ;   0 def)
%            Number of atoms       : 1655 ( 432 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 11170 ( 794   ~; 810   |;   0   &;9566   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  189 ( 189   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   96 (  94 usr;  15 con; 0-6 aty)
%            Number of variables   : 2666 (   0   ^;2666   !;   0   ?;2666   :)

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

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

thf(v_S_type,type,
    v_S: $i ).

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

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

thf(v_KA_type,type,
    v_KA: $i ).

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

thf(v_N_type,type,
    v_N: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_List_Ofilter_type,type,
    c_List_Ofilter: $i > $i > $i > $i ).

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

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

thf(c_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).

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

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

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

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

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

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

thf(c_List_Omember_type,type,
    c_List_Omember: $i > $i > $i > $o ).

thf(c_List_Omap_type,type,
    c_List_Omap: $i > $i > $i > $i > $i ).

thf(c_List_OListMem_type,type,
    c_List_OListMem: $i > $i > $i > $o ).

thf(c_List_OremoveAll_type,type,
    c_List_OremoveAll: $i > $i > $i > $i ).

thf(c_List_Olist__ex_type,type,
    c_List_Olist__ex: $i > $i > $i > $o ).

thf(class_OrderedGroup_Oab__group__add_type,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

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

thf(c_List_Olist__all_type,type,
    c_List_Olist__all: $i > $i > $i > $o ).

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

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

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

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

thf(c_List_OtakeWhile_type,type,
    c_List_OtakeWhile: $i > $i > $i > $i ).

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

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

thf(c_List_Osko__List__Xsplit__list__propE__1__2_type,type,
    c_List_Osko__List__Xsplit__list__propE__1__2: $i > $i > $i > $i ).

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

thf(c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1_type,type,
    c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1: $i > $i > $i ).

thf(c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2_type,type,
    c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2: $i > $i > $i ).

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

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

thf(c_List_Osko__List__Xsplit__list__last__prop__1__3_type,type,
    c_List_Osko__List__Xsplit__list__last__prop__1__3: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__last__propE__1__3_type,type,
    c_List_Osko__List__Xsplit__list__last__propE__1__3: $i > $i > $i > $i ).

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

thf(c_List_Osko__List__Xsplit__list__first__prop__iff__1__2_type,type,
    c_List_Osko__List__Xsplit__list__first__prop__iff__1__2: $i > $i > $i > $i ).

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

thf(c_List_Osko__List__Xsplit__list__first__prop__1__1_type,type,
    c_List_Osko__List__Xsplit__list__first__prop__1__1: $i > $i > $i > $i ).

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

thf(c_List_Osko__List__Xin__set__conv__decomp__last__1__2_type,type,
    c_List_Osko__List__Xin__set__conv__decomp__last__1__2: $i > $i > $i > $i ).

thf(v_sko__Message__Xparts__Xcases__3_type,type,
    v_sko__Message__Xparts__Xcases__3: $i > $i > $i ).

thf(v_sko__Message__Xparts__Xcases__2_type,type,
    v_sko__Message__Xparts__Xcases__2: $i > $i > $i ).

thf(v_sko__Message__Xparts__Xcases__1_type,type,
    v_sko__Message__Xparts__Xcases__1: $i > $i > $i ).

thf(c_and_type,type,
    c_and: $i > $i > $i ).

thf(c_Not_type,type,
    c_Not: $i > $i ).

thf(c_List_Osko__List__Xsplit__list__first__prop__iff__1__1_type,type,
    c_List_Osko__List__Xsplit__list__first__prop__iff__1__1: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__first__propE__1__2_type,type,
    c_List_Osko__List__Xsplit__list__first__propE__1__2: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__last__1__2_type,type,
    c_List_Osko__List__Xsplit__list__last__1__2: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xin__set__conv__decomp__first__1__1_type,type,
    c_List_Osko__List__Xin__set__conv__decomp__first__1__1: $i > $i > $i > $i ).

thf(c_Map_Omap__upds_type,type,
    c_Map_Omap__upds: $i > $i > $i > $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__last__prop__iff__1__3_type,type,
    c_List_Osko__List__Xsplit__list__last__prop__iff__1__3: $i > $i > $i > $i ).

thf(c_Message_Osko__Message__Xparts__singleton__1__1_type,type,
    c_Message_Osko__Message__Xparts__singleton__1__1: $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__last__prop__iff__1__2_type,type,
    c_List_Osko__List__Xsplit__list__last__prop__iff__1__2: $i > $i > $i > $i ).

thf(c_List_Olistsp_type,type,
    c_List_Olistsp: $i > $i > $i > $o ).

thf(c_List_Osko__List__Xsplit__list__last__propE__1__2_type,type,
    c_List_Osko__List__Xsplit__list__last__propE__1__2: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__first__1__1_type,type,
    c_List_Osko__List__Xsplit__list__first__1__1: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__last__prop__1__2_type,type,
    c_List_Osko__List__Xsplit__list__last__prop__1__2: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__first__propE__1__1_type,type,
    c_List_Osko__List__Xsplit__list__first__propE__1__1: $i > $i > $i > $i ).

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

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

thf(c_List_Osko__List__Xsplit__list__prop__1__2_type,type,
    c_List_Osko__List__Xsplit__list__prop__1__2: $i > $i > $i > $i ).

thf(c_List_Osko__List__Xsplit__list__first__prop__1__2_type,type,
    c_List_Osko__List__Xsplit__list__first__prop__1__2: $i > $i > $i > $i ).

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

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).

thf(1190,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(336,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__mono_0) ).

thf(1168,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(909,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(292,axiom,
    ( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__empty_0) ).

thf(1083,plain,
    ( ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop_1) ).

thf(1179,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(555,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(400,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(645,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__cut_0) ).

thf(892,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(370,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono_0) ).

thf(1237,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(179,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OInj_0) ).

thf(846,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(358,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__insert_0) ).

thf(1211,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) @ ( c_Message_Osynth @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1005,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(683,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ A @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).

thf(511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ A @ C @ D ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).

thf(1041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) )
      | ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_lessequals @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__trans_0) ).

thf(873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).

thf(1205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

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

thf(449,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(45,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(533,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(54,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(550,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(715,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(22,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).

thf(1233,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(416,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1327,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(380,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ A @ B @ C @ D ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Issues__def_0) ).

thf(1260,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Event_Oevent_OSays @ A @ B @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ A @ B @ C @ D ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).

thf(945,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(283,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).

thf(1063,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(47,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(538,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).

thf(1222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(133,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).

thf(747,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy )
      | ~ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).

thf(913,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ B @ ( c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 @ B @ A @ C ) @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy )
      | ~ ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(254,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth_0) ).

thf(1001,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).

thf(1127,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1046,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(436,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(383,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(377,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).

thf(1254,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ D @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__sublistD_0) ).

thf(1055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ D @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(396,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(1287,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(382,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).

thf(1264,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(409,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).

thf(1313,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(348,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__idem_0) ).

thf(949,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omember @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_Omember @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).

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

thf(414,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__parts_0) ).

thf(1323,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(619,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(702,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(751,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Notes_0) ).

thf(1059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Olistsp @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_0) ).

thf(1132,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Olistsp @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(59,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(559,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(294,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(1087,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(1147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(193,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).

thf(870,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ A @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(260,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).

thf(1013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(301,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).

thf(1100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Oremove1 @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).

thf(817,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Oremove1 @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__set__sublistI_0) ).

thf(902,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osublist @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ B @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(219,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).

thf(924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

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

thf(591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__singleton_1) ).

thf(1109,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).

thf(1334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OSpy @ A @ B ) @ C @ tc_Event_Oevent ) )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1136,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ D @ C )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(514,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(806,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(344,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).

thf(1183,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ B @ C @ A @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ B @ C @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Issues__def_1) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ ( v_sko__NS__Shared__Mirabelle__XIssues__def__1 @ B @ C @ A @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_OIssues @ B @ C @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(756,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(328,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).

thf(1151,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__drop__subset_0) ).

thf(937,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(277,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).

thf(1051,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).

thf(821,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ C ) @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_OListMem @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ListMem__iff_1) ).

thf(905,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_OListMem @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(480,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(89,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(634,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).

thf(877,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(734,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_1) ).

thf(866,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(453,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Osublist @ A @ B @ C ) @ C ) @ ( c_List_Oset @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__sublist__subset_0) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Osublist @ A @ B @ C ) @ C ) @ ( c_List_Oset @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(98,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(660,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).

thf(988,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).

thf(1201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_OinvKey @ A )
       != ( c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__eq_0) ).

thf(507,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_OinvKey @ A )
       != ( c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).

thf(981,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(766,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).

thf(1104,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oused @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(373,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).

thf(1242,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(678,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(352,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).

thf(1199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(761,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( c_in @ A @ D @ C )
      | ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).

thf(1067,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).

thf(1047,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__idem_0) ).

thf(798,plain,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).

thf(1057,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex__iff_2) ).

thf(1163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(388,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insertI_0) ).

thf(1274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(296,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un_0) ).

thf(1091,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__propE__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__propE_1) ).

thf(825,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__propE__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(339,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Un_0) ).

thf(1174,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).

thf(820,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(2,negated_conjecture,
    ~ ( c_in @ v_X @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(424,plain,
    ~ ( c_in @ v_X @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
      = ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__butlast_0) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
      = ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(163,axiom,
    ( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__empty_0) ).

thf(815,plain,
    ( ( c_Message_Oanalz @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
    = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert2_0) ).

thf(957,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(205,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).

thf(894,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__propE__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__propE_1) ).

thf(1021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__propE__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OKey @ A )
       != ( c_Message_Omsg_OKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).

thf(778,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OKey @ A )
       != ( c_Message_Omsg_OKey @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ A @ B ) @ A @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__singleton_0) ).

thf(1123,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Osko__Message__Xparts__singleton__1__1 @ A @ B ) @ A @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).

thf(862,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_OremoveAll @ A @ B @ C )
        = B )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll__id_0) ).

thf(1217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_List_OremoveAll @ A @ B @ C )
        = B )
      | ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

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

thf(598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).

thf(1032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(183,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__prop__1__3 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop_2) ).

thf(852,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__prop__1__3 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(100,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).

thf(665,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).

thf(1159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(31,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(493,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).

thf(757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).

thf(1195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(551,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(241,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).

thf(974,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ ( c_Message_Oanalz @ A ) ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__pubK_0) ).

thf(1012,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_List_OListMem @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ListMem__iff_0) ).

thf(916,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_List_OListMem @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
        = ( c_List_Oreplicate @ B @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_0) ).

thf(484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
        = ( c_List_Oreplicate @ B @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).

thf(583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).

thf(522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).

thf(830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
        = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(290,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oreplicate @ C @ B @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).

thf(1079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oreplicate @ C @ B @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(266,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).

thf(1027,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg ) )
      | ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(15,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(456,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).

thf(842,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(67,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(578,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).

thf(1089,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1143,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(386,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).

thf(1270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(650,plain,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_0) ).

thf(1017,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(307,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__remove1_1) ).

thf(1111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ~ ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(125,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(725,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).

thf(1138,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(74,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__map_0) ).

thf(593,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).

thf(499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__into__used_0) ).

thf(1329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(291,axiom,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(1082,plain,
    ! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(136,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).

thf(753,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(398,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop_1) ).

thf(1292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing__imp__Un_0) ).

thf(933,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(686,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1016,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(356,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).

thf(1207,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).

thf(1039,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ B @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).

thf(970,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).

thf(1155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem_0) ).

thf(547,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
      | ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).

thf(837,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) )
      | ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OtakeWhile @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(252,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Otake @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__takeD_0) ).

thf(997,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Otake @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(300,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__Un_0) ).

thf(1099,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( c_Message_Osynth @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(375,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(1249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(130,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(738,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(457,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(123,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
      = ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).

thf(721,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
      = ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(569,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(374,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).

thf(1246,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) )
        = ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(317,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).

thf(1131,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).

thf(654,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(245,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( v_sko__Message__Xparts__Xcases__3 @ A @ B ) @ B ) @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ ( v_sko__Message__Xparts__Xcases__2 @ A @ B ) @ B ) @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ B @ ( v_sko__Message__Xparts__Xcases__1 @ A @ B ) ) @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg )
      | ( c_in @ B @ A @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_Ocases_0) ).

thf(984,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( v_sko__Message__Xparts__Xcases__3 @ A @ B ) @ B ) @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ ( v_sko__Message__Xparts__Xcases__2 @ A @ B ) @ B ) @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ B @ ( v_sko__Message__Xparts__Xcases__1 @ A @ B ) ) @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg )
      | ( c_in @ B @ A @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Oparts @ A ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(214,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__prop__1__1 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop_2) ).

thf(911,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__prop__1__1 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(503,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OremoveAll @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OremoveAll @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_1) ).

thf(605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OremoveAll @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_OremoveAll @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Otake @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__take__subset_0) ).

thf(1333,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Otake @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(1318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(218,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ D @ B @ C ) @ C ) @ C )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__remove1_0) ).

thf(921,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ D @ B @ C ) @ C ) @ C )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).

thf(1170,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(395,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).

thf(1286,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).

thf(1071,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ( A = D )
      | ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(335,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).

thf(1167,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).

thf(953,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ B @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(146,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Ofilter @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).

thf(773,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Ofilter @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Gets_0) ).

thf(888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Event_Oused @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OMPair @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).

thf(926,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OMPair @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(390,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omember @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__iff_1) ).

thf(1278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Omember @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(387,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).

thf(1273,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(185,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OFst_0) ).

thf(856,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(403,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__increasing_0) ).

thf(1301,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(1,negated_conjecture,
    c_in @ ( c_Event_Oevent_OSays @ v_S @ v_A @ ( c_Message_Omsg_OCrypt @ v_KA @ ( c_Message_Omsg_OMPair @ v_N @ ( c_Message_Omsg_OMPair @ v_B @ ( c_Message_Omsg_OMPair @ v_K @ v_X ) ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(423,plain,
    c_in @ ( c_Event_Oevent_OSays @ v_S @ v_A @ ( c_Message_Omsg_OCrypt @ v_KA @ ( c_Message_Omsg_OMPair @ v_N @ ( c_Message_Omsg_OMPair @ v_B @ ( c_Message_Omsg_OMPair @ v_K @ v_X ) ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(314,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).

thf(1125,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_Omember @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).

thf(772,plain,
    ! [C: $i,B: $i,A: $i] : ( c_List_Omember @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).

thf(743,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ B @ C )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).

thf(562,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ B @ C )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).

thf(904,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Event_OinitState @ C ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_1) ).

thf(875,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__trans_0) ).

thf(1256,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(365,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__propE__1__1 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__propE_2) ).

thf(1226,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__propE__1__1 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(51,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(545,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(91,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OGets @ A @ B )
       != ( c_Event_Oevent_OGets @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

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

thf(445,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).

thf(572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OremoveAll @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll__filter__not_0) ).

thf(611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_OremoveAll @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).

thf(713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).

thf(1107,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(371,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__shrK_0) ).

thf(1239,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(804,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(379,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__synthD_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Osynth @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_1) ).

thf(947,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).

thf(1224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_OtakeWhile @ A @ C @ D ) @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_0) ).

thf(1209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(1282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(258,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).

thf(1011,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_OinitState @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).

thf(990,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(451,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(129,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(737,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ c_Event_Obad @ tc_Message_Oagent )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ C @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).

thf(1117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
        = A )
      | ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1122,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__set__remove1_0) ).

thf(863,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Oremove1 @ B @ C @ D ) @ D ) @ D )
      | ( c_in @ A @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(340,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).

thf(1175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ C @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__knows__A_0) ).

thf(890,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ B @ C ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).

thf(1339,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(186,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__propE__1__3 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__propE_2) ).

thf(858,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__propE__1__3 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(85,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(621,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OInj_0) ).

thf(1325,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(895,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(143,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

thf(769,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
      = ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(227,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__spies_0) ).

thf(943,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(341,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).

thf(1177,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(114,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(700,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(520,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(327,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Odrop @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__dropD_0) ).

thf(1149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Odrop @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(237,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).

thf(964,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( C = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(462,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ C @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).

thf(1061,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ C ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ C @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__parts__subset__parts_0) ).

thf(959,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Event_Oused @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(273,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__sing_0) ).

thf(1044,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(868,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(200,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).

thf(883,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_ONotes @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(986,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(505,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(658,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(360,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).

thf(1213,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_OSays @ A @ B @ C )
       != ( c_Event_Oevent_OSays @ D @ E @ F ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(170,axiom,
    ! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).

thf(827,plain,
    ! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(182,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).

thf(851,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(302,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__3 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_2) ).

thf(1102,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__3 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(289,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).

thf(1076,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
        = ( c_Message_Oparts @ B ) )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
      | ( A = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).

thf(1034,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
        = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
      | ( A = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(405,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).

thf(1304,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_OSays @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(426,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).

thf(516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Event_Oevent_ONotes @ A @ B )
       != ( c_Event_Oevent_ONotes @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(325,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).

thf(1145,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OBody_0) ).

thf(1049,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(490,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OpublicKey @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).

thf(675,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OpublicKey @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_List_Omember @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__iff_0) ).

thf(1203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_List_Omember @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(72,axiom,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey_0) ).

thf(589,plain,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).

thf(795,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).

thf(680,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Public_OshrK @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__drop_0) ).

thf(663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
      = ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(548,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(319,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).

thf(1134,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oanalz @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_OListMem @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert_0) ).

thf(648,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_OListMem @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

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

thf(487,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(238,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OInj_0) ).

thf(968,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__partsD_0) ).

thf(1181,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Message_Oparts @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).

thf(823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__ex @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).

thf(776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__ex @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).

thf(525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
        = ( c_List_Ofilter @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).

thf(580,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(117,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(705,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).

thf(1252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Obutlast @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(384,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert_0) ).

thf(1267,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oinsert @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).

thf(1230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OGets @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( B = c_Message_Oagent_OSpy ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).

thf(993,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_OremoveAll @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_OremoveAll @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_0) ).

thf(557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_OremoveAll @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = ( c_List_OremoveAll @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(255,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__1 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_2) ).

thf(1003,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__prop__iff__1__1 @ A @ C @ D ) @ D ) @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ E ) )
      | ~ ( c_in @ E @ ( c_List_Oset @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(673,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(154,axiom,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
      = ( c_Public_OshrK @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).

thf(791,plain,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
      = ( c_Public_OshrK @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).

thf(585,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(122,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Olist_OCons @ A @ B @ C )
       != ( c_List_Olist_OCons @ D @ E @ C ) )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(176,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).

thf(840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ D @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ D ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(394,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).

thf(1285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(421,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).

thf(1336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ A @ tc_Message_Omsg ) )
        = ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__synth_0) ).

thf(1220,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Says_0) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oused @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Event_Oused @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut_0) ).

thf(1235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ D @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Set_Oinsert @ D @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xin__set__conv__decomp__first__1__1 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_1) ).

thf(1085,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xin__set__conv__decomp__first__1__1 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(576,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(50,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(544,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(212,axiom,
    ! [A: $i] :
      ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__emptyE_0) ).

thf(907,plain,
    ! [A: $i] :
      ~ ( c_in @ A @ ( c_Message_Oparts @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(323,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      | ~ ( c_in @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).

thf(1023,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OCrypt @ A @ B )
       != ( c_Message_Omsg_OCrypt @ C @ D ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(393,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__increasing_0) ).

thf(1284,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).

thf(600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D )
      | ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(278,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).

thf(1052,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OSays @ A @ B @ C )
     != ( c_Event_Oevent_OGets @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).

thf(1008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(446,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).

thf(595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(298,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__upds @ A @ B @ C @ D @ E @ F )
        = ( hAPP @ A @ D ) )
      | ( c_in @ D @ ( c_List_Oset @ B @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__apply__nontin_0) ).

thf(1094,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__upds @ A @ B @ C @ D @ E @ F )
        = ( hAPP @ A @ D ) )
      | ( c_in @ D @ ( c_List_Oset @ B @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(243,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ C )
       != ( c_Message_Oanalz @ D ) )
      | ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
        = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cong_0) ).

thf(978,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Oanalz @ A )
       != ( c_Message_Oanalz @ B ) )
      | ( ( c_Message_Oanalz @ C )
       != ( c_Message_Oanalz @ D ) )
      | ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
        = ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(322,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).

thf(1140,plain,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__iff_0) ).

thf(1240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ ( c_List_Oset @ C @ D ) @ D )
      | ~ ( c_List_Olist__all @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(249,axiom,
    ( ( c_HOL_Ominus__class_Ominus @ v_A @ v_B @ tc_bool )
    = ( c_and @ v_A @ ( c_Not @ v_B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bool__diff__def__raw_0) ).

thf(991,plain,
    ( ( c_HOL_Ominus__class_Ominus @ v_A @ v_B @ tc_bool )
    = ( c_and @ v_A @ ( c_Not @ v_B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(87,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( A = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

thf(627,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oreplicate @ A @ B @ C )
       != ( c_List_Oreplicate @ D @ E @ C ) )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma2_0) ).

thf(1316,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(102,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(671,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
      | ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(139,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__map_0) ).

thf(759,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
      = ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(178,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).

thf(844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ B ) @ ( c_Message_Oanalz @ D ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ C ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(144,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(771,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).

thf(1157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_ONotes @ B @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Notes_0) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ A @ B ) @ C @ tc_Event_Oevent ) )
      = ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xin__set__conv__decomp__last__1__2 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_1) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xin__set__conv__decomp__last__1__2 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(389,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).

thf(1276,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ A ) @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(236,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ E @ B @ C @ D ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ E @ F ) )
      | ~ ( c_in @ F @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__conv_0) ).

thf(961,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ E @ B @ C @ D ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ E @ F ) )
      | ~ ( c_in @ F @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).

thf(995,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(588,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(113,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(699,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).

thf(786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Olist__all @ A @ B @ C )
      | ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OFst_0) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OMPair @ A @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(399,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).

thf(1294,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).

thf(929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OMPair @ A @ B )
       != ( c_Message_Omsg_OMPair @ C @ D ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(349,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert_0) ).

thf(1193,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Oparts @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ tc_Message_Omsg ) ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(359,axiom,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).

thf(1212,plain,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OCrypt @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).

thf(899,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OCrypt @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(1309,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

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

thf(536,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__propE__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__propE_1) ).

thf(1161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__propE__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__injective_0) ).

thf(800,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).

thf(999,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ A @ B @ tc_Message_Omsg ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ C ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__prop__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__prop_1) ).

thf(1280,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__prop__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(5,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(432,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_OinitState @ c_Message_Oagent_OSpy ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Event_Oevent_ONotes @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__imp__Says__Notes__initState_0) ).

thf(833,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_OinitState @ c_Message_Oagent_OSpy ) @ tc_Message_Omsg )
      | ( c_in @ ( c_Event_Oevent_ONotes @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( c_in @ ( c_Event_Oevent_OSays @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 @ A @ B ) @ ( c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 @ A @ B ) @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ A @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cut_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ C @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ C @ B @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_OtakeWhile @ D @ B @ C ) @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).

thf(854,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_OtakeWhile @ D @ B @ C ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(790,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(190,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).

thf(865,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ) @ ( c_Event_Oused @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(299,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).

thf(1097,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(835,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(62,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

thf(564,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
      = ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).

thf(918,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Ofilter @ A @ B @ C )
       != B )
      | ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insertI_0) ).

thf(1314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(351,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1197,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).

thf(828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Event_Oknows @ B @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ B @ D @ A ) @ ( c_List_Oset @ C @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).

thf(1065,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Message_Oparts @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(696,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(1165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
      | ( c_in @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).

thf(955,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).

thf(886,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) ) ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) @ tc_Message_Omsg )
      | ~ ( c_in @ B @ c_Event_Obad @ tc_Message_Oagent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__1__1 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first_1) ).

thf(1172,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__first__1__1 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__trans_0) ).

thf(897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_lessequals @ C @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ A @ ( c_Message_Osynth @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omember @ A @ B @ C )
      | ( A = D )
      | ~ ( c_List_Omember @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).

thf(728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_List_Omember @ A @ B @ C )
      | ( A = D )
      | ~ ( c_List_Omember @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(19,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Public_OpublicKey @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).

thf(464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Public_OpublicKey @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).

thf(1129,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OCrypt @ C @ A ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ C ) ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ C ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(385,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analzD_0) ).

thf(1268,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ ( c_Message_Oanalz @ B ) ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma1_0) ).

thf(860,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ C @ tc_Message_Omsg ) ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oanalz @ ( c_Set_Oinsert @ B @ C @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ A ) ) @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).

thf(1019,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oanalz @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ A @ ( c_Message_Oanalz @ C ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(528,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(459,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(124,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).

thf(850,plain,
    ! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OpublicKey @ A @ B ) ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(402,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth_0) ).

thf(1299,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_OKey @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_OKey @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != B )
      | ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(194,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).

thf(871,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ B ) ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ C @ D @ A ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_1) ).

thf(1120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xsplit__list__last__prop__iff__1__2 @ A @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) )
      | ~ ( c_in @ D @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).

thf(1093,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(624,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(418,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
      | ( c_in @ D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(223,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__mono_0) ).

thf(935,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Message_Osynth @ A ) @ ( c_Message_Osynth @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ B @ C )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1184,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
       != ( c_Set_Oinsert @ A @ D @ C ) )
      | ( c_in @ A @ D @ C )
      | ( c_in @ A @ B @ C )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).

thf(708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OshrK @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).

thf(972,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ C ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).

thf(940,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__1__2 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last_1) ).

thf(1037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ ( c_List_Oset @ ( c_List_Osko__List__Xsplit__list__last__1__2 @ A @ B @ C ) @ C ) @ C )
      | ~ ( c_in @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(560,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(496,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
        = ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(286,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).

thf(1069,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OMPair @ C @ D ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ E @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(1342,plain,
    $false,
    inference(e,[status(thm)],[1190,1168,1105,909,1083,1179,555,1295,645,892,1237,846,1211,1005,683,1290,511,614,1041,741,1073,873,1205,449,533,550,715,472,1233,1327,1260,945,1063,538,1222,747,913,1001,1127,782,1046,436,1265,1228,1254,1055,1287,1264,1313,1191,949,542,1323,619,702,751,1059,1132,559,638,1087,1147,870,1013,881,1100,817,902,924,591,1109,1334,1136,514,806,1183,1302,756,1151,937,1051,821,905,480,634,877,734,866,453,1119,660,988,1201,507,602,981,766,1104,1242,439,678,793,1199,761,1311,1067,1047,798,1057,1163,1274,1091,825,1174,820,424,429,788,815,957,894,1021,778,1123,862,1217,598,1032,879,852,665,1159,493,757,1195,551,974,1012,916,467,566,484,583,522,830,1079,1027,456,842,578,1089,1143,1270,650,1017,1111,725,1138,593,499,1329,1082,753,1292,933,686,476,1016,1207,1039,970,1155,547,837,1114,997,1099,1249,1297,738,457,721,569,1246,1131,654,984,911,503,605,1333,1318,938,921,1170,1286,1071,1187,1167,953,773,888,926,1278,1273,856,1301,423,694,1125,772,743,562,904,875,711,1256,1226,545,641,445,572,611,713,1107,1239,804,1258,947,1224,540,1209,1282,1011,990,451,737,1307,784,1117,616,1122,863,1175,890,811,631,1339,858,621,1325,895,769,943,668,1177,848,700,520,1149,964,462,1061,959,1044,868,883,608,986,505,658,1213,827,851,1102,1076,1034,1304,426,531,749,516,1145,553,1049,490,675,1203,589,795,680,663,548,1134,648,487,968,1181,823,776,525,580,705,1252,1267,1230,993,557,1003,673,791,585,717,840,1285,1336,1220,1262,1235,1085,576,951,808,544,907,703,1141,1023,1284,600,1052,1008,446,595,1094,978,1140,1240,991,627,1316,482,671,759,844,771,1157,1321,976,688,1276,961,652,995,588,699,731,786,1030,433,1294,929,1193,478,1212,763,899,1309,536,1161,800,999,1280,432,833,818,854,790,865,1097,835,564,918,1314,1197,828,1065,696,1165,955,886,1172,897,474,728,464,1129,1268,860,1019,528,459,723,850,1299,691,442,871,1120,1093,624,1331,935,1184,708,972,469,940,1037,560,496,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem  : SWV721-1 : TPTP v8.1.2. Released v4.1.0.
% 0.02/0.09  % Command  : run_Leo-III %s %d
% 0.07/0.27  % Computer : n032.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 300
% 0.07/0.27  % DateTime : Fri May 19 02:23:21 EDT 2023
% 0.07/0.28  % CPUTime  : 
% 0.74/0.76  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.31/0.97  % [INFO] 	 Parsing done (208ms). 
% 1.31/0.98  % [INFO] 	 Running in sequential loop mode. 
% 2.02/1.19  % [INFO] 	 eprover registered as external prover. 
% 2.02/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 2.02/1.20  % [INFO] 	 Scanning for conjecture ... 
% 2.38/1.31  % [INFO] 	 Found a conjecture and 440 axioms. Running axiom selection ... 
% 2.66/1.41  % [INFO] 	 Axiom selection finished. Selected 420 axioms (removed 20 axioms). 
% 3.40/1.56  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 3.40/1.57  % [INFO] 	 Type checking passed. 
% 3.40/1.58  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 9.77/3.02  % External prover 'e' found a proof!
% 9.77/3.02  % [INFO] 	 Killing All external provers ... 
% 9.77/3.02  % Time passed: 2612ms (effective reasoning time: 2043ms)
% 9.77/3.02  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.77/3.03  % Axioms used in derivation (420): cls_set__subset__Cons_0, cls_Crypt__notin__initState_0, cls_shrK__in__initState_0, cls_parts_OBody_0, cls_subset__insert_1, cls_MPair__synth__analz_0, cls_not__parts__not__analz_0, cls_sup__ge1_0, cls_ListMem__iff_0, cls_parts__partsD_0, cls_MPair__used_0, cls_equalityI_0, cls_remove1_Osimps_I2_J_0, cls_in__listsp__conv__set_0, cls_list__all_Osimps_I2_J_1, cls_insertE_0, cls_knows__Spy__Gets_0, cls_split__list__last_1, cls_parts_OInj_0, cls_parts_OFst_0, cls_Un__subset__iff_0, cls_split__list__propE_1, cls_knows__Notes_0, cls_subset__empty_1, cls_synth__analz__mono_0, cls_initState__subset__knows_0, cls_used__Says_0, cls_Un__empty__left_0, cls_le__funD_0, cls_map__replicate_0, cls_set__ConsD_0, cls_sup__bot__right_0, cls_insert__code_1, cls_Issues__def_0, cls_list_Oinject_0, cls_filter__is__subset_0, cls_Says__imp__used_0, cls_knows__Says_0, cls_map__upds__apply__nontin_0, cls_inf__sup__aci_I6_J_0, cls_Un__commute_0, cls_Cons__eq__map__conv_3, cls_analz__cong_0, cls_UnCI_1, cls_split__list__first__propE_2, cls_analz__subset__iff_1, cls_bool__diff__def__raw_0, cls_Un__upper1_0, cls_insert__absorb_0, cls_analz__subset__parts_0, cls_used__Notes_0, cls_removeAll_Osimps_I2_J_0, cls_remove1__filter__not_0, cls_Fake__parts__insert_0, cls_mem__def_1, cls_msg_Osimps_I49_J_0, cls_msg_Osimps_I6_J_1, cls_Says__imp__parts__knows__Spy_0, cls_empty__iff_0, cls_not__Cons__self2_0, cls_insert__iff_1, cls_Crypt__synth__eq_1, cls_filter__eq__ConsD_2, cls_Crypt__synth__analz_0, cls_knows__subset__knows__Says_0, cls_Gets__imp__knows__agents_0, cls_le__sup__iff_0, cls_set__rev__mp_0, cls_analz__idem_0, cls_insert__subset_0, cls_List_Omember_Osimps_I2_J_0, clsarity_fun__Lattices_Oupper__semilattice, cls_knows__subset__knows__Cons_0, cls_split__list__last__propE_2, cls_in__set__remove1_0, cls_set__remove1__subset_0, cls_in__set__takeD_0, cls_list__all_Osimps_I2_J_0, cls_subset__insert__iff_2, cls_publicKey__into__used_0, cls_Key__synth__eq_1, cls_parts__empty_0, cls_drop__map_0, cls_synth__insert_0, cls_Un__left__commute_0, cls_analz__image__freshK__simps_I61_J_0, cls_ns__sharedp_OFake_0, cls_shrK__in__knows_0, cls_filter_Osimps_I2_J_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_replicate__eq__replicate_0, cls_synth_OCrypt_0, cls_Says__imp__spies_0, cls_parts__increasing_0, cls_split__list__first__prop__iff_1, cls_analz__image__freshK__simps_I65_J_0, cls_analz__Crypt__if_1, cls_knows__Spy__Notes_1, cls_le__supI_0, cls_Un__subset__iff_1, cls_Un__empty_2, cls_le__iff__sup_1, cls_synth__synthD_0, cls_notin__set__remove1_0, cls_msg_Osimps_I7_J_0, cls_parts__subset__iff_1, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_analz__cut_0, cls_in__parts__UnE_0, cls_le__iff__sup_0, cls_publicKey__inject_0, cls_Fake__parts__sing__imp__Un_0, cls_synth_OMPair_0, cls_parts_Ocases_0, cls_Un__absorb2_0, cls_parts__emptyE_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_lemma1_0, cls_parts__mono_0, cls_parts__insert__MPair_0, cls_sup__eq__bot__eq2_0, cls_split__list__first__prop_1, cls_Un__upper2_0, cls_Issues__def_1, cls_removeAll__filter__not_0, cls_analz__empty_0, cls_parts__knows__Spy__subset__used_0, cls_UnCI_0, cls_analz__subset__iff_0, cls_split__list__first__propE_1, cls_singleton__iff_1, cls_msg_Osimps_I40_J_0, cls_Spy__spies__bad__shrK_0, cls_subset__iff_0, cls_parts__Un_0, cls_parts_OSnd_0, clsarity_fun__HOL_Oord, cls_map__eq__Cons__conv_3, cls_pushes_I5_J_0, cls_analz__mono__contra_I3_J_0, cls_event_Osimps_I9_J_0, cls_Spy__spies__bad__privateKey_0, cls_insert__code_2, cls_in__set__replicateD_0, cls_event_Osimps_I6_J_0, cls_subset__empty_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_parts__insert_0, cls_List_Omember_Osimps_I2_J_1, cls_synth__analz__insert__eq_0, cls_analz__conj__parts_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_event_Osimps_I3_J_0, cls_synth__trans_0, cls_shrK__in__used_0, cls_removeAll__id_0, cls_Un__insert__left_0, cls_Says__imp__analz__Spy_0, cls_doubleton__eq__iff_2, cls_take__map_0, cls_Fake__analz__insert_0, cls_msg_Osimps_I7_J_1, cls_knows__Gets_0, cls_insert__subset_1, cls_ex__in__conv_0, cls_sup__commute_0, cls_analz_OFst_0, cls_set__eq__subset_2, cls_parts__insert__subset__Un_0, cls_Un__mono_0, cls_split__list__last__prop__iff_2, cls_privateKey__neq__publicKey_0, cls_analz_OInj_0, cls_parts__insertI_0, cls_shrK__neq__priK_0, cls_synth__increasing_0, cls_Un__subset__iff_2, cls_split__list__first__prop__iff_2, cls_linorder__linear_0, cls_Un__empty_0, clsarity_fun__Lattices_Olattice, cls_filter__replicate_0, cls_msg_Osimps_I4_J_0, cls_analz__parts_0, cls_pushes_I12_J_0, cls_parts__singleton_0, cls_not__Cons__self_0, cls_insert__is__Un_0, cls_in__set__butlastD_0, cls_subset__trans_0, cls_insertI1_0, cls_analz__insert__Crypt__subset_0, cls_parts__cut__eq_0, cls_empty__not__insert_0, cls_knows__Spy__Says_0, cls_sup__assoc_0, cls_split__list__first__prop_2, cls_analz__Crypt__if_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_le__supE_0, cls_analz__insert__cong_0, cls_msg_Osimps_I48_J_0, cls_butlast__drop_0, cls_MPair__synth_1, cls_event_Osimps_I2_J_1, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup1E_0, cls_synth__Un_0, cls_parts__cut_0, cls_sup__least_0, cls_subset__refl_0, cls_analz__shrK__Decrypt_0, cls_parts__subset__iff_0, cls_synth__subset__iff_1, cls_analz__Un_0, cls_analz_ODecrypt_0, cls_empty__subsetI_0, cls_drop__butlast_0, cls_sup1CI_1, cls_split__list__last__prop_1, cls_insertCI_0, cls_Notes__imp__knows__Spy_0, cls_msg_Osimps_I42_J_0, cls_Crypt__synth__eq_0, cls_spies__pubK_0, cls_Spy__in__bad_0, cls_singletonE_0, cls_parts__insert__knows__A_0, cls_Crypt__synth__analz_1, cls_event_Osimps_I7_J_0, cls_analz__spies__pubK_0, cls_bot1E_0, cls_Fake__analz__eq_0, cls_event_Osimps_I1_J_1, cls_Notes__imp__used_0, cls_analz__mono__contra_I2_J_0, cls_split__list__first_1, cls_insert__mono_0, cls_priK__in__initState_0, cls_Un__assoc_0, cls_publicKey__neq__privateKey_0, cls_parts__insert2_0, cls_bex__empty_0, cls_le__supI2_0, cls_synth__analz__insert__eq_1, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_shrK__injective_0, cls_synth_OInj_0, cls_synth__idem_0, cls_UnE_0, cls_subset__insertI2_0, cls_Un__absorb_0, cls_MPair__used_1, cls_parts__trans_0, clsarity_bool__Lattices_Olattice, cls_event_Osimps_I4_J_0, cls_event_Osimps_I2_J_0, cls_neq__shrK_0, cls_usedI_0, cls_analz__analzD_0, cls_invKey__eq_0, clsarity_bool__Lattices_Obounded__lattice, cls_parts__analz_0, cls_mem__iff_0, cls_split__list__last__prop__iff_1, cls_pubK__neq__shrK_0, cls_MPair__synth__analz_2, cls_analz__insert__MPair_0, cls_eq__eqI_0, cls_map__eq__conv_0, cls_parts__insert__Key_0, cls_knows__Spy__imp__Says__Notes__initState_0, cls_invKey__shrK_0, cls_Crypt__Spy__analz__bad_0, cls_parts__singleton_1, cls_parts__Un__subset2_0, cls_insert__subset_2, cls_le__supI1_0, cls_le__eqI_0, cls_sup__left__idem_0, cls_insert__not__empty_0, cls_analz__synth__Un_0, cls_list__ex__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_list__ex_Osimps_I2_J_1, cls_subsetD_0, cls_Key__synth_0, cls_map_Osimps_I2_J_0, cls_le__sup__iff_2, cls_Crypt__synth_0, cls_analz_OSnd_0, cls_subset__singletonD_0, cls_takeWhile__eq__all__conv_0, cls_event_Osimps_I8_J_0, cls_in__set__conv__decomp__last_1, cls_insert__absorb2_0, cls_analz__mono_0, cls_doubleton__eq__iff_1, cls_analz__mono__contra_I1_J_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_analz__insert__eq_0, cls_analz__analz__Un_0, cls_Un__left__absorb_0, cls_event_Osimps_I1_J_0, cls_split__list__last__prop_2, cls_Crypt__synth_1, cls_synth__subset__iff_0, cls_filter__id__conv_0, cls_emptyE_0, cls_inf__sup__aci_I5_J_0, cls_eq__eqI_1, cls_list__all_Osimps_I2_J_2, cls_singleton__inject_0, cls_set__takeWhileD_1, cls_mem__iff_1, cls_initState__into__used_0, cls_analz__increasing_0, cls_subset__insert_0, cls_sup__idem_0, cls_msg_Osimps_I41_J_0, cls_ListMem__iff_1, cls_inf__sup__ord_I3_J_0, cls_MPair__synth_0, cls_set__take__subset_0, cls_knows__subset__knows__Notes_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_Un__empty_1, cls_parts__Un__subset1_0, cls_split__list__prop_1, cls_remove1_Osimps_I2_J_1, cls_Fake__parts__sing_0, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_split__list__last__propE_1, cls_Un__least_0, cls_sup1CI_0, cls_shrK__neq__pubK_0, cls_sup__ge2_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_parts__idem_0, cls_set__takeWhileD_0, cls_set__sublist__subset_0, cls_in__set__sublistD_0, cls_analz__insertI_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_knows__Spy__subset__knows__Spy__Says_0, cls_lemma2_0, cls_List_Omember_Osimps_I2_J_2, cls_invKey_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_insert__code_0, cls_subset__insertI_0, cls_analz__trans_0, cls_used__Gets_0, cls_msg_Osimps_I6_J_0, cls_in__set__conv__decomp__first_1, cls_elem_0, cls_takeWhile_Osimps_I2_J_0, cls_le__eqI_1, cls_Says__imp__knows_0, cls_analz__subset__cong_0, cls_list__ex_Osimps_I2_J_0, cls_list__ex_Osimps_I2_J_2, cls_sup__bot__left_0, cls_gen__analz__insert__eq_0, cls_set__drop__subset_0, cls_in__set__dropD_0, cls_in__set__remove1_1, cls_notin__set__sublistI_0, cls_used__parts__subset__parts_0, cls_insert__commute_0, cls_insert__iff_2, cls_MPair__synth__analz_1, cls_knows__imp__Says__Gets__Notes__initState_0, cls_parts__synth_0, cls_filter_Osimps_I2_J_1, cls_Un__insert__right_0, cls_equalityE_0, cls_publicKey__inject_1, cls_list__all__iff_0, cls_Cons__eq__filterD_2, cls_event_Osimps_I5_J_0, cls_sup__absorb1_0, cls_parts__insert__Crypt_0, cls_knows__Spy__Notes_0, cls_priK__neq__shrK_0, cls_Fake__parts__insert__in__Un_0, cls_removeAll_Osimps_I2_J_1, cls_insert_0, cls_privateKey__into__used_0, cls_pushes_I6_J_0, cls_publicKey__in__initState_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_ball__empty_0, cls_synth__mono_0, cls_synth__cut_0, cls_Notes__imp__knows_0, cls_subset__insert__iff_1, cls_analz__into__parts_0, cls_predicate1D_0, cls_analz__insert_0, cls_parts__insert__spies_0
% 9.77/3.03  % No. of inferences in proof: 845
% 9.77/3.03  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2612 ms resp. 2043 ms w/o parsing
% 10.60/3.18  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.60/3.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------