TSTP Solution File: SWV722-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWV722-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 : Tue May 21 05:48:10 EDT 2024

% Result   : Unsatisfiable 13.81s 4.59s
% Output   : Refutation 15.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  590
% Syntax   : Number of formulae    : 1090 ( 373 unt;  91 typ;   0 def)
%            Number of atoms       : 1935 ( 548 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives : 13454 ( 952   ~; 936   |;   0   &;11566   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  186 ( 186   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   93 (  91 usr;  14 con; 0-6 aty)
%            Number of variables   : 3200 (   0   ^3200   !;   0   ?;3200   :)

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

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

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

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

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

thf(v_NA_type,type,
    v_NA: $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_HOL_Oord_type,type,
    class_HOL_Oord: $i > $o ).

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

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

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

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

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_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_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).

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

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

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

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

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

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_List_OtakeWhile_type,type,
    c_List_OtakeWhile: $i > $i > $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_NS__Shared__Mirabelle_Ons__sharedp_type,type,
    c_NS__Shared__Mirabelle_Ons__sharedp: $i > $o ).

thf(c_Event_Oused_type,type,
    c_Event_Oused: $i > $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_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(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(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( 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)],[63]) ).

thf(234,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/sandbox/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).

thf(1036,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)],[234]) ).

thf(492,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(1586,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)],[492]) ).

thf(374,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/sandbox/benchmark/theBenchmark.p',cls_in__parts__UnE_0) ).

thf(1337,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)],[374]) ).

thf(390,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Agent_0) ).

thf(1369,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(115,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/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(760,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)],[115]) ).

thf(430,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/sandbox/benchmark/theBenchmark.p',cls_MPair__synth_0) ).

thf(1454,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)],[430]) ).

thf(269,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__knows__A_0) ).

thf(1105,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)],[269]) ).

thf(232,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).

thf(1031,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)],[232]) ).

thf(171,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/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(893,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)],[171]) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(518,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)],[10]) ).

thf(122,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(777,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)],[122]) ).

thf(475,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I2_J_0) ).

thf(1549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(272,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/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(1110,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)],[272]) ).

thf(259,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_1) ).

thf(1083,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)],[259]) ).

thf(201,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OKey @ A )
       != ( c_Message_Omsg_OKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).

thf(962,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)],[201]) ).

thf(116,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/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(762,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)],[116]) ).

thf(220,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(1005,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)],[220]) ).

thf(250,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/sandbox/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).

thf(1068,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)],[250]) ).

thf(460,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).

thf(1522,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)],[460]) ).

thf(425,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(1443,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)],[425]) ).

thf(215,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/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(994,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)],[215]) ).

thf(253,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/sandbox/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).

thf(1073,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)],[253]) ).

thf(472,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).

thf(1544,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)],[472]) ).

thf(495,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/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).

thf(1591,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)],[495]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(511,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(466,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).

thf(1533,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)],[466]) ).

thf(415,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).

thf(1422,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)],[415]) ).

thf(484,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/sandbox/benchmark/theBenchmark.p',cls_lemma2_0) ).

thf(1569,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)],[484]) ).

thf(161,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/sandbox/benchmark/theBenchmark.p',cls_analz__Un_0) ).

thf(873,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)],[161]) ).

thf(314,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/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__insert_0) ).

thf(1205,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)],[314]) ).

thf(286,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).

thf(1142,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)],[286]) ).

thf(342,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/sandbox/benchmark/theBenchmark.p',cls_parts_OBody_0) ).

thf(1269,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)],[342]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(1041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( c_in @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(155,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/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(861,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)],[155]) ).

thf(300,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert2_0) ).

thf(1173,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)],[300]) ).

thf(444,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/sandbox/benchmark/theBenchmark.p',cls_neq__shrK_0) ).

thf(1486,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)],[444]) ).

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

thf(533,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)],[16]) ).

thf(1,negated_conjecture,
    c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_A @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(500,plain,
    c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_A @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( 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(95,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/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).

thf(715,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)],[95]) ).

thf(345,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/sandbox/benchmark/theBenchmark.p',cls_in__set__sublistD_0) ).

thf(1275,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)],[345]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

thf(747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Olist_OCons @ A @ B @ C )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(945,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)],[193]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).

thf(1222,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)],[322]) ).

thf(256,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/sandbox/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).

thf(1078,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)],[256]) ).

thf(417,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/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(1426,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)],[417]) ).

thf(338,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/sandbox/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).

thf(1260,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)],[338]) ).

thf(89,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/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(698,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)],[89]) ).

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

thf(538,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(382,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/sandbox/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).

thf(1354,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)],[382]) ).

thf(309,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).

thf(1196,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)],[309]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1001,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( 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)],[218]) ).

thf(424,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/sandbox/benchmark/theBenchmark.p',cls_knows__Says_0) ).

thf(1441,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)],[424]) ).

thf(93,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/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).

thf(709,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)],[93]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_OremoveAll @ A @ B @ C ) @ C )
      = ( c_HOL_Ominus__class_Ominus @ ( c_List_Oset @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__removeAll_0) ).

thf(1359,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oset @ ( c_List_OremoveAll @ A @ B @ C ) @ C )
      = ( c_HOL_Ominus__class_Ominus @ ( c_List_Oset @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(439,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).

thf(1475,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)],[439]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(973,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(168,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

thf(885,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)],[168]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS1_0) ).

thf(1046,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ C ) ) ) ) @ D @ tc_Event_Oevent ) )
      | ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ D ) @ tc_Message_Omsg )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(325,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/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I61_J_0) ).

thf(1228,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)],[325]) ).

thf(442,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/sandbox/benchmark/theBenchmark.p',cls_parts__cut_0) ).

thf(1482,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)],[442]) ).

thf(351,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/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).

thf(1287,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)],[351]) ).

thf(34,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/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(570,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)],[34]) ).

thf(419,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).

thf(1430,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)],[419]) ).

thf(356,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(1298,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__inject_1) ).

thf(802,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)],[131]) ).

thf(347,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/sandbox/benchmark/theBenchmark.p',cls_used__Notes_0) ).

thf(1279,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)],[347]) ).

thf(488,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/sandbox/benchmark/theBenchmark.p',cls_parts_OInj_0) ).

thf(1577,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)],[488]) ).

thf(307,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).

thf(1191,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)],[307]) ).

thf(21,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/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(542,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)],[21]) ).

thf(243,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/sandbox/benchmark/theBenchmark.p',cls_parts__Un__subset2_0) ).

thf(1055,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)],[243]) ).

thf(409,axiom,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).

thf(1409,plain,
    c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(587,plain,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(366,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/sandbox/benchmark/theBenchmark.p',cls_parts__Un_0) ).

thf(1323,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)],[366]) ).

thf(53,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/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(619,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)],[53]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Public_OpublicKey @ A @ B )
       != ( c_Public_OpublicKey @ C @ D ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_publicKey__inject_0) ).

thf(917,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)],[180]) ).

thf(111,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/sandbox/benchmark/theBenchmark.p',cls_removeAll__filter__not_0) ).

thf(751,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)],[111]) ).

thf(473,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/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).

thf(1545,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)],[473]) ).

thf(174,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/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(902,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)],[174]) ).

thf(288,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/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).

thf(1147,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)],[288]) ).

thf(49,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_OinvKey @ A )
       != ( c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__eq_0) ).

thf(606,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_OinvKey @ A )
       != ( c_Message_OinvKey @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(119,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).

thf(770,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)],[119]) ).

thf(267,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ B @ C ) @ ( c_List_Oset @ E @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__map__eq__map_0) ).

thf(1100,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ B @ C ) @ ( c_List_Oset @ E @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(327,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/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).

thf(1232,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)],[327]) ).

thf(60,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/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(638,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)],[60]) ).

thf(152,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OAgent @ A )
       != ( c_Message_Omsg_OAgent @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I1_J_0) ).

thf(853,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_OAgent @ A )
       != ( c_Message_Omsg_OAgent @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(1087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(456,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/sandbox/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).

thf(1514,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)],[456]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(1319,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(160,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(870,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)],[160]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__notin__initState_0) ).

thf(1398,plain,
    ! [B: $i,A: $i] :
      ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_Event_OinitState @ B ) ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(166,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/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).

thf(881,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)],[166]) ).

thf(446,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(1489,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(113,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/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(756,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)],[113]) ).

thf(126,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).

thf(789,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)],[126]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(271,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/sandbox/benchmark/theBenchmark.p',cls_parts__Un__subset1_0) ).

thf(1109,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)],[271]) ).

thf(413,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop_1) ).

thf(1418,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)],[413]) ).

thf(372,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_2) ).

thf(1334,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)],[372]) ).

thf(284,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/sandbox/benchmark/theBenchmark.p',cls_in__set__remove1_0) ).

thf(1136,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)],[284]) ).

thf(8,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(514,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(132,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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(806,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)],[132]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ B @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(966,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_in @ B @ A @ C )
      | ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(138,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/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).

thf(821,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)],[138]) ).

thf(175,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono_0) ).

thf(905,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)],[175]) ).

thf(289,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/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__sing__imp__Un_0) ).

thf(1151,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)],[289]) ).

thf(189,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/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(937,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)],[189]) ).

thf(226,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).

thf(1020,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)],[226]) ).

thf(36,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/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_0) ).

thf(574,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)],[36]) ).

thf(304,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).

thf(1183,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)],[304]) ).

thf(349,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/sandbox/benchmark/theBenchmark.p',cls_usedI_0) ).

thf(1283,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)],[349]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).

thf(1215,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)],[318]) ).

thf(164,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/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(877,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)],[164]) ).

thf(401,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/sandbox/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).

thf(1394,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)],[401]) ).

thf(380,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/sandbox/benchmark/theBenchmark.p',cls_set__sublist__subset_0) ).

thf(1351,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)],[380]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_OListMem @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_elem_0) ).

thf(660,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)],[70]) ).

thf(217,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/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(998,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)],[217]) ).

thf(213,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_OGets @ A @ B )
     != ( c_Event_Oevent_ONotes @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).

thf(988,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)],[213]) ).

thf(407,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/sandbox/benchmark/theBenchmark.p',cls_parts__mono_0) ).

thf(1405,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)],[407]) ).

thf(312,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).

thf(1201,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)],[312]) ).

thf(499,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).

thf(1600,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)],[499]) ).

thf(13,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(527,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(47,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/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(602,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)],[47]) ).

thf(210,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/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(981,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)],[210]) ).

thf(298,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/sandbox/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).

thf(1169,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)],[298]) ).

thf(84,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(687,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)],[84]) ).

thf(427,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).

thf(1447,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)],[427]) ).

thf(198,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).

thf(956,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)],[198]) ).

thf(276,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/sandbox/benchmark/theBenchmark.p',cls_publicKey__in__initState_0) ).

thf(1119,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)],[276]) ).

thf(120,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(774,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(254,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/sandbox/benchmark/theBenchmark.p',cls_MPair__used_1) ).

thf(1074,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)],[254]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(942,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)],[191]) ).

thf(79,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/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(678,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)],[79]) ).

thf(71,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/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(661,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)],[71]) ).

thf(127,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/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(793,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)],[127]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(925,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(359,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OOops_0) ).

thf(1306,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ B ) @ ( c_Message_Omsg_OKey @ C ) ) ) ) @ D @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ E @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ F ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ C ) @ G ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ F @ E @ ( c_Message_Omsg_OCrypt @ C @ ( c_Message_Omsg_ONonce @ B ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(311,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/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__insert_0) ).

thf(1199,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)],[311]) ).

thf(290,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/sandbox/benchmark/theBenchmark.p',cls_set__drop__subset_0) ).

thf(1153,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)],[290]) ).

thf(361,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/sandbox/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).

thf(1311,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)],[361]) ).

thf(129,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(798,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)],[129]) ).

thf(295,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/sandbox/benchmark/theBenchmark.p',cls_MPair__synth_1) ).

thf(1163,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)],[295]) ).

thf(177,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

thf(910,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(263,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).

thf(1091,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)],[263]) ).

thf(377,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/sandbox/benchmark/theBenchmark.p',cls_in__set__remove1_1) ).

thf(1343,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)],[377]) ).

thf(227,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/sandbox/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).

thf(1021,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)],[227]) ).

thf(196,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(952,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).

thf(1519,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)],[459]) ).

thf(450,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/sandbox/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).

thf(1502,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)],[450]) ).

thf(445,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/sandbox/benchmark/theBenchmark.p',cls_list__all__iff_0) ).

thf(1487,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)],[445]) ).

thf(136,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/sandbox/benchmark/theBenchmark.p',cls_publicKey__neq__privateKey_0) ).

thf(815,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)],[136]) ).

thf(102,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(729,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)],[102]) ).

thf(480,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/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(1560,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)],[480]) ).

thf(87,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/sandbox/benchmark/theBenchmark.p',cls_analz__synth_0) ).

thf(693,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)],[87]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(630,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(416,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/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(1423,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)],[416]) ).

thf(388,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).

thf(1365,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)],[388]) ).

thf(165,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/sandbox/benchmark/theBenchmark.p',cls_analz__analz__Un_0) ).

thf(879,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)],[165]) ).

thf(432,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).

thf(1457,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)],[432]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(583,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ 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)],[39]) ).

thf(169,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/sandbox/benchmark/theBenchmark.p',cls_map__replicate_0) ).

thf(889,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)],[169]) ).

thf(293,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__spies_0) ).

thf(1159,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)],[293]) ).

thf(316,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_2) ).

thf(1210,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)],[316]) ).

thf(257,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).

thf(1079,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)],[257]) ).

thf(281,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/sandbox/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).

thf(1128,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)],[281]) ).

thf(348,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset__Un_0) ).

thf(1281,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)],[348]) ).

thf(148,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/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(842,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)],[148]) ).

thf(486,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/sandbox/benchmark/theBenchmark.p',cls_knows__Notes_0) ).

thf(1573,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)],[486]) ).

thf(150,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/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(847,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)],[150]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(566,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)],[32]) ).

thf(355,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/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_1) ).

thf(1296,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)],[355]) ).

thf(73,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/sandbox/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).

thf(665,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)],[73]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(682,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)],[81]) ).

thf(408,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/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).

thf(1407,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)],[408]) ).

thf(405,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__propE_1) ).

thf(1402,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)],[405]) ).

thf(262,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/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(1089,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)],[262]) ).

thf(162,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/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(874,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)],[162]) ).

thf(65,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/sandbox/benchmark/theBenchmark.p',cls_synth__mono_0) ).

thf(650,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)],[65]) ).

thf(52,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).

thf(615,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)],[52]) ).

thf(248,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__propE_2) ).

thf(1064,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)],[248]) ).

thf(100,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

thf(725,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(209,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/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(980,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)],[209]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Nonce_0) ).

thf(1096,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(44,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/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).

thf(593,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)],[44]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(869,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(50,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/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).

thf(610,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)],[50]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(857,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(467,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).

thf(1534,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)],[467]) ).

thf(224,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/sandbox/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).

thf(1017,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)],[224]) ).

thf(369,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/sandbox/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).

thf(1329,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)],[369]) ).

thf(230,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/sandbox/benchmark/theBenchmark.p',cls_split__list__propE_1) ).

thf(1028,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)],[230]) ).

thf(386,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/sandbox/benchmark/theBenchmark.p',cls_parts__singleton_0) ).

thf(1361,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)],[386]) ).

thf(26,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/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(554,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)],[26]) ).

thf(433,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/sandbox/benchmark/theBenchmark.p',cls_removeAll__id_0) ).

thf(1461,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)],[433]) ).

thf(83,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/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(686,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)],[83]) ).

thf(411,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/sandbox/benchmark/theBenchmark.p',cls_list__ex__iff_2) ).

thf(1414,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)],[411]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I1_J_0) ).

thf(1584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OKey @ A ) @ C @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(315,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ ( c_List_OremoveAll @ B @ C @ D ) @ D @ E )
        = ( c_List_OremoveAll @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ ( c_List_Oset @ C @ D ) @ D ) @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__removeAll__inj__on_0) ).

thf(1207,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ ( c_List_OremoveAll @ B @ C @ D ) @ D @ E )
        = ( c_List_OremoveAll @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ ( c_List_Oset @ C @ D ) @ D ) @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(23,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/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(547,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)],[23]) ).

thf(353,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/sandbox/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).

thf(1292,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)],[353]) ).

thf(187,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/sandbox/benchmark/theBenchmark.p',cls_drop__map_0) ).

thf(933,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)],[187]) ).

thf(235,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__imp__Says__Notes__initState_0) ).

thf(1039,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)],[235]) ).

thf(204,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Osynth @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__increasing_0) ).

thf(970,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)],[204]) ).

thf(146,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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(837,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)],[146]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OCrypt @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).

thf(1114,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)],[274]) ).

thf(90,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).

thf(701,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)],[90]) ).

thf(106,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_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(738,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_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(340,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(1266,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)],[340]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey_0) ).

thf(721,plain,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(418,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/sandbox/benchmark/theBenchmark.p',cls_publicKey__into__used_0) ).

thf(1429,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)],[418]) ).

thf(332,axiom,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).

thf(1246,plain,
    c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

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/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(503,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(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I37_J_0) ).

thf(1525,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(64,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(647,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)],[64]) ).

thf(339,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Message_OinvKey @ ( c_Public_OpublicKey @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_priK__neq__shrK_0) ).

thf(1263,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)],[339]) ).

thf(493,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/sandbox/benchmark/theBenchmark.p',cls_initState__into__used_0) ).

thf(1588,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)],[493]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I11_J_0) ).

thf(985,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(9,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(515,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)],[9]) ).

thf(333,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/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__sing_0) ).

thf(1249,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)],[333]) ).

thf(464,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/sandbox/benchmark/theBenchmark.p',cls_split__list__prop_1) ).

thf(1530,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)],[464]) ).

thf(470,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONS3_0) ).

thf(1539,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ A @ c_Message_Oagent_OServer @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_ONonce @ E ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ~ ( c_in @ ( c_Event_Oevent_OSays @ F @ A @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ A ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ E ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ B ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OKey @ G ) @ C ) ) ) ) ) @ ( c_List_Oset @ D @ tc_Event_Oevent ) @ tc_Event_Oevent )
      | ( A = c_Message_Oagent_OServer )
      | ~ ( c_NS__Shared__Mirabelle_Ons__sharedp @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(431,axiom,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).

thf(1456,plain,
    c_in @ c_Message_Oagent_OSpy @ c_Event_Obad @ tc_Message_Oagent,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(397,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(1382,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(282,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/sandbox/benchmark/theBenchmark.p',cls_ListMem__iff_0) ).

thf(1131,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)],[282]) ).

thf(67,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/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(654,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)],[67]) ).

thf(246,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/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).

thf(1060,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)],[246]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(1050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
      | ( c_in @ A @ C @ D )
      | ~ ( c_in @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(371,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth_OAgent_0) ).

thf(1333,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(421,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert_0) ).

thf(1434,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)],[421]) ).

thf(330,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).

thf(1241,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)],[330]) ).

thf(5,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/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(508,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)],[5]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__idem_0) ).

thf(921,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oanalz @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(20,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(541,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(482,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/sandbox/benchmark/theBenchmark.p',cls_analz__insertI_0) ).

thf(1563,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)],[482]) ).

thf(242,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/sandbox/benchmark/theBenchmark.p',cls_analz__spies__pubK_0) ).

thf(1054,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)],[242]) ).

thf(457,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/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(1515,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)],[457]) ).

thf(197,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(953,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)],[197]) ).

thf(435,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/sandbox/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).

thf(1466,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)],[435]) ).

thf(28,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(558,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(252,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/sandbox/benchmark/theBenchmark.p',cls_notin__set__remove1_0) ).

thf(1071,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)],[252]) ).

thf(305,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/sandbox/benchmark/theBenchmark.p',cls_synth_OInj_0) ).

thf(1187,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)],[305]) ).

thf(77,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(674,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)],[77]) ).

thf(229,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/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).

thf(1026,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)],[229]) ).

thf(297,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).

thf(1167,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)],[297]) ).

thf(334,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/sandbox/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).

thf(1251,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)],[334]) ).

thf(7,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(513,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth__eq_1) ).

thf(1103,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(357,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).

thf(1301,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)],[357]) ).

thf(85,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/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).

thf(689,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)],[85]) ).

thf(393,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/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(1374,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)],[393]) ).

thf(104,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/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(733,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)],[104]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(750,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(454,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/sandbox/benchmark/theBenchmark.p',cls_Issues__def_0) ).

thf(1510,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)],[454]) ).

thf(320,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/sandbox/benchmark/theBenchmark.p',cls_spies__pubK_0) ).

thf(1219,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)],[320]) ).

thf(140,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/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(824,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)],[140]) ).

thf(291,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).

thf(1154,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)],[291]) ).

thf(30,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

thf(562,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(399,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/sandbox/benchmark/theBenchmark.p',cls_in__set__dropD_0) ).

thf(1388,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)],[399]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONonce @ A )
       != ( c_Message_Omsg_ONonce @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I3_J_0) ).

thf(743,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Message_Omsg_ONonce @ A )
       != ( c_Message_Omsg_ONonce @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(468,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/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(1535,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)],[468]) ).

thf(279,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/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(1124,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)],[279]) ).

thf(141,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/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(826,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)],[141]) ).

thf(37,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/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(577,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)],[37]) ).

thf(336,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last_1) ).

thf(1256,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)],[336]) ).

thf(324,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/sandbox/benchmark/theBenchmark.p',cls_MPair__used_0) ).

thf(1226,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)],[324]) ).

thf(22,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/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(545,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)],[22]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I16_J_0) ).

thf(1139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(35,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/sandbox/benchmark/theBenchmark.p',cls_analz__subset__cong_0) ).

thf(572,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)],[35]) ).

thf(329,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/sandbox/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).

thf(1239,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)],[329]) ).

thf(337,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth__eq_0) ).

thf(1258,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Nonce_0) ).

thf(1356,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oparts @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(343,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).

thf(1271,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)],[343]) ).

thf(391,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/sandbox/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).

thf(1371,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)],[391]) ).

thf(245,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(1058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(270,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/sandbox/benchmark/theBenchmark.p',cls_synth__cut_0) ).

thf(1107,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)],[270]) ).

thf(434,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/sandbox/benchmark/theBenchmark.p',cls_parts__synth_0) ).

thf(1464,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)],[434]) ).

thf(194,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(947,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)],[194]) ).

thf(308,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).

thf(1194,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)],[308]) ).

thf(143,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(831,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)],[143]) ).

thf(222,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/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).

thf(1011,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)],[222]) ).

thf(379,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/sandbox/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).

thf(1349,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)],[379]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__idem_0) ).

thf(996,plain,
    ! [A: $i] :
      ( ( c_Message_Osynth @ ( c_Message_Osynth @ A ) )
      = ( c_Message_Osynth @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(447,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).

thf(1492,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)],[447]) ).

thf(471,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop_1) ).

thf(1542,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)],[471]) ).

thf(287,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OMPair @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).

thf(1144,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)],[287]) ).

thf(237,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).

thf(1043,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)],[237]) ).

thf(278,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/sandbox/benchmark/theBenchmark.p',cls_parts__emptyE_0) ).

thf(1122,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)],[278]) ).

thf(117,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/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(764,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)],[117]) ).

thf(48,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(604,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)],[48]) ).

thf(124,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

thf(784,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Oinj__on @ A @ B @ C @ D )
      | ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(275,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/sandbox/benchmark/theBenchmark.p',cls_notin__set__sublistI_0) ).

thf(1117,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)],[275]) ).

thf(239,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/sandbox/benchmark/theBenchmark.p',cls_analz_OInj_0) ).

thf(1048,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)],[239]) ).

thf(105,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/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).

thf(736,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)],[105]) ).

thf(485,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I8_J_0) ).

thf(1571,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(394,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/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).

thf(1376,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)],[394]) ).

thf(423,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/sandbox/benchmark/theBenchmark.p',cls_mem__iff_0) ).

thf(1439,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)],[423]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(301,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/sandbox/benchmark/theBenchmark.p',cls_used__parts__subset__parts_0) ).

thf(1175,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)],[301]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(437,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/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).

thf(1471,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)],[437]) ).

thf(375,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).

thf(1339,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)],[375]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( 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 @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( 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 @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(17,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(535,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)],[17]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Event_Oevent_ONotes @ A @ B )
     != ( c_Event_Oevent_OGets @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).

thf(621,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)],[54]) ).

thf(367,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).

thf(1325,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)],[367]) ).

thf(179,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/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(915,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)],[179]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
      = ( c_Public_OshrK @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).

thf(1556,plain,
    ! [A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OshrK @ A ) )
      = ( c_Public_OshrK @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).

thf(943,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)],[192]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I13_J_0) ).

thf(668,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_OAgent @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(302,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/sandbox/benchmark/theBenchmark.p',cls_map__eq__conv_0) ).

thf(1177,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)],[302]) ).

thf(186,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert_0) ).

thf(932,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)],[186]) ).

thf(273,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/sandbox/benchmark/theBenchmark.p',cls_synth__trans_0) ).

thf(1112,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)],[273]) ).

thf(211,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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(983,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)],[211]) ).

thf(402,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/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).

thf(1396,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)],[402]) ).

thf(497,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).

thf(1594,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)],[497]) ).

thf(199,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_List_Omember @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).

thf(959,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)],[199]) ).

thf(88,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/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(695,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)],[88]) ).

thf(123,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

thf(780,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)],[123]) ).

thf(167,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/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(883,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)],[167]) ).

thf(223,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/sandbox/benchmark/theBenchmark.p',cls_analz__empty_0) ).

thf(1015,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)],[223]) ).

thf(440,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/sandbox/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).

thf(1477,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)],[440]) ).

thf(448,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/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).

thf(1496,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)],[448]) ).

thf(69,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/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).

thf(658,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)],[69]) ).

thf(481,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/sandbox/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).

thf(1562,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)],[481]) ).

thf(178,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/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(912,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)],[178]) ).

thf(11,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(521,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)],[11]) ).

thf(299,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).

thf(1171,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)],[299]) ).

thf(249,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/sandbox/benchmark/theBenchmark.p',cls_lemma1_0) ).

thf(1066,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)],[249]) ).

thf(426,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).

thf(1445,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)],[426]) ).

thf(463,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/sandbox/benchmark/theBenchmark.p',cls_mem__iff_1) ).

thf(1528,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)],[463]) ).

thf(255,axiom,
    ! [B: $i,A: $i] :
      ~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(1076,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)],[255]) ).

thf(313,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/sandbox/benchmark/theBenchmark.p',cls_in__set__takeD_0) ).

thf(1203,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)],[313]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(531,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)],[15]) ).

thf(80,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/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(680,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)],[80]) ).

thf(72,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/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).

thf(663,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)],[72]) ).

thf(414,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/sandbox/benchmark/theBenchmark.p',cls_parts__partsD_0) ).

thf(1420,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)],[414]) ).

thf(184,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/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(927,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)],[184]) ).

thf(346,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).

thf(1277,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)],[346]) ).

thf(258,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/sandbox/benchmark/theBenchmark.p',cls_analz__trans_0) ).

thf(1081,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)],[258]) ).

thf(190,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/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(939,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)],[190]) ).

thf(225,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/sandbox/benchmark/theBenchmark.p',cls_analz__cut_0) ).

thf(1018,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)],[225]) ).

thf(112,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(754,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)],[112]) ).

thf(476,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/sandbox/benchmark/theBenchmark.p',cls_Issues__def_1) ).

thf(1551,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)],[476]) ).

thf(203,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/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(968,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)],[203]) ).

thf(139,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oanalz @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__increasing_0) ).

thf(823,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)],[139]) ).

thf(38,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/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(580,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)],[38]) ).

thf(61,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I31_J_0) ).

thf(640,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OKey @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(205,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/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(971,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)],[205]) ).

thf(341,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/sandbox/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).

thf(1267,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)],[341]) ).

thf(266,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/sandbox/benchmark/theBenchmark.p',cls_used__Gets_0) ).

thf(1098,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)],[266]) ).

thf(474,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/sandbox/benchmark/theBenchmark.p',cls_Key__synth_0) ).

thf(1547,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)],[474]) ).

thf(121,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/sandbox/benchmark/theBenchmark.p',cls_synth__Un_0) ).

thf(776,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)],[121]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(712,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
        = B )
      | ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(219,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(1003,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)],[219]) ).

thf(91,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/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(705,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)],[91]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OKey @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).

thf(1156,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)],[292]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(1225,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)],[323]) ).

thf(404,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/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).

thf(1400,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)],[404]) ).

thf(92,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/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(707,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)],[92]) ).

thf(326,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__propE_1) ).

thf(1230,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)],[326]) ).

thf(443,axiom,
    ~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).

thf(1484,plain,
    ~ ( c_in @ c_Message_Oagent_OServer @ c_Event_Obad @ tc_Message_Oagent ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(449,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/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).

thf(1499,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)],[449]) ).

thf(420,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).

thf(1432,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)],[420]) ).

thf(429,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).

thf(1452,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)],[429]) ).

thf(40,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/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).

thf(585,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)],[40]) ).

thf(96,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/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).

thf(717,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)],[96]) ).

thf(363,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/sandbox/benchmark/theBenchmark.p',cls_parts__empty_0) ).

thf(1317,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)],[363]) ).

thf(260,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).

thf(1085,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)],[260]) ).

thf(133,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/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(808,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)],[133]) ).

thf(489,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(1579,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
      | ( B = C )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(321,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pushes_I9_J_0) ).

thf(1220,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Set_Oinsert @ ( c_Message_Omsg_OCrypt @ A @ B ) @ D @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(176,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OKey @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I30_J_0) ).

thf(907,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OKey @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(350,axiom,
    ! [H: $i,G: $i,F: $i,E: $i,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 @ ( c_Message_Omsg_OCrypt @ E @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ H @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).

thf(1285,plain,
    ! [H: $i,G: $i,F: $i,E: $i,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 @ ( c_Message_Omsg_OCrypt @ E @ ( c_Message_Omsg_OMPair @ F @ ( c_Message_Omsg_OMPair @ G @ ( c_Message_Omsg_OMPair @ H @ A ) ) ) ) ) @ ( c_List_Oset @ B @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(319,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/sandbox/benchmark/theBenchmark.p',cls_priK__in__initState_0) ).

thf(1218,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)],[319]) ).

thf(373,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/sandbox/benchmark/theBenchmark.p',cls_privateKey__into__used_0) ).

thf(1336,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)],[373]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(643,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(51,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/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(613,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)],[51]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(600,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Public_OpublicKey @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pubK__neq__shrK_0) ).

thf(1008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OshrK @ A )
     != ( c_Public_OpublicKey @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(392,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/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_0) ).

thf(1372,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)],[392]) ).

thf(344,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).

thf(1272,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)],[344]) ).

thf(163,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/sandbox/benchmark/theBenchmark.p',cls_synth__insert_0) ).

thf(876,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)],[163]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OKey @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I12_J_0) ).

thf(991,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OKey @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(406,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).

thf(1404,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)],[406]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(1358,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)],[384]) ).

thf(68,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/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).

thf(656,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)],[68]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( B = E )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ B @ C ) @ ( c_List_Oset @ E @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__inj__on_0) ).

thf(1023,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_List_Omap @ A @ B @ C @ D )
       != ( c_List_Omap @ A @ E @ C @ D ) )
      | ( B = E )
      | ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_List_Oset @ B @ C ) @ ( c_List_Oset @ E @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(241,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/sandbox/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).

thf(1052,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)],[241]) ).

thf(452,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/sandbox/benchmark/theBenchmark.p',cls_parts__trans_0) ).

thf(1506,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)],[452]) ).

thf(451,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/sandbox/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).

thf(1504,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)],[451]) ).

thf(101,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/sandbox/benchmark/theBenchmark.p',cls_take__map_0) ).

thf(727,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)],[101]) ).

thf(264,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/sandbox/benchmark/theBenchmark.p',cls_Spy__spies__bad__privateKey_0) ).

thf(1094,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)],[264]) ).

thf(208,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/sandbox/benchmark/theBenchmark.p',cls_drop__butlast_0) ).

thf(978,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)],[208]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( c_in @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(1180,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
        = ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
      | ( c_in @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(27,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/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(556,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)],[27]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(539,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(477,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).

thf(1553,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)],[477]) ).

thf(76,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/sandbox/benchmark/theBenchmark.p',cls_analz__cong_0) ).

thf(671,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)],[76]) ).

thf(365,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/sandbox/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).

thf(1321,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)],[365]) ).

thf(207,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/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).

thf(976,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)],[207]) ).

thf(12,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(524,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)],[12]) ).

thf(410,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first_1) ).

thf(1412,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)],[410]) ).

thf(458,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/sandbox/benchmark/theBenchmark.p',cls_analz__analzD_0) ).

thf(1517,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)],[458]) ).

thf(114,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/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(759,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)],[114]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(891,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)],[170]) ).

thf(280,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop_2) ).

thf(1126,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)],[280]) ).

thf(306,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).

thf(1189,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)],[306]) ).

thf(400,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/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).

thf(1390,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)],[400]) ).

thf(487,axiom,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__parts_0) ).

thf(1575,plain,
    ! [A: $i] :
      ( ( c_Message_Oanalz @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I35_J_0) ).

thf(1289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_ONonce @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(149,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/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(844,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)],[149]) ).

thf(494,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/sandbox/benchmark/theBenchmark.p',cls_set__take__subset_0) ).

thf(1590,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)],[494]) ).

thf(368,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/sandbox/benchmark/theBenchmark.p',cls_map__upds__apply__nontin_0) ).

thf(1326,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)],[368]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      | ~ ( c_in @ B @ A @ D )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(58,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I10_J_0) ).

thf(632,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_ONonce @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(331,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/sandbox/benchmark/theBenchmark.p',cls_analz_OFst_0) ).

thf(1244,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)],[331]) ).

thf(461,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/sandbox/benchmark/theBenchmark.p',cls_parts__insertI_0) ).

thf(1523,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)],[461]) ).

thf(479,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/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).

thf(1558,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)],[479]) ).

thf(42,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/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(588,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)],[42]) ).

thf(335,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/sandbox/benchmark/theBenchmark.p',cls_knows__Gets_0) ).

thf(1253,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)],[335]) ).

thf(135,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/sandbox/benchmark/theBenchmark.p',cls_butlast__drop_0) ).

thf(813,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)],[135]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__neq__pubK_0) ).

thf(1385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Public_OpublicKey @ A @ B )
     != ( c_Public_OshrK @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(376,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/sandbox/benchmark/theBenchmark.p',cls_parts__singleton_1) ).

thf(1341,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)],[376]) ).

thf(172,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/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).

thf(896,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)],[172]) ).

thf(247,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/sandbox/benchmark/theBenchmark.p',cls_parts_OFst_0) ).

thf(1062,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)],[247]) ).

thf(453,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/sandbox/benchmark/theBenchmark.p',cls_synth__synthD_0) ).

thf(1508,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)],[453]) ).

thf(103,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/sandbox/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).

thf(731,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)],[103]) ).

thf(125,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/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(786,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)],[125]) ).

thf(231,axiom,
    ! [A: $i] : ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ A ) ) @ ( c_Event_OinitState @ A ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).

thf(1030,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)],[231]) ).

thf(33,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/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(568,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)],[33]) ).

thf(185,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).

thf(929,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)],[185]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I19_J_0) ).

thf(1308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OCrypt @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ B @ C )
        = B )
      | ~ ( c_in @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(1212,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)],[317]) ).

thf(173,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/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(899,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)],[173]) ).

thf(82,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/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_0) ).

thf(684,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)],[82]) ).

thf(24,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/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(549,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)],[24]) ).

thf(74,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/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(667,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)],[74]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nonce__synth_0) ).

thf(1294,plain,
    ! [B: $i,A: $i] :
      ( ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ B @ tc_Message_Omsg )
      | ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(294,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/sandbox/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).

thf(1161,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)],[294]) ).

thf(130,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/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(800,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)],[130]) ).

thf(283,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/sandbox/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).

thf(1133,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)],[283]) ).

thf(455,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/sandbox/benchmark/theBenchmark.p',cls_used__Says_0) ).

thf(1512,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)],[455]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      | ~ ( c_lessequals @ 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)],[144]) ).

thf(137,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/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(818,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)],[137]) ).

thf(358,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/sandbox/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).

thf(1303,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)],[358]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(195,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).

thf(950,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)],[195]) ).

thf(145,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/sandbox/benchmark/theBenchmark.p',cls_analz__image__freshK__simps_I65_J_0) ).

thf(835,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)],[145]) ).

thf(496,axiom,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Agent__synth_0) ).

thf(1593,plain,
    ! [B: $i,A: $i] : ( c_in @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Osynth @ B ) @ tc_Message_Omsg ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(396,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/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(1380,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)],[396]) ).

thf(157,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(865,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)],[157]) ).

thf(441,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).

thf(1480,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)],[441]) ).

thf(31,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(564,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)],[31]) ).

thf(422,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I36_J_0) ).

thf(1436,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(506,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

thf(767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( A
     != ( c_List_Olist_OCons @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(244,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop_2) ).

thf(1056,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)],[244]) ).

thf(142,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/sandbox/benchmark/theBenchmark.p',cls_privateKey__neq__publicKey_0) ).

thf(828,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)],[142]) ).

thf(378,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).

thf(1346,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)],[378]) ).

thf(128,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/sandbox/benchmark/theBenchmark.p',cls_insert_0) ).

thf(796,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)],[128]) ).

thf(387,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/sandbox/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).

thf(1363,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)],[387]) ).

thf(362,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/sandbox/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).

thf(1314,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)],[362]) ).

thf(233,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ( B = C )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(1033,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ A @ C ) )
      | ~ ( c_in @ C @ D @ E )
      | ~ ( c_in @ B @ D @ E )
      | ( B = C )
      | ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(310,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/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_1) ).

thf(1197,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)],[310]) ).

thf(200,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/sandbox/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).

thf(960,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)],[200]) ).

thf(59,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/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(635,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)],[59]) ).

thf(438,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__propE_2) ).

thf(1473,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)],[438]) ).

thf(97,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/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(720,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)],[97]) ).

thf(296,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__idem_0) ).

thf(1165,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oparts @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(107,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/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_1) ).

thf(740,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)],[107]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I17_J_0) ).

thf(1236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OMPair @ A @ B )
     != ( c_Message_Omsg_OAgent @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(381,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_1) ).

thf(1352,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)],[381]) ).

thf(469,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/sandbox/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).

thf(1537,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)],[469]) ).

thf(490,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Agent_0) ).

thf(1582,plain,
    ! [B: $i,A: $i] :
      ( ( c_Message_Oanalz @ ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ B @ tc_Message_Omsg ) )
      = ( c_Set_Oinsert @ ( c_Message_Omsg_OAgent @ A ) @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(528,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)],[14]) ).

thf(99,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/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(723,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)],[99]) ).

thf(151,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(850,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)],[151]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I34_J_0) ).

thf(1597,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_ONonce @ A )
     != ( c_Message_Omsg_OMPair @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(86,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/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).

thf(691,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)],[86]) ).

thf(277,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/sandbox/benchmark/theBenchmark.p',cls_ListMem__iff_1) ).

thf(1120,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)],[277]) ).

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

thf(501,plain,
    ~ ( c_in @ v_K @ ( 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(55,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/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).

thf(624,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)],[55]) ).

thf(147,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/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(839,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)],[147]) ).

thf(465,axiom,
    ! [A: $i] : ( c_lessequals @ A @ ( c_Message_Oparts @ A ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__increasing_0) ).

thf(1532,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)],[465]) ).

thf(154,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(860,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(45,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).

thf(596,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)],[45]) ).

thf(395,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/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(1378,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)],[395]) ).

thf(370,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/sandbox/benchmark/theBenchmark.p',cls_Fake__parts__insert__in__Un_0) ).

thf(1331,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)],[370]) ).

thf(389,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).

thf(1367,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)],[389]) ).

thf(188,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/sandbox/benchmark/theBenchmark.p',cls_analz__synth__Un_0) ).

thf(935,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)],[188]) ).

thf(182,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/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(923,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)],[182]) ).

thf(483,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__injective_0) ).

thf(1565,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Public_OshrK @ A )
       != ( c_Public_OshrK @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(29,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/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(560,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)],[29]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__analz_0) ).

thf(1416,plain,
    ! [A: $i] :
      ( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
      = ( c_Message_Oparts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(78,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/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(676,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)],[78]) ).

thf(428,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_OinvKey @ ( c_Public_OpublicKey @ A @ B ) )
     != ( c_Public_OshrK @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__neq__priK_0) ).

thf(1449,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)],[428]) ).

thf(436,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I18_J_0) ).

thf(1468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Message_Omsg_OAgent @ A )
     != ( c_Message_Omsg_OCrypt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1069,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_in @ A @ B @ C )
      | ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(1603,plain,
    $false,
    inference(e,[status(thm)],[645,1036,1586,1337,1369,760,1454,1105,1031,893,518,777,1549,1110,1083,962,762,1005,1068,1522,1443,994,1073,1544,1591,511,1533,1422,1569,873,1205,1142,1269,1041,861,1173,1486,533,500,715,1275,747,945,1222,1078,1426,1260,698,538,1354,1196,1001,1441,709,1359,1475,973,885,1046,1228,1482,1287,570,1430,1298,802,1279,1577,1191,542,1055,1409,587,1323,619,917,751,1545,902,1147,606,770,1100,1232,638,853,1087,1514,1319,870,1398,881,1489,756,789,591,1109,1418,1334,1136,514,806,966,821,905,1151,937,1020,574,1183,1283,1215,877,1394,1351,660,998,988,1405,1201,1600,527,602,981,1169,687,1447,956,1119,774,1074,942,678,661,793,925,1306,1199,1153,1311,798,1163,910,1091,1343,1021,952,1519,1502,1487,815,729,1560,693,630,1423,1365,879,1457,583,889,1159,1210,1079,1128,1281,842,1573,847,566,1296,665,682,1407,1402,1089,874,650,615,1064,725,980,1096,593,869,610,857,1534,1017,1329,1028,1361,554,1461,686,1414,1584,1207,547,1292,933,1039,970,837,1114,701,738,1266,721,1429,1246,503,1525,647,1263,1588,985,515,1249,1530,1539,1456,1382,1131,654,1060,1050,1333,1434,1241,508,921,541,1563,1054,1515,953,1466,558,1071,1187,674,1026,1167,1251,513,1103,1301,689,1374,733,750,1510,1219,824,1154,562,1388,743,1535,1124,826,577,1256,1226,545,1139,572,1239,1258,1356,1271,1371,1058,1107,1464,947,1194,831,1011,1349,996,1492,1542,1144,1043,1122,764,604,784,1117,1048,736,1571,1376,1439,863,1175,811,1471,1339,552,535,621,1325,915,1556,943,668,1177,932,1112,983,1396,1594,959,695,780,883,1015,1477,1496,658,1562,912,521,1171,1066,1445,1528,1076,1203,531,680,663,1420,927,1277,1081,939,1018,754,1551,968,823,580,640,971,1267,1098,1547,776,712,1003,705,1156,1225,1400,707,1230,1484,1499,1432,1452,585,717,1317,1085,808,1579,1220,907,1285,1218,1336,643,613,600,1008,1372,1272,876,991,1404,1358,656,1023,1052,1506,1504,727,1094,978,627,1180,556,539,1553,671,1321,976,524,1412,1517,759,891,1126,1189,1390,1575,1289,844,1590,1326,652,632,1244,1523,1558,588,1253,813,1385,1341,896,1062,1508,731,786,1030,568,929,1308,1212,899,684,549,667,1294,1161,800,1133,1512,833,818,1303,867,950,835,1593,1380,865,1480,564,1436,506,767,1056,828,1346,796,1363,1314,1033,1197,960,635,1473,720,1165,740,1236,1352,1537,1582,528,723,850,1597,691,1120,501,624,839,1532,860,596,1378,1331,1367,935,923,1565,560,1416,676,1449,1468,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWV722-1 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.13  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun May 19 08:00:24 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 1.04/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.02/1.33  % [INFO] 	 Parsing done (327ms). 
% 2.02/1.34  % [INFO] 	 Running in sequential loop mode. 
% 2.85/1.71  % [INFO] 	 eprover registered as external prover. 
% 2.85/1.72  % [INFO] 	 cvc4 registered as external prover. 
% 2.85/1.72  % [INFO] 	 Scanning for conjecture ... 
% 3.45/1.91  % [INFO] 	 Found a conjecture (or negated_conjecture) and 517 axioms. Running axiom selection ... 
% 4.16/2.11  % [INFO] 	 Axiom selection finished. Selected 497 axioms (removed 20 axioms). 
% 4.98/2.36  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.22/2.38  % [INFO] 	 Type checking passed. 
% 5.22/2.38  % [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 ... 
% 13.81/4.58  % External prover 'e' found a proof!
% 13.81/4.58  % [INFO] 	 Killing All external provers ... 
% 13.81/4.58  % Time passed: 4082ms (effective reasoning time: 3230ms)
% 13.81/4.58  % Axioms used in derivation (497): cls_set__subset__Cons_0, cls_Crypt__notin__initState_0, cls_Diff__cancel_0, cls_shrK__in__initState_0, cls_parts_OBody_0, cls_subset__insert_1, cls_Diff__iff_2, cls_MPair__synth__analz_0, cls_not__parts__not__analz_0, cls_sup__ge1_0, cls_Un__Diff_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_synth__analz__mono_0, cls_initState__subset__knows_0, cls_used__Says_0, cls_Un__empty__left_0, cls_le__funD_0, cls_subset__empty_1, cls_pushes_I9_J_0, cls_map__replicate_0, cls_set__ConsD_0, cls_sup__bot__right_0, cls_insert__code_1, cls_Issues__def_0, cls_set__removeAll_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_Agent__synth_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_ns__sharedp_ONS3_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_insert__absorb_0, cls_analz__subset__parts_0, cls_used__Notes_0, cls_removeAll_Osimps_I2_J_0, cls_Fake__parts__insert_0, cls_msg_Osimps_I34_J_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_Diff__subset__conv_0, cls_remove1__filter__not_0, cls_msg_Osimps_I12_J_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_analz__idem_0, cls_insert__subset_0, cls_List_Omember_Osimps_I2_J_0, clsarity_fun__Lattices_Oupper__semilattice, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_knows__subset__knows__Cons_0, cls_split__list__last__propE_2, cls_in__set__remove1_0, cls_msg_Osimps_I3_J_0, cls_set__remove1__subset_0, cls_in__set__takeD_0, cls_list__all_Osimps_I2_J_0, cls_ns__sharedp_OOops_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_NS3__msg__in__parts__spies_0, cls_agent_Osimps_I5_J_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_Server__not__bad_0, 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, cls_inj__on__insert_0, 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_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_Diff__idemp_0, 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__Diff__single_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_pushes_I8_J_0, cls_parts__insert_0, cls_List_Omember_Osimps_I2_J_1, cls_analz__conj__parts_0, clsarity_bool__Lattices_Oupper__semilattice, cls_msg_Osimps_I43_J_0, cls_event_Osimps_I3_J_0, cls_subset__insert__iff_3, cls_shrK__in__used_0, cls_removeAll__id_0, cls_diff__single__insert_0, cls_synth__analz__insert__eq_0, cls_parts__insert__Agent_0, cls_synth__trans_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_agent_Osimps_I4_J_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_Nonce__synth__eq_1, 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_msg_Osimps_I19_J_0, cls_msg_Osimps_I1_J_0, 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_double__diff_0, cls_in__set__butlastD_0, cls_subset__trans_0, cls_pushes_I2_J_0, cls_not__Cons__self_0, cls_insert__is__Un_0, cls_map__inj__on_0, cls_insertI1_0, cls_DiffI_0, cls_msg_Osimps_I36_J_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_insert__Diff1_0, cls_msg_Osimps_I16_J_0, cls_msg_Osimps_I35_J_0, cls_event_Osimps_I2_J_1, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup1E_0, cls_parts__cut_0, cls_sup__least_0, cls_subset__refl_0, cls_analz__shrK__Decrypt_0, cls_analz__insert__Agent_0, cls_parts__subset__iff_0, cls_synth__subset__iff_1, cls_analz__Un_0, cls_analz_ODecrypt_0, cls_empty__subsetI_0, cls_Diff__insert2_0, cls_synth__Un_0, cls_inj__on__iff_0, cls_insert__Diff_0, cls_drop__butlast_0, cls_inj__on__empty_0, cls_DiffE_0, cls_sup1CI_1, cls_msg_Osimps_I13_J_0, 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_Un__Diff__cancel_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_Un__Diff__cancel2_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_Diff__mono_0, cls_msg_Osimps_I18_J_0, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_inj__on__def_0, cls_Un__absorb_0, cls_MPair__used_1, cls_parts__trans_0, clsarity_bool__Lattices_Olattice, 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_event_Osimps_I4_J_0, cls_subset__insert__iff_4, cls_pubK__neq__shrK_0, cls_MPair__synth__analz_2, cls_analz__insert__MPair_0, cls_eq__eqI_0, cls_msg_Osimps_I30_J_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_map__removeAll__inj__on_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_pushes_I1_J_0, cls_Crypt__synth_0, cls_analz_OSnd_0, cls_subset__insert__iff_0, cls_subset__singletonD_0, cls_event_Osimps_I8_J_0, cls_in__set__conv__decomp__last_1, cls_insert__absorb2_0, cls_analz__mono_0, cls_takeWhile__eq__all__conv_0, cls_Nonce__synth__eq_0, cls_doubleton__eq__iff_1, cls_analz__mono__contra_I1_J_0, cls_analz__synth_0, cls_event_Osimps_I1_J_2, cls_Nonce__synth_0, cls_analz__insert__eq_0, cls_parts__insert__Nonce_0, cls_analz__analz__Un_0, cls_Diff__empty_0, cls_inj__on__map__eq__map_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_msg_Osimps_I17_J_0, cls_inf__sup__aci_I5_J_0, cls_eq__eqI_1, cls_list__all_Osimps_I2_J_2, cls_set__takeWhileD_1, cls_mem__iff_1, cls_initState__into__used_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_subset__inj__on_0, cls_singleton__inject_0, cls_msg_Osimps_I31_J_0, cls_analz__increasing_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_inj__on__contraD_0, cls_sup1CI_0, cls_inj__onD_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_inj__on__diff_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_Diff__subset__conv_1, cls_insert__code_0, cls_subset__insertI_0, cls_analz__trans_0, cls_used__Gets_0, cls_msg_Osimps_I6_J_0, cls_DiffE_1, cls_elem_0, cls_takeWhile_Osimps_I2_J_0, cls_le__eqI_1, cls_in__set__conv__decomp__first_1, cls_Nonce__notin__initState_0, cls_Says__imp__knows_0, cls_analz__subset__cong_0, cls_sup__bot__left_0, cls_gen__analz__insert__eq_0, cls_set__drop__subset_0, cls_msg_Osimps_I10_J_0, cls_inj__on__Un_1, 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_list__ex_Osimps_I2_J_0, cls_Diff__insert__absorb_0, cls_Diff__partition_0, cls_list__ex_Osimps_I2_J_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_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_equalityE_0, cls_msg_Osimps_I37_J_0, cls_insert_0, cls_privateKey__into__used_0, cls_ns__sharedp_ONS1_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_analz__insert__Nonce_0, cls_Notes__imp__knows_0, cls_msg_Osimps_I11_J_0, cls_subset__insert__iff_1, cls_Diff__subset_0, cls_analz__into__parts_0, cls_predicate1D_0, cls_empty__Diff_0, cls_synth_OAgent_0, cls_analz__insert_0, cls_parts__insert__spies_0
% 13.81/4.58  % No. of inferences in proof: 999
% 13.81/4.59  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4082 ms resp. 3230 ms w/o parsing
% 15.16/4.88  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.30/4.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------